diff options
Diffstat (limited to 'Master/texmf-dist/doc/latex')
17 files changed, 14949 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/mathspic/HELP.txt b/Master/texmf-dist/doc/latex/mathspic/HELP.txt new file mode 100644 index 00000000000..43a72e81f6a --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/HELP.txt @@ -0,0 +1,615 @@ +HELP.txt +A .txt version of the manpage for MS-Windows users + +copyright (c) 2005 A Syropoulos and RWD Nickalls +mathsPIC February 2005 + +NAME: mathsPIC (Perl version 1.0) + +AUTHORS: A. Syropoulos and R.W.D. Nickalls + apostolo[at]<ocean1><ee><duth><gr> + dicknickalls[at]<compuserve><com> + +DESCRIPTION +----------- +mathsPIC is a Perl filter program for PiCTeX. mathsPIC has its own macro and macro library capability, and allows use of mathsPIC, PiCTeX, TeX and LaTeX commands. A significant feature of mathsPIC is that it allows access to the command-line, and so allows the user to extend mathsPIC commands by calling Perl and other programs written to perform particular drawing actions. See the package manual for full details and examples. The latest version can be downloaded from + +CTAN: tex-archive/graphics/pictex/mathspic/perl + +Commands which can be used in the mathsPIC script file fall into four main groups (a)-mathsPIC macro commands (prefixed with %def), (b)-regular mathsPIC commands (do not have a backslash), (c)-regular PiCTeX commands (all have a backslash), and (d)-regular TeX and LaTeX commands (all have a backslash). + +The following mathematics functions can used (note that decimal fractions having an absolute value less than 1 must have a leading zero). Note also that all the trignometric functions require their argument in radians. + +Trigonometric: sin(), cos(), tan(), asin(), acos(), atan() +Remainder: rem(); eg var r=12 rem(5) +Integer: int(); eg var r= int(3.87) --> 3 +Sign (returns -1, 0, +1): sgn(); eg var s=sgn(-3.27) --> -1 +Square root: sqrt(); eg var s = sqrt(14) +Exponentiation: **; eg var j = r**2 +Pi constant: _Pi_ and _pi_ (3.14159...) +e constant: _E_ and _e_ (2.71828...) +Linethickness: _linethickness_ ; eg var t = _linethickness_ + +COMMAND-LINE USE +---------------- +perl mathspic.pl [-b] [-c] [-h] [-o <outfile>] <infile> + -b enables beep if mathsPIC detects an error + -c disables the writing of comments to output file + -h displays the help file + -o defines the output file name + +MACRO COMMANDS +-------------- +macro definition commands are prefixed with %def and can take either 0, 1, or more parameters. Macros will generally be used as part of a +var command as shown below. Macros are deleted using the %undef command. + + -----syntax: + %def MACRONAME(parameters)<macrodefinition> + %undef MACRONAME(parameters) + + -----notes: + Notes: (a)-the () must be used in the definition even if no parameters are used, (b)-the name can be any combination of upper and lower case characters and numbers, (c)-when the macro is used in a command it is prefixed by a & symbol, (d)-it is a good idea to always place a % symbol at the end of the definition, (e)-comments (prefixed by a % symbol) can be placed after the macro definition just as in TeX or LaTeX. + + -----examples: + %def d2r()_pi_/180% % degrees2radians + %def AreaOfRectangle(x,y)x*y% % width x, length y + %undef d2r() % delete the macro + + -----use: + var j2= 6*(&d2r(45) + 23) + var a3 = 3*&AreaOfRectangle(5,7) + +GENERAL COMMANDS +---------------- + + NUMERICAL EXPRESSIONS + + When dealing with commands we will refer frequently to the term `numerical expression' by which is meant either (a) a number (integer or decimal), (b) a numeric variable or constant (defined using the var or const command), (c) any mathsPIC function, macro, or mathematical expression which evaluates to a number, or (d) a pair of point names (e.g. AB) representing the Pythagorean distance between the two points. A leading zero must be used with decimal fractions less than one. + + In general, if a command's argument accepts a number then it will also accept a `numerical expression' (<expr>) as defined above. Sometimes a following <unit> is associated with the number or numerical expression, in which case the number or numerical expression can be delimited by a round bracket (or separated from the unit by a <space>), as shown in the following examples. + + -----examples: + ArrowShape(3mm, 20,40) + var h=4 + ArrowShape(h mm, 20, 40) + ArrowShape((2*h)mm,20,40) + + ============================== + + BACKSLASH \ + + A leading backslash without a following space indicates that it is part of a PiCTeX, TeX or LaTeX command, in which case mathsPIC simply copies the whole line verbatim into the output file. A leading backslash followed by one or more spaces makes mathsPIC copy the whole line verbatim into the output file but without the backslash. + + ============================== + + USING THE COLOR PACKAGE + + The standard COLOR package can be used with mathsPIC, but note that it is important to load the COLOR package after the mathsPIC package. + + It is best to place a comment symbol % at the end of LaTeX and TeX commands to limit white space at the end. + + In order to prevent color commands in a diagram from influencing any following text (in the document) we recommend that the \normalcolor command is used as a delimiter within the \beginpicture... \endpicture environment as shown in the example below. i.e.-use two \normalcolor commands; one just after the \beginpicture command, and one just before the \endpicture command. + + -----example: + \usepackage{mathspic, color} + ... + \beginpicture + \normalcolor + ... + \color{red}% + drawline{AB} + \color{blue}% + drawcircle(C,5) + ... + \normalcolor + \endpicture + +============================== + + ARROWSHAPE + + This command defines the shape of an arrowhead, and allows +different arrowheads to be customised. + +The default arrow shape is equivalent to the Arrowshape(2mm,30,40) command. +This default arrowhead shape can be reset using the Arrowshape(default) command, as shown in the following example. + + -----syntax: + arrowshape(<length>[units], <angledeg>, <angledeg>) + + -----examples: + Arrowshape(4mm,30,60) + drawArrow(AB) + Arrowshape(default) + +============================== + + beginLOOP...endLOOP + + This is an environment which cycles a block of code a specified number of times. + + -----syntax: + beginLoop <expr> + ... + endLoop + + -----notes: + The block of code which lies within the environment is input <expr> times. + + -----example: + beginLoop 5 + ... + endLoop + +============================== + + beginSKIP...endSKIP + + This is an `environment' within which commands are not actioned. It is useful in development for testing isolated commands and excluding other commands. + +============================== + + CONST + + The const command is used to define scalar constants. Note that a constant-name must begin with a single letter (either upper or lower case), and may have up to a maximum of three following digits. Note that constants, variables and points have the same name structure, and a constant could have the same name as a point (and so we suggest points have uppercase letters and variables and constants have lowercase letters). The scalar argument can be any numeric expression. New values cannot be re-allocated to existing constant-names. If this occurs mathsPIC will issue an error message. + + -----syntax: + const name = <expr> + + -----examples: + const r = 20, r4 = r3*tan(0.3) + +============================== + + DashArray + + The dasharray command takes an arbitrary number of paired arguments that are used to specify a dash pattern. + + -----syntax + dasharray(d1 , g1 , d2 , g2 , ... ) + + -----notes + The ds denotes the length of a dash and the gs denotes the length of the gap between two consecutive dashes. There must be an even number of arguments. If a variable or expression is used then it should be separated from the unit either by a <space> or with round brackets ( ) as shown below. + + -----example + dasharray(6pt, 2pt, 1pt, 2pt) + var d=2 + dasharray(6pt, 2pt, 1pt, d pt) + dasharray(6pt, 2pt, 1pt, (d)pt) + dasharray(6pt, 2pt, 1pt, (3*d)pt) + +============================== + + DrawAngleArc + + This command draws an arc in the specified angle, a distance <radius> from the angle. The angle is either <internal> (less than 180 deg) or <external> (greater than 180 deg). The direction of the arc is either <clockwise> or <anticlockwise>, and this direction must correspond with the letter sequence specified for the angle. +Strange and unexpected results will be produced if the four parameters are not internally consistent. The option order angle/radius/internal/clockwise is important. The <radius> parameter can be any numerical expression. + + -----syntax: + DrawAngleArc{angle(), radius(), external, clockwise} + + -----example: + DrawAngleArc{angle(ABC), radius(3), external, clockwise} + var r=3 + DrawAngleArc{angle(ABC), radius(r), external, clockwise} + +============================== + + DrawAngleArrow + + This command draws a curved arrow in the specified angle, a distance <radius> from the angle. The angle is either <internal> (less than 180 deg) or <external> (greater than 180 deg). The direction of the arrow is either <clockwise> or <anticlockwise>, and this direction must correspond with the letter sequence specified for the angle. +Strange and unexpected results will be produced if the four parameters are not internally consistent. The option order angle/radius/internal/clockwise is important. The <radius> parameter can be any numerical expression. + + -----syntax: + DrawAngleArrow{angle(), radius(), external, clockwise} + + -----example: + DrawAngleArrow{angle(ABC), radius(3), external, clockwise} + var r=3 + DrawAngleArrow{angle(ABC), radius(r), external, clockwise} + +============================== + + DrawArrow + + This command draws an arrow(s) joining two points. The direction of the arrow is in the point order specified. + + -----syntax: + drawArrow(<line> [,<line>] ... ) + + -----notes: + The length option can only refer to one arrow + + -----example: + drawArrow(AB) + drawArrow(FG, HJ) + +============================== + + DrawCircle + + This command draws a circle defined by its radius and the point-name of its centre. The <radius> can be any numerical expression. If the units of the X and Y axes are different, circles may be drawn strangely, and mathsPIC therefore generates a warning message to this effect. + + -----syntax: + DrawCircle(<center>, <radius>) + + -----examples: + drawCircle(C2,5) + drawCircle(C2,r2) + drawCircle(C2,r2/tan(1.3)) + drawCircle(C2,AB) + +============================== + + DrawCircumcircle + + This command draws the circumcircle of a triangle. + + -----syntax: + DrawCircumcircle(<triangle>) + + -----example: + drawCircumcircle(ABC) + +============================== + + DrawCurve + + This command draws a smooth quadratic curve through three points in the point order specified. Note that curves drawn using this command do not break to avoid line-free zones associated with the points. + + -----syntax: + DrawCurve(<point><point><point>) + + -----example: + drawCurve(ABC) + +============================== + + DrawExcircle + + This command draws the excircle touching one side of a triangle. + + -----syntax: + DrawExcircle(<triangle>, <side>) + + -----example: + drawExcircle(ABC, BC) + +============================== + + DrawIncircle + + This command draws the incircle of a triangle. + + -----syntax: + DrawIncircle(<triangle>) + + -----example: + drawIncircle(ABC) + +============================== + + DrawLine + + This command draws a line joining two or more points. Use the Linethickness command to vary thickness. + + -----syntax: + DrawLine( <points> [, <points>] ) + + -----notes: + <points> is any sequence of two or more point names. + <expr> is any numerical expression. + Lines are drawn in the order specified. + Lines are separated by a comma. + + -----examples: + drawline(AB) + drawline(BCDE) + drawline(FG, HJK, PQRST) + +============================== + + DrawPerpendicular + + This command draws the perpendicular from a point to a line. + + -----syntax: + DrawPerpendicular(<point>, <line) + + -----example: + drawPerpendicular(P,AB) + +============================== + + DrawPoint + + This command draws the point-symbol at the point-location. Commas must not be used to separate point names. The default point-symbol is \$\bullet\$, unless an optional point-symbol (or string of characters) is specified in the associated point command. + + -----syntax: + DrawPoint(<point> [<point> ..]) + + -----examples: + drawpoint(T4) + drawpoint(ABCDEF) + drawpoint(P1 P2 P3 P4) + +============================== + + DrawRightangle + + This command draws the standard right-angle symbol in the internal angle specified at the size specified by <expr>. + + -----syntax: + DrawRightangle(<angle>, <expr>) + + -----notes: + The <expr> can be any numerical expression. + + -----example: + drawRightangle(ABC,3) + drawRightangle(ABC,PQ) + var d=5 + drawRightangle(ABC,d) + +============================== + + DrawSquare + + This command draws a square defined by its side and the point-name of its centre. The <sidelength> can be any numerical expression. + + -----syntax: + DrawSquare(<centerpoint>, <sidelength>) + + -----examples: + drawSquare(P,5) + var s2=3, j=2 + drawSquare(P,s2) + drawSquare(P, s2*4/(3*j)) + drawSquare(P,AB) + +============================== + + DrawThickArrow + + This command draws a thick arrow(s) joining two points. The direction of the arrow is in the point order specified. The shape of the arrowhead is controlled by the ArrowShape command. + + -----syntax: + drawThickArrow(<line> [,<line>,...]) + + -----examples: + drawThickarrow(BC) + drawThickarrow(PQ, RS) + +============================== + + DrawThickLine + + This command draws a thick line(s) joining two points. The direction of the line is in the point order specified. Use the Linethickness command to vary thickness of a line. + + -----syntax: + drawThickLine(<line> [,<line>,...]) + + -----examples: + drawThickline(BC) + drawThickline(PQ, RS) + +============================== + + InputFile + + This command inputs a plain text file containing mathsPIC commands. Optionally, the file can be input several times, in which case this command functions like a DO--LOOP. +The <loopnumber> can be any numerical expression. If the <loopnumber> is not an integer then mathsPIC will round the value down to the nearest integer. + + -----syntax: + inputFile[*](<filename>)[<loopnumber>] + + -----notes: + The inputfile* command is used to input a file in verbatim, i.e. a file with no mathsPIC commands, for example, a file containing only PiCTeX commands or data-points +for plotting etc. Note that the inputfile* command has no <loopnumber> option. + + -----examples: + inputFile(myfile.dat)[4] + inputFile*(mycurvedata.dat) + +============================== + + LineThickness + + This command sets a particular linethickness. The command linethickness(default) restores the working linethickness to the default value of 0.4pt. +The current value of the linethickness (in current units) can be accessed using the var command (this can be useful when drawing figures using thick lines) . + + -----syntax: + LineThickness(<expr><units>) + LineThickness(default) + var t = _linethickness_ + + -----notes: + This command also sets the font to \verb!cmr! and plotsymbol to \CM . and also sets the rule thickness for drawing horizontal and vertical lines. It is important to include a leading zero with decimal fractions less than one. + + -----examples: + linethickness(2pt) + var t=3 + linethickness((t)pt) + lineThickness((2*t)pt) + linethickness(default) + var t = _linethickness_ + + -----caution: + Note that there is a similar PiCTeX command with the same name (but with a different syntax). + +============================== + + PAPER + + Defines the plotting area in terms of the options units(), xrange(), yrange(), axes(), and ticks(). The units() argument must contain a numeric value and a valid TeX length unit mm, cm, pt, pc(pica), in(inch), bp(big point), dd(didot), cc(cicero), sp(scaled point). The X and Y axes can have different units (see second example below). The axes() arguments XYTBLR refer to the X and Y axes, and the Top, Bottom, Left and Right axes. A * following one of the axes disables ticks on that axis. The X and Y axes pass through the zeros. + + -----examples: + paper{units(1cm),xrange(0,10),yrange(0,10)} + paper{units(2cm,1cm),xrange(0,10),yrange(0,10),axes(LB)} + paper{units(1mm),xrange(0,100),yrange(0,100),axes(XY)} + paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRTBXY),ticks(1,1)} + paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRT*B*)} + +============================== + + POINT + + Defines a new point by allocating coordinates to a new point name. The * option re-allocates coordinates to an existing point name. + + -----syntax: + POINT[*](<name>){<point>}[symbol=<chars>, radius=<expr>] + POINT[*](<name>){<location>}[symbol=<chars>, radius=<expr>] + + -----notes: + <name> one leading letter plus maximum of three trailing digits + <chars> any TeX string allowed in an \hbox{} + <expr> any numerical expression + The polar(r,theta) option defaults to radians for the angle theta. To work in degrees then must append <deg> eg: polar(r,theta deg). Can use <direction()> and <directiondeg()> to replace theta. + + -----examples: + point(A){5,5} + point(B2){22,46}[symbol=$\odot$] + point(B2){22,46}[symbol=circle(2),radius=5] + var r=3 + point(B2){22,46}[symbol=square(3),radius=r] + point(B123){22,46}[radius=5] + point(D2){B2, shift(5,5)} + var s = 3 + point(D2){B2, shift(2*s,4*s)} + point(D3){D2, polar(6,32 deg)} + point(D4){D2, polar(6,1.2 rad)} + point(D4){D2, polar(6, direction(AB))} %% radians by default + point(D4){D2, polar(6, directiondeg(AB) deg)} + point(G2){Q, rotate(P, 23 deg)} + point(G2){Q, vector(AB)} + point(D2){intersection(AB,CD)} + point(F){PointOnLine(AB,5.3)} + point(G){perpendicular(P,AB)} + point(H){circumcircleCenter(ABC)} + point(J){incircleCenter(ABC)} + point(K){excircleCenter(ABC,BC)} + point*(A){6,3} + point*(P){Q} + point*(B){B, shift(5,0)} + point*(P){xcoord(J),ycoord(K)} + +============================== + + PointSymbol + + This command allows the default point-symbol \bullet (with zero line-free radius) to be changed. The PointSymbol command is particularly useful where a set of points uses the same point-symbol, for example, when drawing graphs. The point-symbol can be reset to the default \bullet using the command PointSymbol(default). + + -----syntax: + PointSymbol(<symbol>, <line-free-radius>) + PointSymbol(default) + + -----notes: + The PointSymbol command only influences subsequent point commands. + The optional square bracket of the point command overrides the PointSymbol command. + + -----examples: + PointSymbol($\odot$, 0.7) + PointSymbol(default) + +============================== + + SYSTEM + + This command allows the user to access the command line and execute standard Linux commands. A important use for this command is to run a Perl program. + + -----syntax: + System("<command>") + + -----notes: + The <command> string must be in inverted commas. + + -----example: + system("dir > mydir-listing.txt") + system("perl myperlprogram.pl") + +============================== + + SHOW.... + + This command makes mathsPIC return the value of a calculation or specified parameter; for example, the value of a particular angle, or the length of a line. The result is shown in the output-file as a commented line. This allows mathsPIC commands to be adjusted in the light of calculations. There are currently five such commands as follows. + + -----syntax: + showLength(AB) + showAngle(ABC) % returns angle in radians + showAngledeg(ABC) % returns angle in degrees + showArea(ABC) + showPoints + showVariables + +============================== + + TEXT + + This command places a text-string at a specific location. By default the text is centered vertically and horizontally at the specified point. Optionally, text can be placed relative to a point using appropriate combinations of the PiCTeX `position' options l t r B b to align the (l)eft edge, (r)ight edge, (t)op edge, (B)aseline, (b)ottom edge respectively of the text box with the point-location. + + Remember that the default units for the angle argument of the polar() expression is radians; hence you MUST append `deg' if you want to work in degrees + + -----syntax: + text(<string>){<location>}[<position options>] + text(<string>){<pointname>, shift(<x>,<y>)}[] + text(<string>){<pointname>, polar(<r>,<angle>[rad])}[] + + -----examples: + text(A){5,6} + text($A_1$){A1, shift(2, 2)} + text(Z2){Z2, shift(5, -5)}[tr] + text(Z3){Z2, polar(5, 20 deg)}[Br] + text(Z4){Z2, polar(5, 1.34 rad)} + text(\framebox{Z5}){Z5} + +============================== + + VAR + + The var command is used to define scalar variables. It can be any numerical expression. A variable-name must begin with a single letter (either upper or lower case), and may have up to a maximum of three following digits. If a more detailed variable name is required, then a simple alternative is to use a mathsPIC macro---as any string can be allocated via macros (see the beginning of this chapter for details on macros). + + Note that variables, constants and points have the same name structure, and a variable can have the same name as a point (and so we suggest points have uppercase letters and variables and constants have lowercase letters). New values can be re-allocated to existing variable-names; however, when this occurs then mathsPIC does not issue a warning message to hightlight this fact. + + If it is important to be warned if a potential variable is accidentally reallocated then one should consider using the const command instead (since mathsPIC does generate an error message if a constant is reallocated). + + -----syntax: + var <name> = <expr> + + -----notes: + In addition to the mathematical functions mathsPIC functions which can be used with the var command are: + + angle(<three-points>) % returns angle in radians + angledeg(<three-points>) % returns angle in degrees + area(<three-points>) + xcoord(<point>) + ycoord(<point>) + direction(<two-points>) % returns angular direction in radians + directiondeg(<two-points>) % returns angular direction in degrees + + -----examples: + var r = 20, r4 = r3*tan(0.3), j = (r*2e3)**2, r5 = AB + var e = _e_, p1 = _Pi_ + var t = _linethickness_ % returns linethickness in current units + var g137 = angle(ABC) %(default: returns in radians) + var g = angledeg(ABC) % angle in degrees + var h = area(ABC) + var x2 = xcoord(A), y2 = ycoord(A) + var m5 = 12 rem 3 % remainder after dividing by 3 + var r1 = direction(PQ) % in radians + var d1 = directiondeg(PQ) + +============================== + + SEE ALSO + -------- + +The mathsPIC package manual and examples + +============================== + + BUGS + ---- + +Please report bugs to Dick Nickalls (see manual and above for address) + +------------------------END--------------------- diff --git a/Master/texmf-dist/doc/latex/mathspic/MATHSPIC.BAT b/Master/texmf-dist/doc/latex/mathspic/MATHSPIC.BAT new file mode 100755 index 00000000000..1a865ad7c73 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/MATHSPIC.BAT @@ -0,0 +1,2 @@ +perl mathspic.pl %1 %2 %3 %4 %5 + diff --git a/Master/texmf-dist/doc/latex/mathspic/README.txt b/Master/texmf-dist/doc/latex/mathspic/README.txt new file mode 100644 index 00000000000..e84f830431c --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/README.txt @@ -0,0 +1,114 @@ +%% readme.txt +%% for mathsPIC (version 1.00) + +Name:- mathsPIC (Perl version) +Authors:- A. Syropoulos and R.W.D. Nickalls +Affiliation:- see manual +Date:- February 2005 + +(1) INTRODUCTION +----------------- +MathsPIC is an open-source `filter' program for the PiCTeX graphics package, which enables complicated drawings/diagrams to be constructed very easily (allows the flexible use of LaTeX commands, relative addressing, macros, libraries, and perl programs). + +MathsPIC is a Perl program which processes an input script file (containing mathsPIC, TeX, LaTeX, and PiCTeX commands) into a .tex file which can be processed in the usual way (by TeX or LaTeX) to generate the final graphic. Please read the comprehensive manual for details of commands, usage, examples, installation etc. + +MathsPIC will run on any platform having a working Perl and TeX/LaTeX installation. However, there may of course be minor differences regarding installation and usage between platforms. + +MathsPIC has been well tested using a Solaris x86 box and GNU/Linux which the authors are familiar with. Feedback regarding installation and usage on other platforms will be greatly appreciated, and included in future manuals. + +For details see the manual (mp1manual*.pdf). + +(2) HISTORY +----------- +MathsPIC was originally an MS-DOS program (September 1999). mathsPIC was implemented in Perl in order to (a) greatly improve its utility, and (b) to make it available to the wide range of platforms which run Perl. An early version of the Perl mathsPIC was presented at the TUG2000 conference (Oxford, UK). + +(3) REQUIRED SYSTEMS +-------------------- +-perl (an interpreter for the perl language, see http://www.perl.com) + + +(4) PACKAGE FILES +------------------ +The following files are included in the mathsPIC package. + +readme.txt % this file +mathspic.pl % mathsPIC program (perl) +mathspic.sty % style option +mathspic.1 % unix/Linux manpage file +HELP.TXT % text version of the Unix manpage +mathspic.sh % an example BASH file for running the program +MATHSPIC.BAT % an example batch file (MS-Windows) +mathsPICa4.pdf % manual (PDF) in A4 size +mathsPICa4.ps % manual (PostScript) in A4 size +mathsPICa5.pdf % manual (PDF) in A5 size +mathsPICa5.ps % manual (PostScript) in A5 size +drawcube.pl % perl program described in the manual +drawcurvedarrow.pl % perl program described in the manual +grabtexdata.tex % tex file (see manual) for accessing texfile data +mathspic.lib % example library file of macros +sourcecode.pdf/.html % perl source code +sourcecode.nw % perl source code (noweb) +figures.tgz % compressed file of all figure files in manual + + +(5) INSTALLATION (Unix/Linux) +----------------------------- +Four files need to be placed in specific locations as follows +(see also USAGE regarding the BASH script file) + +(a) mathsPIC program (mathspic.pl) +This needs to be placed where your shell can find it +(typically: /usr/local/bin) + +(b) mathsPIC BASH script (mathspic.sh) +This needs to be placed where your shell can find it +(typically: /usr/local/bin) + +(c) LaTeX package (mathspic.sty) +This needs to be placed with the other style options +(typically: /usr/share/texmf/tex/latex/base/). + +(d) manpage (mathspic.1) +place this file in the /man1/ directory +(typically: /usr/share/man/man1/) + +Actually, there is no need to install the shell script. Instead one +can just copy the file mathspic.pl to a directory where his/her shell +can find it and to rename it mathspic. Then one just need to make +executable the file mathspic (e.g., by issuing the command +chmod 755 mathspic). + +(6) USAGE (see manual for full details) +---------------------------------------- +In Unix/Linux one way of running mathsPIC is to type the following at the command-line (options are shown in square brackets). Note this requires both the perl program (mathspic.pl) and the input file to be in the same directory. + +Syntax: + perl mathspic.pl [-b] [-c] [-h] infile [-o outfile] + +Options: + -b enables bell/sound if errors are detected + -c disables writing of comments to output file + -o to be followed by the <outfile> + -h displays help info + +However, it is generally much more convenient to run mathsPIC via a batch file, since we can then run mathsPIC from any directory. + +For example (Unix/Linux) rename the example BASH file <mathspic.sh> to <mathspic>. Now change the user permissions to make it a read/write/executable file. Finally, copy the file to a place where your shell will find it, typically the directory /usr/local/bin/. Now you will be able to run mathsPIC from the command-line in any directory using the command:- + +mathspic [-b] [-c] [-h] infile [-o outfile] + +MS-Windows users can use the example MATHSPIC.BAT file similarly. + +(7) LICENSE (LPPL): +------------- + This program is free software; you can redistribute it and/or modify it under the terms of the LaTeX Project Public License. + + This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. +----------------- +End of README.txt +----------------- + + + +========================= + diff --git a/Master/texmf-dist/doc/latex/mathspic/cleanmathspic.pl b/Master/texmf-dist/doc/latex/mathspic/cleanmathspic.pl new file mode 100644 index 00000000000..02efc598804 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/cleanmathspic.pl @@ -0,0 +1,23 @@ +#!/usr/bin/perl +### cleanmathsPIC.pl +## for Unix/Linux only +## removes all unnecessary files to facilitate archiving etc +## RWD Nickalls 2005 +##--------------------------------------- + +## -w ## turned off for the moment +##------------------ +system ("mv -vf *.dvi ~/allfiles/trashcan"); +system ("mv -vf *.aux ~/allfiles/trashcan"); + +system ("mv -vf *.mt ~/allfiles/trashcan"); +system ("mv -vf *.mlg ~/allfiles/trashcan"); + +#system ("mv -vf *.idx ~/allfiles/trashcan"); +#system ("mv -vf *.ind ~/allfiles/trashcan"); +#system ("mv -vf *.glo ~/allfiles/trashcan"); +#system ("mv -vf *.bbl ~/allfiles/trashcan"); + +## ask permission for the .pic/.log/.gnu just in case +system ("mv -vf *.log ~/allfiles/trashcan"); + __END__ diff --git a/Master/texmf-dist/doc/latex/mathspic/drawcube.pl b/Master/texmf-dist/doc/latex/mathspic/drawcube.pl new file mode 100644 index 00000000000..21b92cef689 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/drawcube.pl @@ -0,0 +1,50 @@ +#!/usr/bin/perl +## drawcube.pl +# requires latex Color package +# command line parameters Pointname,sidelength,temp-filename +# use: system("perl drawcube.pl P s3 temp.txt") +# see mathsPIC manual +#=========================== +my ($argnumber) = $#ARGV +1; +if ($argnumber != 3){ + print "============================\n"; + print "ERROR: drawcube.pl requires 3 arguments\n"; + print "USE: drawcube.pl <pointname> <sidelength> <filename> \n"; + print "============================\n"; + exit(1); +} +my ($point, $side, $filename)=@ARGV; +open (outfile, ">$filename")|| die "ERROR can't create file $filename\n"; +print (outfile <<EOF); +\%\%------mathsPIC code---------------- +var r=$side*sqrt(2)/2 +var a=30 %% angle degrees +Point*(P990){$point, polar(r/2, (a-180) deg)} +Point*(P991){P990, polar(r, 45 deg)} +Point*(P992){P991, rotate(P990, 90)} +Point*(P993){P991, rotate(P990, 180)} +Point*(P994){P991, rotate(P990, 270)} +Point*(P995){P991, polar(r, a deg)} +Point*(P996){P992, polar(r, a deg)} +Point*(P997){P993, polar(r, a deg)} +Point*(P998){P994, polar(r, a deg)} +%% draw the sides +\\color{blue} +drawline(P991 P992 P993 P994 P991, P994 P998 P995 P996 P992, P991 P995) +\\setdashes +drawline(P993 P997 P998, P997 P996) +%% draw the diagonals +\\color{red} +drawline(P991 P997, P992 P998, P996 P994, P995 P993) +%% draw the points and labels +\\setsolid\\color{black} +drawpoint($point P991 P992 P993 P994 P995 P996 P997 P998) +text(\$$point\$){$point, shift(-0.4,-0.1)} +text(\$P991\$){P991, shift(-0.3,0.3)} +text(\$P995\$){P995, shift(-0.3,0.3)} +%%---------------------------- +EOF +# now delete the temp file +print (outfile qq(system("rm $filename")\n)); +close outfile +__END__ diff --git a/Master/texmf-dist/doc/latex/mathspic/drawcurvedarrow.pl b/Master/texmf-dist/doc/latex/mathspic/drawcurvedarrow.pl new file mode 100644 index 00000000000..ba2bca83e8c --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/drawcurvedarrow.pl @@ -0,0 +1,10 @@ +#!/usr/bin/perl +## drawcurvedarrow.pl +# command-line parameters A B C h filename +my ($A, $B, $C, $h, $filename)=@ARGV; +open (outfile, ">$filename")|| die "ERROR can't create file $filename\n"; +print (outfile "Point*(P999){pointonline($B$A, -($A$B)/3)}\n"); +print (outfile "Point*(H999){pointonline($C P999,$h)}\n"); +print (outfile "Drawcurve($A$B H999)\n"); +print (outfile "drawArrow(H999 $C)\n"); +close (outfile); diff --git a/Master/texmf-dist/doc/latex/mathspic/figures.tgz b/Master/texmf-dist/doc/latex/mathspic/figures.tgz Binary files differnew file mode 100644 index 00000000000..10f011dc2fd --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/figures.tgz diff --git a/Master/texmf-dist/doc/latex/mathspic/grabtexdata.tex b/Master/texmf-dist/doc/latex/mathspic/grabtexdata.tex new file mode 100644 index 00000000000..d69d318b7ca --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/grabtexdata.tex @@ -0,0 +1,39 @@ +%% grabtexdata.tex (from oxford.tex) +%% RWD Nickalls (c) Jan 2005 +%% for extracting data into mathspic var commands +%%======================================== +\scrollmode % prevent LaTeX stopping if there are errors +%--------------------- +% make a print command macro +\newcommand{\print}[1]{\immediate\write\outfile{#1}} +%--------------------- +% make a comment % command macro +% first need to define percentchar for the write statement +% (From "TeX for the Impatient" (1990), p 292) +{\catcode`\%=12 \global\def\percentchar{%}}% +\newcommand{\comment}{\percentchar\space} +% +% make a \macro command --> %def<space> +\newcommand{\mydef}{def} +\newcommand{\macro}{\percentchar\mydef\space} +%---------------------- +% create and open a new file with filename = textfiledata.dat +\newwrite\outfile +\immediate\openout\outfile=texfiledata.dat +%---------------------- +%% write file header & general info +\print{\percentchar\percentchar\space file: texdata.dat} +\print{\percentchar\percentchar\space accessing TeX parameter values} +%--------------------- +%% now get \textwidth and \textheight values from the tex file +\print{\comment ============} +\print{var w555 = \number\textwidth\comment\textwidth=scaled points} +\print{var w556 = \number\textwidth\comment\textwidth=\the\textwidth} +\print{var w557 = \number\textwidth/1864679.8\comment (\textwidth in cms)} +\print{\macro textwidthcms()\number\textwidth/1864679.8\comment} +\print{\macro textheightcms()\number\textheight/1864679.8\comment} +\print{\comment ============} +%-------------------- +% close the file +\immediate\closeout\outfile +%%=========end========================= diff --git a/Master/texmf-dist/doc/latex/mathspic/mathpic.pl b/Master/texmf-dist/doc/latex/mathspic/mathpic.pl new file mode 100644 index 00000000000..21a3b5c6167 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/mathpic.pl @@ -0,0 +1,3341 @@ +#!/usr/bin/perl +# +#(c) Copyright 2005-2007 +# Apostolos Syropoulos & R.W.D. Nickalls +# asyropoulos@yahoo.com dicknickalls@compuserve.com +# +# This program can be redistributed and/or modified under the terms +# of the LaTeX Project Public License Distributed from CTAN +# archives in directory macros/latex/base/lppl.txt; either +# version 1 of the License, or any later version. +# +package DummyFH; +my $index = 0; +sub TIEHANDLE { + my $class = shift; + my $self= shift; + bless $self, $class; +} +sub READLINE { + my $self = shift; + #shift @$self; + if ($index > $#$self) { + $index = 0; + return undef; + } + else { + return $self->[$index++]; + } +} + +package main; +use Math::Trig; +our $version_number = "1.10 Feb 18, 2007"; +our $commandLineArgs = join(" ", @ARGV); +our $command = ""; +our $curr_in_file = ""; +our %PointTable = (); +our %VarTable = (); +our %ConstTable = (); +our $no_errors = 0; +our $xunits = "1pt"; +our $yunits = "1pt"; +our $units = "pt|pc|in|bp|cm|mm|dd|cc|sp"; +our $defaultsymbol = "\$\\bullet\$"; +our $defaultLFradius = 0; +use constant PI => atan2(1,1)*4; +use constant R2D => 180 / PI; +use constant D2R => PI / 180; +our $arrowLength = 2; +our $arrowLengthUnits = "mm"; +our $arrowAngleB = 30; +our $arrowAngleC = 40; +our %DimOfPoint = (); +our $GlobalDimOfPoints = 0; +our @Macros = (); +our $LineThickness = 0.4; + + sub mpp { + my $in_line; + chomp($in_line = shift); + my $LC = shift; + my $out_line = $in_line; + my $macro_name = ""; + my @macro_param = (); + my $macro_code = ""; + if ($in_line =~ s/^%def\s*//) { + if ($in_line =~ s/^(\w+)\s*//){ + $macro_name = $1; + } + else { + PrintErrorMessage("No macro name has been found",$LC); + return "" + } + if ($in_line =~ s/^\(\s*//) { + # do nothing + } + else { + PrintErrorMessage("No left parenthesis after macro name has been found",$LC); + return ""; + } + if ($in_line =~ s/^\)//) { + # Macro has no parameters! + } + else { + MACROS: while (1) { + if ($in_line =~ s/^(\w+)\s*//) { + push (@macro_param, $1); + } + else { + PrintErrorMessage("No macro parameter name has been found",$LC); + return ""; + } + if ($in_line =~ s/^,\s*//) { + next MACROS; + } + else { + last MACROS; + } + } + if ($in_line =~ s/^\)//) { + # do nothing! + } + else { + PrintErrorMessage("No closing parenthesis after macro parameters",$LC); + return ""; + } + } + $in_line =~ s/([^%]+)(%.*)/$1/; + $macro_code = $in_line; + push ( @Macros , { 'macro_name' => $macro_name, + 'macro_code' => $macro_code, + 'macro_param' => \@macro_param }); + return $out_line; + } + elsif ($in_line =~ s/^%undef\s*//) { + if ($in_line =~ s/^(\w+)//) { + my $undef_macro = $1; + for(my $i = $#Macros; $i >= 0; $i--) { + if ($Macros[$i]->{'macro_name'} eq $undef_macro) { + splice(@Macros,$i,1); + } + } + } + return $out_line; + } + elsif ($in_line =~ s/^\s*%//) { + return $out_line; + } + else { + my $comment = $2 if $in_line =~ s/([^%]+)(%.+)/$1/; + EXPANSIONLOOP: while () { + my $org_in_line = $in_line; + for(my $i = $#Macros; $i >= 0; $i--) { + my $macro_name = $Macros[$i]->{'macro_name'}; + if ($in_line =~ /&$macro_name\b/) { ############################ + my $num_of_macro_args = @{$Macros[$i]->{'macro_param'}}; + if ( $num_of_macro_args > 0 ) { + # Macro with parameters + my $pattern = "&$macro_name\\("; + foreach my $p ( 1..$num_of_macro_args ) { + my $comma = ($p == $num_of_macro_args) ? "\\s*" : "\\s*,\\s*"; + $pattern .= "\\s*[^\\s\\)]+$comma"; + } + $pattern .= "\\)"; + while($in_line =~ /&$macro_name\b/) { + if ($in_line =~ /$pattern/) { + my $before = $`; + my $after = $'; + my $match = $&; + my $new_code = $Macros[$i]->{'macro_code'}; + $match =~ s/^&$macro_name\(\s*//; + $match =~ s/\)$//; + foreach my $arg ( 0..($num_of_macro_args - 1) ) { + my $old = $Macros[$i]->{'macro_param'}->[$arg]; + my $comma = ($arg == ($num_of_macro_args - 1)) ? "" : ","; + $match =~ s/^\s*([^\s,]+)\s*$comma//; + my $new = $1; + # 'g': Parameter may occur several times + # in $new_code. + # '\b': Substitute only whole words + # not x in xA + $new_code =~ s/\b$old\b/$new/g; + } + $in_line = "$before$new_code$after"; + } + else { + PrintErrorMessage("Usage of macro &$macro_name does not " . + "match its definition", $LC); + return ""; + } + } + } + else { + # Macro without parameters + my $replacement = $Macros[$i]->{'macro_code'}; + # '\b': Substitute only whole words + # not x in xA + $in_line =~ s/&$macro_name\b/$replacement/g; + } + } + } + last EXPANSIONLOOP if ( $org_in_line eq $in_line ); + } + return "$in_line$comment"; + } + } + + sub PrintErrorMessage { + my $errormessage = shift; + my $error_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($error_line); + + for my $fh (STDOUT, LOG) { + print $fh "$curr_in_file", "Line $error_line: $A\n"; + print $fh " " x $l ,$_,"***Error: $errormessage\n"; + } + if ($comments_on) { #print to output file file + print OUT "%% *** $curr_in_file", "Line $error_line: $A\n"; + print OUT "%% *** "," " x $l ,$_,"%% ... Error: $errormessage\n"; + } + $no_errors++; + } + + sub PrintWarningMessage { + my $warningMessage = shift; + my $warning_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($warning_line); + + for my $fh (STDOUT, LOG) { + print $fh "$curr_in_file", "Line $warning_line: $A\n"; + print $fh " " x $l ,$_,"***Warning: $warningMessage\n"; + } + if ($comments_on) { #print to output file file + print OUT "%% *** $curr_in_file", "Line $warning_line: $A\n"; + print OUT "%% *** "," " x $l ,$_,"%% ... Warning: $warningMessage\n"; + } + } + + sub PrintFatalError { + my $FatalMessage = shift; + my $fatal_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($fatal_line); + + die "$curr_in_file", "Line $fatal_line: $A\n" . + (" " x $l) . $_ . "***Fatal Error: $FatalMessage\n"; + } + + sub chk_lparen { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if (/^[^\(]/) { + PrintErrorMessage("Missing ( after $token",$lc); + } + else { + s/^\(\s*//; + } + } + + sub chk_rparen { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if (s/^\)//) { + s/\s*//; + } + else { + PrintErrorMessage("Missing ) after $token",$lc); + } + } + + + sub chk_lcb { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if ($_ !~ /^\{/) { + PrintErrorMessage("Missing { after $token",$lc); + } + else { + s/^{\s*//; + } + } + + sub chk_rcb { + my $token = $_[0]; + my $lc = $_[1]; + if ($_ !~ /^\s*\}/) { + PrintErrorMessage("Missing } after $token",$lc); + } + else { + s/^\s*}\s*//; + } + } + + sub chk_lsb { + my $token = $_[0]; + my $lc = $_[1]; + + s/\s*//; + if ($_ !~ /^\[/) { + PrintErrorMessage("Missing [ after $token",$lc); + } + else { + s/^\[\s*//; + } + } + + sub chk_rsb { + my $token = $_[0]; + my $lc = $_[1]; + + s/\s*//; + if ($_ !~ /^\]/) { + PrintErrorMessage("Missing ] after $token",$lc); + } + else { + s/^\]\s*//; + } + } + + sub chk_comma { + my $lc = $_[0]; + + s/\s*//; + if (/^[^,]/) { + PrintErrorMessage("Did not find expected comma",$lc); + } + else { + s/^,\s*//; + } + } + + sub chk_comment { + my $lc = $_[0]; + + s/\s*//; + if (/^%/) { + # do nothing! + } + elsif (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } + } + + sub print_headers + { + my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localtime; + $year+=1900; + $mon+=1; + $now_string = "$year/" . ($mon>9 ? "$mon/" : "0$mon/") . + ($mday>9 ? "$mday " : "0$mday ") . + ($hour>9 ? "$hour:" : "0$hour:") . + ($min>9 ? "$min:" : "0$min:") . + ($sec>9 ? "$sec" : "0$sec"); + print OUT "%* -----------------------------------------------\n"; + print OUT "%* mathspic (Perl version $version_number)\n"; + print OUT "%* A filter program for use with PiCTeX\n"; + print OUT "%* Copyright (c) 2005 A Syropoulos & RWD Nickalls \n"; + print OUT "%* Command line: $0 $commandLineArgs\n"; + print OUT "%* Input filename : $source_file\n"; + print OUT "%* Output filename: $out_file\n"; + print OUT "%* Date & time: $now_string\n"; + print OUT "%* -----------------------------------------------\n"; + # + print LOG "----\n"; + print LOG "$now_string\n"; + print LOG "mathspic (Perl version $version_number)\n"; + print LOG "Copyright (c) 2005 A Syropoulos & RWD Nickalls \n"; + print LOG "Input file = $source_file\n"; + print LOG "Output file = $out_file\n"; + print LOG "Log file = $log_file\n"; + print LOG "----\n"; + } + + sub get_point { + + my ($lc) = $_[0]; + my ($PointName); + + if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name + $PointName = $1; + if (!exists($PointTable{lc($PointName)})) { + PrintErrorMessage("Undefined point $PointName",$lc); + return "_undef_"; + } + else { + return lc($PointName); + } + } + else { + PrintErrorMessage("Point name expected",$lc); + return "_undef_"; + } + } + + sub perpendicular { + my ($xP, $yP, $xA, $yA, $xB, $yB) = @_; + my ($xF, $yF, $deltax, $deltay, $m1, $m2, $c1, $c2, $factor); + + $deltax = $xA - $xB; + return ($xA, $yP) if abs($deltax) < 0.0000001; + $deltay = $yA - $yB; + return ($xP, $yA) if abs($deltay) < 0.0000001; + $m1 = $deltay / $deltax; + eval { $m2 = (-1) / $m1;}; + PrintFatalError("Division by zero",$lc) if $@; + $c1 = $yA - $m1 * $xA; + $c2 = $yP - $m2 * $xP; + eval { $factor = 1 / ($m1 - $m2)}; + PrintFatalError("Division by zero",$lc) if $@; + return (($c2 - $c1) * $factor, ($m1 * $c2 - $m2 * $c1) * $factor); + } + + sub Length { + my ($xA, $yA, $xB, $yB)=@_; + return sqrt(($xB - $xA)**2 + ($yB - $yA)**2); + } + + sub triangleArea { + my ($xA, $yA, $xB, $yB, $xC, $yC)=@_; + my ($lenAB, $lenBC, $lenCA, $s); + + $lenAB = Length($xA,$yA,$xB,$yB); + $lenBC = Length($xB,$yB,$xC,$yC); + $lenCA = Length($xC,$yC,$xA,$yA); + $s = ($lenAB + $lenBC + $lenCA) / 2; + return sqrt($s * ($s - $lenAB)*($s - $lenBC)*($s - $lenCA)); + } + + sub pointOnLine { + my ($xA, $yA, $xB, $yB, $dist)=@_; + my ($deltax, $deltay, $xPol, $yPol); + + $deltax = $xB - $xA; + $deltay = $yB - $yA; + $xPol = $xA + ($dist * $deltax / &Length($xA,$yA,$xB,$yB)); + $yPol = $yA + ($dist * $deltay / &Length($xA,$yA,$xB,$yB)); + return ($xPol, $yPol); + } + + + + sub circumCircleCenter { + my ($xA, $yA, $xB, $yB, $xC, $yC, $lc)=@_; + my ($deltay12, $deltax12, $xs12, $ys12); + my ($deltay23, $deltax23, $xs23, $ys23); + my ($xcc, $ycc); + my ($m23, $mr23, $c23, $m12, $mr12, $c12); + my ($sideA, $sideB, $sideC, $a, $radius); + + if (abs(triangleArea($xA, $yA, $xB, $yB, $xC, $yC)) < 0.0000001) + { + PrintErrorMessage("Area of triangle is zero!",$lc); + return (0,0,0); + } + $deltay12 = $yB - $yA; + $deltax12 = $xB - $xA; + $xs12 = $xA + $deltax12 / 2; + $ys12 = $yA + $deltay12 / 2; + # + $deltay23 = $yC - $yB; + $deltax23 = $xC - $xB; + $xs23 = $xB + $deltax23 / 2; + $ys23 = $yB + $deltay23 / 2; + # + CCXYLINE:{ + if (abs($deltay12) < 0.0000001) + { + $xcc = $xs12; + if (abs($deltax23) < 0.0000001) + { + $ycc = $ys23; + last CCXYLINE; + } + else + { + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $ycc = $mr23 * $xs12 + $c23; + last CCXYLINE; + } + } + if (abs($deltax12) < 0.0000001) + { + $ycc = $ys12; + if (abs($deltay23) < 0.0000001) + { + $xcc = $xs23; + last CCXYLINE; + } + else + { + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $xcc = ($ys12 - $c23) / $mr23; + last CCXYLINE; + } + } + if (abs($deltay23) < 0.0000001) + { + $xcc = $xs23; + if (abs($deltax12) < 0.0000001) + { + $ycc = $ys12; + last CCXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + $ycc = $mr12 * $xcc + $c12; + last CCXYLINE; + } + } + if (abs($deltax23) < 0.0000001) + { + $ycc = $ys23; + if (abs($deltay12) < 0.0000001) + { + $xcc = $xs12; + last CCXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + $xcc = ($ycc - $c12) / $mr12; + last CCXYLINE; + } + } + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + #----- + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $xcc = ($c23 - $c12) / ($mr12 - $mr23); + $ycc = ($c23 * $mr12 - $c12 * $mr23) / ($mr12 - $mr23); + } + # + $sideA = &Length($xA,$yA,$xB,$yB); + $sideB = &Length($xB,$yB,$xC,$yC); + $sideC = &Length($xC,$yC,$xA,$yA); + $a = triangleArea($xA, $yA, $xB, $yB, $xC, $yC); + $radius = ($sideA * $sideB * $sideC) / (4 * $a); + # + return ($xcc, $ycc, $radius); + } + + sub ComputeDist { + my ($lc) = $_[0]; + my ($v1, $v2); + + if (s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//) #is it a number? + { + return ($1, 1); + } + elsif (/^[^\W\d_]\d{0,3}[^\W\d_]\d{0,3}/) #it is a pair of IDs? + { + s/^([^\W\d_]\d{0,3})//i; + $v1 = $1; + if (!exists($PointTable{lc($v1)})) { + if (exists($VarTable{lc($v1)})) { + return ($VarTable{lc($v1)}, 1); + } + PrintErrorMessage("Point $v1 has not been defined", $lc); + s/^\s*[^\W\d_]\d{0,3}//i; + return (0,0); + } + $v1 = lc($v1); + s/^\s*([^\W\d_]\d{0,3})//i; + $v2 = $1; + if (!exists($PointTable{lc($v2)})) + { + PrintErrorMessage("Point $v2 has not been defined", $lc); + return (0,0); + } + $v2 = lc($v2); + my ($x1,$y1,$pSV1,$pS1) = unpack("d3A*",$PointTable{$v1}); + my ($x2,$y2,$pSV2,$pS2) = unpack("d3A*",$PointTable{$v2}); + return (Length($x1,$y1,$x2,$y2), 1); + } + elsif (s/^([^\W\d_]\d{0,3})//i) # it is a single id + { + $v1 = $1; + if (!exists($VarTable{lc($v1)})) #it isn't a variable + { + PrintErrorMessage("Variable $v1 has not been defined", $lc); + return (0,0); + } + return ($VarTable{lc($v1)}, 1); + } + else + { + PrintErrorMessage("Unexpected token", $lc); + return (0,0); + } + } + + sub intersection4points { + my ($x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4) = @_; + my ($deltay12, $deltax12, $deltay34, $deltax34); + my ($xcc, $ycc, $m34, $c34, $m12, $c12); + + $deltay12 = $y2 - $y1; + $deltax12 = $x2 - $x1; + # + $deltay34 = $y4 - $y3; + $deltax34 = $x4 - $x3; + I4PXYLINE:{ + if (abs($deltay12) < 0.0000001) + { + $ycc = $y1; + if (abs($deltax34) < 0.0000001) + { + $xcc = $x3; + last I4PXYLINE; + } + else + { + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $xcc = ($ycc - $c34) / $m34; + last I4PXYLINE; + } + } + if (abs($deltax12) < 0.0000001) + { + $xcc = $x1; + if (abs($deltay34) < 0.0000001) + { + $ycc = $y3; + last I4PXYLINE; + } + else + { + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $ycc = $m34 * $xcc + $c34; + last I4PXYLINE; + } + } + if (abs($deltay34) < 0.0000001) + { + $ycc = $y3; + if (abs($deltax12) < 0.0000001) + { + $xcc = $x1; + last I4PXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $xcc = ($ycc - $c12) / $m12; + last I4PXYLINE; + } + } + if (abs($deltax34) < 0.0000001) + { + $xcc = $x3; + if (abs($deltay12) < 0.0000001) + { + $ycc = $y1; + last I4PXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $ycc = $m12 * $xcc + $c12; + last I4PXYLINE; + } + } + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $xcc = ($c34 - $c12) / ($m12 - $m34); + $ycc = ($c34 * $m12 - $c12 * $m34) / ($m12 - $m34); + } + return ($xcc, $ycc); + } + + sub IncircleCenter { + my ($Ax, $Ay, $Bx, $By, $Cx, $Cy) = @_; + my ($sideA, $sideB, $sideC); + my ($ba1, $xA1, $yA1, $cb1, $ac1, $xB1, $yB1, $xC1, $yC1, $a, $s, $r); + + #determine the lengths of the sides + $sideA = Length($Bx, $By, $Cx, $Cy); + $sideB = Length($Cx, $Cy, $Ax, $Ay); + $sideC = Length($Ax, $Ay, $Bx, $By); + # + $ba1 = ($sideC * $sideA) / ($sideB + $sideC); + ($xA1, $yA1) = pointOnLine($Bx, $By, $Cx, $Cy, $ba1); + $cb1 = ($sideA * $sideB) / ($sideC + $sideA); + ($xB1, $yB1) = pointOnLine($Cx, $Cy, $Ax, $Ay, $cb1); + $ac1 = ($sideB * $sideC) / ($sideA + $sideB); + ($xC1, $yC1) = pointOnLine($Ax, $Ay, $Bx, $By, $ac1); + ($xcenter, $ycenter) = &intersection4points($Ax, $Ay, $xA1, $yA1, + $Bx, $By, $xB1, $yB1); + # get radius + $a = &triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $s = ($sideA + $sideB +$sideC) / 2; + $r = $a / $s; + return ($xcenter, $ycenter, $r); + } + + sub Angle { + my ($Ax, $Ay, $Bx, $By, $Cx, $Cy) = @_; + my ($RAx, $RAy, $RBx, $RBy, $RCx, $RCy, $deltax, $deltay); + my ($lineBA, $lineBC, $lineAC, $k, $kk, $angle); + my ($T, $cosT, $sinT) = (0.3, cos(0.3), sin(0.3)); + + $RAx = $Ax * $cosT + $Ay * $sinT; + $RAy = -$Ax * $sinT + $Ay * $cosT; + $RBx = $Bx * $cosT + $By * $sinT; + $RBy = -$Bx * $sinT + $By * $cosT; + $RCx = $Cx * $cosT + $Cy * $sinT; + $RCy = -$Cx * $sinT + $Cy * $cosT; + $deltax = $RBx - $RAx; + $deltay = $RBy - $RAy; + $lineBA = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineBA < 0.0000001) + { + return -500; + } + $deltax = $RBx - $RCx; + $deltay = $RBy - $RCy; + $lineBC = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineBC < 0.0000001) + { + return -500; + } + $deltax = $RAx - $RCx; + $deltay = $RAy - $RCy; + $lineAC = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineAC < 0.0000001) + { + return -500; + } + $k = ($lineBA*$lineBA + $lineBC*$lineBC - $lineAC*$lineAC ) / + (2 * $lineBA * $lineBC); + $k = -1 if $k < -0.99999; + $k = 1 if $k > 0.99999; + $kk = $k * $k; + if (($kk * $kk) == 1) + { + $angle = PI if $k == -1; + $angle = 0 if $k == 1; + } + else + { + $angle = (PI / 2) - atan2($k / sqrt(1 - $kk),1); + } + return $angle * 180 / PI; + } + + sub excircle { + my ($A, $B, $C, $D, $E) = @_; + my ($Ax,$Ay,$Bx,$By,$Dx,$Dy,$Ex,$Ey,$ASVA,$ASA); + ($Ax,$Ay,$ASVA,$ASA)=unpack("d3A*",$PointTable{$A}); + ($Bx,$By,$ASVA,$ASA)=unpack("d3A*",$PointTable{$B}); + ($Cx,$Cy,$ASVA,$ASA)=unpack("d3A*",$PointTable{$C}); + ($Dx,$Dy,$ASVA,$ASA)=unpack("d3A*",$PointTable{$D}); + ($Ex,$Ey,$ASVA,$ASA)=unpack("d3A*",$PointTable{$E}); + my ($sideA, $sideB, $sideC, $s, $R, $theAdeg, $d); + my ($Xmypoint, $Ymypoint, $deltax, $deltay, $mylength, $xc, $yc); + + $sideA = &Length($Bx, $By, $Cx, $Cy); + $sideB = &Length($Cx, $Cy, $Ax, $Ay); + $sideC = &Length($Ax, $Ay, $Bx, $By); + $s = ($sideA + $sideB + $sideC) / 2; + $R = triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy) / + ($s - &Length($Dx, $Dy, $Ex, $Ey)); + if (($D eq $A && $E eq $B) || ($D eq $B && $E eq $A)) + { + $theAdeg = &Angle($Bx, $By, $Cx, $Cy, $Ax, $Ay); + $Xmypoint = $Cx; + $Ymypoint = $Cy; + } + elsif (($D eq $B && $E eq $C) || ($D eq $C && $E eq $B)) + { + $theAdeg = &Angle($Cx, $Cy, $Ax, $Ay, $Bx, $By); + $Xmypoint = $Ax; + $Ymypoint = $Ay; + } + elsif (($D eq $C && $E eq $A) || ($D eq $A && $E eq $C)) + { + $theAdeg = &Angle($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $Xmypoint = $Bx; + $Ymypoint = $By; + } + else + { + return (0,0,0); + } + $d = $R / sin($theAdeg * PI / 180 / 2); + my ($xIn, $yIn, $rin) = &IncircleCenter($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $deltax = $xIn - $Xmypoint; + $deltay = $yIn - $Ymypoint; + $mylength = sqrt($deltax*$deltax + $deltay*$deltay); + $xc = $Xmypoint + $d * $deltax / $mylength; + $yc = $Ymypoint + $d * $deltay / $mylength; + return ($xc, $yc, $R); + } + + sub DrawLineOrArrow { + my $draw_Line = shift; + my $lc = shift; + my $lineLength = -1; + my $stacklen = 0; + my @PP = (); + # if ($draw_Line != 2) { + # s/\s*//; + # if (s/^\[\s*//) { # optional length specifier + # $lineLength = expr($lc); + # if ($lineLength <= 0) { + # PrintErrorMessage("length must greater than zero",$lc); + # $lineLength = -1; + # } + # chk_rsb("optional part",$lc); + # } + # } + chk_lparen("$cmd",$lc); + DRAWLINES:while(1) { + @PP = () ; + while(1) { + if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name + $P = $1; + if (!exists($PointTable{lc($P)})) { + PrintErrorMessage("Undefined point $P",$lc); + } + else { + push (@PP,$P); + } + } + else { + $stacklen = @PP; + if ($draw_Line != 2) { + if ($stacklen <= 1) { + PrintErrorMessage("Wrong number of points",$lc); + } + else { + push(@PP,$lc); + if ($draw_Line == 0) { + drawarrows(@PP); + } + elsif ($draw_Line == 1) { + drawlines(@PP); + } + } + } + if (s/^,\s*// and $draw_Line != 2) { + next DRAWLINES; + } + else { + last DRAWLINES; + } + } + } + } + if ($draw_Line == 2) { + $stacklen = @PP; + if ($stacklen < 2) { + PrintErrorMessage("Wrong number of points",$lc); + } + elsif ($stacklen % 2 == 0) { + PrintErrorMessage("Number of points must be odd",$lc); + } + else { + drawCurve(@PP); + } + } + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + } + + sub drawarrows { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p, $q, $r12, $d12); + my ($px,$py,$pSV,$pS, $qx,$qy,$qSV,$qS); + + $NumberOfPoints = $NoArgs - 1; + LOOP: for(my $i=0; $i < $NumberOfPoints - 1; $i++) + { + $p = $_[$i]; + $q = $_[$i+1]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + ($qx,$qy,$qSV,$qS) = unpack("d3A*",$PointTable{lc($q)}); + $pSV = $defaultLFradius if $pSV == 0; + $qSV = $defaultLFradius if $qSV == 0; + $r12 = $pSV + $qSV; + $d12 = Length($px,$py,$qx,$qy); + if ($d12 <= $r12) + { + if($d12 == 0) + { + PrintErrorMessage("points $p and $q are the same", $lc); + next LOOP; + } + PrintWarningMessage("arrow $p$q not drawn: points too close or ". + "radii too big", $lc); + next LOOP; + } + ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV > 0; + ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV > 0; + my ($beta, $gamma); + $beta = tan($arrowAngleB * D2R / 2); + $gamma = 2 * tan($arrowAngleC * D2R / 2); + printf OUT "\\arrow <%.5f%s> [%.5f,%.5f] from %.5f %.5f to %.5f %.5f\n", + $arrowLength, $arrowLengthUnits, $beta, $gamma, $px, $py, $qx, $qy; + } + } + + sub drawlines { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p, $q, $r12, $d12); + my ($px,$py,$pSV,$pS, $qx,$qy,$qSV,$qS); + + $NumberOfPoints = $NoArgs - 1; + LOOP: for(my $i=0; $i < $NumberOfPoints - 1; $i++) + { + $p = $_[$i]; + $q = $_[$i+1]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + ($qx,$qy,$qSV,$qS) = unpack("d3A*",$PointTable{lc($q)}); + $pSV = $defaultLFradius if $pSV == 0; + $qSV = $defaultLFradius if $qSV == 0; + $r12 = $pSV + $qSV; + $d12 = Length($px,$py,$qx,$qy); + if ($d12 <= $r12) + { + if($d12 == 0) + { + PrintErrorMessage("points $p and $q are the same", $lc); + next LOOP; + } + PrintWarningMessage("line $p$q not drawn: points too close or ". + "radii too big", $lc); + next LOOP; + } + ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV > 0; + ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV > 0; + if ($px == $qx || $py == $qy) + { + printf OUT "\\putrule from %.5f %.5f to %.5f %.5f %%%% %s%s\n", + $px,$py,$qx,$qy,$p,$q; + } + else + { + printf OUT "\\plot %.5f %.5f\t%.5f %.5f / %%%% %s%s\n", + $px, $py,$qx,$qy,$p,$q; + } + } + } + + sub drawCurve { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p); + + $NumberOfPoints = $NoArgs - 1; + print OUT "\\setquadratic\n\\plot\n"; + for(my $i=0; $i <= $NumberOfPoints; $i++) + { + $p = $_[$i]; + my ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + printf OUT "\t%0.5f %0.5f", $px, $py; + print OUT (($i == $NumberOfPoints) ? " / %$p\n" : " %$p\n"); + } + print OUT "\\setlinear\n"; + } + + sub drawpoints { + my ($NumberOfPoints,$p); + $NumberOfPoints = @_; + my ($px,$py,$pSV,$pS); + + for($i=0; $i < $NumberOfPoints; $i++) + { + $p = $_[$i]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + if ($pS eq "" and $defaultsymbol =~ /circle|square/) { + $pS = $defaultsymbol; + } + POINTSWITCH: { + if ($pS eq "") # no plot symbol specified + { + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", + $defaultsymbol, $px, $py, $p; + last POINTSWITCH; + } + if ($pS eq "circle") # plot symbol is a circle + { + my $radius = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} : + $GlobalDimOfPoints; + if ($radius > 0) # draw a circle using the current units + { + if ($radius == 1.5) # use \bigcirc + { + printf OUT "\\put {\$\\bigcirc\$} at %.5f %.5f %%%% %s\n", + $px, $py, $p; + } + else + { + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f %%%% %s\n", + $px+$radius, $py, $px, $py, $p; + } + } + else #use \circ symbol + { + printf OUT "\\put {\$\\circ\$} at %.5f %.5f %%%% %s\n", + $px,$py,$p; + } + last POINTSWITCH; + } + if ($pS eq "square") + { + my $side = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} : + $GlobalDimOfPoints; + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", + drawsquare($side), $px, $py, $p; + last POINTSWITCH; + } + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", $pS,$px,$py,$p; + } + } + } + + sub drawAngleArc { + my ($P1, $P2, $P3, $radius, $inout, $direction) = @_; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + + my $internalAngle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + my $externalAngle = 360 - $internalAngle; + my ($x, $y) = pointOnLine($x2, $y2, $x1, $y1, $radius); + my $code = ""; + if ($inout eq "internal" and $direction eq "clockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + -1 * $internalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "internal" and $direction eq "anticlockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + $internalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "external" and $direction eq "clockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + -1 * $externalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "external" and $direction eq "anticlockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + $externalAngle, $x, $y, $x2, $y2; + } + return $code; + } + + sub drawAngleArrow { + my ($P1, $P2, $P3, $radius, $inout, $direction) = @_; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + + my $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction); + + my ($xqp, $yqp) = pointOnLine($x2, $y2, $x1, $y1, $radius); + my ($deltax, $deltay) = ($x1 - $x2, $y1 - $y2); + my $AL; + + if ($xunits =~ /mm/) { + $AL = 1; + } + elsif ($xunits =~ /cm/) { + $AL = 0.1; + } + elsif ($xunits =~ /pt/) { + $AL = 2.845; + } + elsif ($xunits =~ /bp/) { + $AL = 2.835; + } + elsif ($xunits =~ /pc/) { + $AL = 0.2371; + } + elsif ($xunits =~ /in/) { + $AL = 0.03937; + } + elsif ($xunits =~ /dd/) { + $AL = 2.659; + } + elsif ($xunits =~ /cc/) { + $AL = 0.2216; + } + elsif ($xunits =~ /sp/) { + $AL = 186467.98; + } + my $halfAL = $AL / 2; + my $d = sqrt($radius * $radius - $halfAL * $halfAL); + my $alpha = atan2($d / $halfAL, 1) * R2D; + my $beta = 2 * (90 - $alpha); + my $thetaqr; + if (abs($deltay) < 0.00001) { + if ($deltax > 0 ) {$thetaqr = 0 } + elsif ($deltax < 0) {$thetaqr = -180} + } + else { + if (abs($deltax) < 0.00001) { + $thetaqr = 90; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + } + my ($xqr, $yqr) = pointOnLine($x2, $y2, $x3, $y3, $radius); + $deltax = $x3 - $x2; + $deltay = $y3 - $y2; + $alpha = atan2(sqrt($radius * $radius - $halfAL * $halfAL) / $halfAL, 1) / + D2R; + $beta = 2 * (90 - $alpha); + LINE2 : { + if (abs($deltax) < 0.00001) { + if ($deltay > 0) { $thetaqr = 90 } + elsif ($deltay < 0) { $thetaqr = - 90 } + last LINE2; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + if (abs($deltay) < 0.00001) { + if ($deltax > 0) { $thetaqr = 0 } + elsif ($deltax < 0) { $thetaqr = -180 } + last LINE2; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + if ($deltax < 0 and $deltay > 0) { $thetaqr += 180 } + elsif ($deltax < 0 and $deltay < 0) { $thetaqr += 180 } + elsif ($deltax > 0 and $deltay < 0) { $thetaqr += 360 } + } + my $xqrleft = $x2 + $radius * cos(($thetaqr + $beta) * D2R); + my $yqrleft = $y2 + $radius * sin(($thetaqr + $beta) * D2R); + my $xqrright = $x2 + $radius * cos(($thetaqr - $beta) * D2R); + my $yqrright = $y2 + $radius * sin(($thetaqr - $beta) * D2R); + if ($inout eq "internal" and $direction eq "clockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrleft, $yqrleft, $xqr, $yqr; + } + elsif ($inout eq "internal" and $direction eq "anticlockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrright, $yqrright, $xqr, $yqr; + } + elsif ($inout eq "external" and $direction eq "clockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrleft, $yqrleft, $xqr, $yqr; + } + elsif ($inout eq "external" and $direction eq "anticlockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrright, $yqrright, $xqr, $yqr; + } + return $code; + } + + sub expr { + my $lc = $_[0]; + my($left,$op,$right); + + $left = term($lc); + while ($op = addop()) { + $right = term($lc); + if ($op eq '+') + { $left += $right } + else + { $left -= $right } + } + return $left; + } + + sub addop { + s/^([+-])// && $1; + } + + sub term { + my $lc = $_[0]; + my ($left, $op, $right); + $left = factor($lc); + while ($op = mulop()) { + $right = factor($lc); + if ($op eq '*') + { $left *= $right } + elsif ($op =~ /rem/i) { + eval {$left %= $right}; + PrintFatalError("Division by zero", $lc) if $@; + } + else { + eval {$left /= $right}; + PrintFatalError("Division by zero", $lc) if $@; + } + } + return $left; + } + + sub mulop { + (s#^([*/])## || s/^(rem)//i) && lc($1); + } + + sub factor { + my $lc = $_[0]; + my ($left); + + $left = primitive($lc); + if (s/^\*\*//) { + $left **= factor($lc); + } + return $left; + } + + sub primitive { + my $lc = $_[0]; + my $val; + s/\s*//; + if (s/^\(//) { #is it an expr in parentheses + $val = expr($lc); + s/^\)// || PrintErrorMessage("Missing right parenthesis", $lc); + } + elsif (s/^-//) { # is it a negated primitive + $val = - primitive(); + } + elsif (s/^\+//) { # is it a positive primitive + $val = primitive(); + } + elsif (s/^angledeg//i) { + chk_lparen("angledeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $d12 = Length($x1, $y1, $x2, $y2); + my $d23 = Length($x2, $y2, $x3, $y3); + my $d31 = Length($x3, $y3, $x1, $y1); + if ( $d12 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_2' are the same", $lc); + $val = 0; + } + elsif ( $d23 == 0 ) { + PrintErrorMessage("points `$point_2' and `$point_3' are the same", $lc); + $val = 0; + } + elsif ( $d31 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_3' are the same", $lc); + $val = 0; + } + else { + $val = Angle($x1, $y1, $x2, $y2, $x3, $y3); + $val = 0 if $val == -500; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^angle//i) { + chk_lparen("angle".$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $d12 = Length($x1, $y1, $x2, $y2); + my $d23 = Length($x2, $y2, $x3, $y3); + my $d31 = Length($x3, $y3, $x1, $y1); + if ( $d12 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_2' are the same", $lc); + $val = 0; + } + elsif ( $d23 == 0 ) { + PrintErrorMessage("points `$point_2' and `$point_3' are the same", $lc); + $val = 0; + } + elsif ( $d31 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_3' are the same", $lc); + $val = 0; + } + else { + $val = Angle($x1, $y1, $x2, $y2, $x3, $y3); + if ($val == -500) { + $val = 0; + } + else { + $val = D2R * $val; + } + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^area//i) { + chk_lparen("angledeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + $val = triangleArea($x1, $y1, $x2, $y2, $x3, $y3); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^asin//i) { + chk_lparen("asin"); + $val = expr(); + PrintFatalError("Can't take asin of $val", $lc) if $val < -1 || $val > 1; + $val = asin($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^acos//i) { + chk_lparen("acos"); + $val = expr(); + PrintFatalError("Can't take acos of $val", $lc) if $val < -1 || $val > 1 ; + $val = acos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^atan//i) { + chk_lparen("atan"); + $val = expr(); + $val = atan($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^cos//i) { + chk_lparen("cos"); + $val = expr(); + $val = cos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^directiondeg//i) { + chk_lparen("directiondeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $x3 = $x1+1; + if ( ($y2 - $y1) >= 0) { + $val = Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + } + else { + $val = 360 - Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^direction//i) { + chk_lparen("direction",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $x3 = $x1+1; + if ( ($y2 - $y1) >= 0) { + $val = Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + $val = D2R * $val; + } + else { + $val = 360 - Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + $val = D2R * $val; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^exp//i) { + chk_lparen("exp"); + $val = expr(); + $val = exp($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^int//i) { + chk_lparen("int"); + $val = expr(); + $val = int($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^log//i) { + chk_lparen("log"); + $val = expr(); + PrintFatalError("Can't take log of $val", $lc) if $val <= 0; + $val = log($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sin//i) { + chk_lparen("sin"); + $val = expr(); + $val = sin($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sgn//i) { + chk_lparen("sgn"); + $val = expr(); + if ($val > 0) { + $val = 1; + } + elsif ($val == 0) { + $val = 0; + } + else { + $val = -1; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sqrt//i) { + chk_lparen("sqrt"); + $val = expr(); + $val = sqrt($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^tan//i) { + chk_lparen("tan"); + $val = expr(); + $val = sin($val)/cos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^xcoord//i) { + chk_lparen("xcoord"); + my $point_name = get_point; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_name}); + $val = $x1; + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^ycoord//i) { + chk_lparen("ycoord"); + my $point_name = get_point; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_name}); + $val = $y1; + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^_pi_//i) { + $val = PI; + } + elsif (s/^_e_//i) { + $val = 2.71828182845905; + } + elsif (s/^_linethickness_//i) { + $val = $LineThickness / $xunits; + } + else { + my $err_code; + ($val,$err_code) = ComputeDist($lc); + } + s/\s*//; + return $val; + } + + sub memberOf { + my $elem = shift(@_); + + my $found = 0; + foreach $item (@_){ + if ($item eq $elem){ + $found = 1; + last; + } + } + return $found; + } + + sub tand { + my $d = $_[0]; + $d = $d * PI / 180; + return sin($d)/cos($d); + } + + sub get_string { + my $string = shift; + my $lc = shift; + + $string =~ s/^\s+//; + if ($string !~ s/^\"//) { + PrintErrorMessage("No starting \" found",$lc); + return (1,$string,$string); + } + my @ch = split //,$string; + my @cmd; + while (@ch and $ch[0] ne "\"") { + if ($ch[0] eq "\\" and (defined $ch[1]) and $ch[1] eq "\"") { + shift @ch; + push @cmd, $ch[0]; + shift @ch; + } + else { + push @cmd, $ch[0]; + shift @ch; + } + } + if (! defined $ch[0]) { + PrintErrorMessage("No closing \" found",$lc); + return (1,join("",@cmd), join("",@ch)) + } + else { + shift @ch; + return (0, join("",@cmd), join("",@ch)) + } + } + + sub is_tainted { + my $arg = shift; + my $nada = substr($arg,0,0); + local $@; + eval { eval "# $nada"}; + return length($@) != 0; + } + + sub noOfDigits { + my $num = $_[0]; + + if ($num =~ /^[\+-]?\d+(?!\.)/) { + return 0; + } + elsif ($num =~ /^[\+-]\d+\.(\d+)?/) { + return length($1); + } + } + + sub drawsquare { + my $s = $_[0]; + #$s *= sqrt(2); + $s = sprintf "%.5f", $s; + my $code = "\\setlength{\\unitlength}{$xunits}%\n"; + $code .= "\\begin{picture}($s,$s)\\put(0,0)" . + "{\\framebox($s,$s){}}\\end{picture}"; + return $code; + } + + sub X2sp { + my $LT = shift; + my $units = shift; + + if ($units eq "pc") { + return $LT * 786432; + } + elsif ($units eq "pt") { + return $LT * 65536; + } + elsif ($units eq "in") { + return $LT * 4736286.72; + } + elsif ($units eq "bp") { + return $LT * 65781.76; + } + elsif ($units eq "cm") { + return $LT * 1864679.811023622; + } + elsif ($units eq "mm") { + return $LT * 186467.981102362; + } + elsif ($units eq "dd") { + return $LT * 70124.086430424; + } + elsif ($units eq "cc") { + return $LT * 841489.037165082; + } + elsif ($units eq "sp") { + return $LT; + } + } + + + sub sp2X { + my $LT = shift; + my $units = shift; + + if ($units eq "pc") { + return $LT / 786432; + } + elsif ($units eq "pt") { + return $LT / 65536; + } + elsif ($units eq "in") { + return $LT / 4736286.72; + } + elsif ($units eq "bp") { + return $LT / 65781.76; + } + elsif ($units eq "cm") { + return $LT / 1864679.811023622; + } + elsif ($units eq "mm") { + return $LT / 186467.981102362; + } + elsif ($units eq "dd") { + return $LT / 70124.086430424; + } + elsif ($units eq "cc") { + return $LT / 841489.037165082; + } + elsif ($units eq "sp") { + return $LT; + } + } + + sub setLineThickness { + my $Xunits = shift; + my $LT = shift; + $Xunits =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//; + my $xlength = "$1"; + $Xunits =~ s/^\s*($units)//; + my $x_in_units = $1; + $LT =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//; + my $LTlength = "$1"; + $LT =~ s/^\s*($units)//; + my $LT_in_units = $1; + $LTlength = X2sp($LTlength,$LT_in_units); + $LTlength = sp2X($LTlength,$x_in_units); + return $LTlength; + } + + sub process_input { + my ($INFILE,$currInFile) = @_; + my $lc = 0; + my $no_output = 0; + $curr_in_file = $currInFile; + LINE: while(<$INFILE>) { + $lc++; + chomp($command = $_); + s/^\s+//; + if (/^beginSkip\s*/i) { + $no_output = 1; + print OUT "%%$_" if $comments_on; + next LINE; + } + elsif (/^endSkip\s*/i) { + if ($no_output == 0) { + PrintErrorMessage("endSkip without beginSkip",$lc); + } + else { + $no_output = 0; + } + print OUT "%%$_" if $comments_on and !$no_output; + next LINE; + } + elsif ($no_output == 1) { + next LINE; + } + else { + if (/^[^\\]/) { + my $out_line = mpp($command,$lc) unless /^\\/; #call macro pre-processor + $_ = "$out_line\n"; + } + + if (/^\s*%/) + { + print OUT "$_" if $comments_on; + } + elsif (s/^\s*(beginloop(?=\W))//i) { + s/\s+//; + my $times = expr($lc); + print OUT "%% BEGINLOOP $times\n" if $comments_on; + my @C = (); + REPEATCOMMS: while (<$INFILE>) { + if (/^\s*endloop/i) { + last REPEATCOMMS; + } + else { + push @C, $_; + } + } + if (! /^\s*endloop/i) { + PrintFatalError("unexpected end of file",$lc); + } + else { + s/^\s*endloop//i; + for(my $i=1; $i<=$times; $i++) { + tie *DUMMY, 'DummyFH', \@C; + process_input(DUMMY, $currInFile); + untie *DUMMY; + } + print OUT "%% ENDLOOP\n" if $comments_on; + } + } + elsif (s/^\s*(ArrowShape(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + + chk_lparen("$cmd",$lc); + if (s/^default//i) { + $arrowLength = 2; + $arrowLengthUnits = "mm"; + $arrowAngleB = 30; + $arrowAngleC = 40; + } + else { + my ($LocalArrowLength, $LocalArrowAngleB ,$LocalArrowAngleC) = (0,0,0); + $LocalArrowLength = expr($lc); + if (s/^\s*($units)//i) { + $arrowLengthUnits = "$1"; + } + else { + $xunits =~ /(\d+(\.\d+)?)\s*($units)/; + $LocalArrowLength *= $1; + $arrowLengthUnits = "$3"; + } + chk_comma($lc); + $LocalArrowAngleB = expr($lc); + chk_comma($lc); + $LocalArrowAngleC = expr($lc); + $arrowLength = ($LocalArrowLength == 0 ? 2 : $LocalArrowLength); + $arrowLengthUnits = ($LocalArrowLength == 0 ? "mm" : $arrowLengthUnits); + $arrowAngleB = ($LocalArrowAngleB == 0 ? 30 : $LocalArrowAngleB); + $arrowAngleC = ($LocalArrowAngleC == 0 ? 40 : $LocalArrowAngleC); + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + print OUT "%% arrowLength = $arrowLength$arrowLengthUnits, ", + "arrowAngleB = $arrowAngleB ", + "and arrowAngleC = $arrowAngleC\n" if $comments_on; + + } + elsif (s/^\s*(const(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + do{ + s/\s*//; + PrintErrorMessage("no identifier found after token const",$lc) + if $_ !~ s/^([^\W\d_]\d{0,3})//i; + my $Constname = $1; + my $constname = lc($Constname); + if (exists $ConstTable{$constname}) { + PrintErrorMessage("Redefinition of constant $constname",$lc); + } + s/\s*//; #remove leading white space + PrintErrorMessage("did not find expected = sign",$lc) + if $_ !~ s/^[=]//i; + my $val = expr($lc); + $VarTable{$constname} = $val; + $ConstTable{$constname} = 1; + print OUT "%% $Constname = $val\n" if $comments_on; + }while (s/^,//); + chk_comment($lc); + s/\s*//; + if (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } + + } + elsif (s/^\s*(dasharray(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen($cmd,$lc); + my @DashArray = (); + my $dash = ""; + my $dashpattern = ""; + PATTERN: while (1) { + $dash = sprintf("%.5f", expr($lc)); + if (s/^\s*($units)//i) { + push (@DashArray, "$dash$1"); + } + else { + PrintErrorMessage("Did not found unit after expression", $lc); + } + s/\s*//; + if (/^[^,]/) { + last PATTERN; + } + else { + s/^,\s*//; + } + } + print OUT "\\setdashpattern <"; + while (@DashArray) { + $dashpattern .= shift @DashArray; + $dashpattern .= ","; + } + $dashpattern =~ s/,$//; + print OUT $dashpattern, ">\n"; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + + } + elsif (s/^\s*(drawAngleArc(?=\W))//i or s/^\s*(drawAngleArrow(?=\W))//i ) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + + chk_lcb($cmd,$lc); + my ($P1, $P2, $P3); + if (s/^angle(?=\W)//i) { + chk_lparen("token angle of command $cmd",$lc); + $P1 = get_point($lc); + next LINE if $P1 eq "_undef_"; + $P2 = get_point($lc); + next LINE if $P2 eq "_undef_"; + $P3 = get_point($lc); + next LINE if $P3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + my $Angle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + if ($Angle <= 0) { + if ($Angle == 0) { + PrintErrorMessage("Angle is equal to zero",$lc); + next LINE; + } + elsif ($Angle < -400) { + PrintErrorMessage("Something is wrong with the points",$lc); + next LINE; + } + } + chk_rparen("angle part of command $cmd",$lc); + } + else { + PrintErrorMessage("Did not find expected angle part",$lc); + next LINE; + } + + s/^,\s*// or s/\s*//; #parse optional comma + + my $radius; + if (s/^radius(?=\W)//i) { + chk_lparen("token radius of command $cmd",$lc); + $radius = expr($lc); + chk_rparen("radius part of command $cmd",$lc); + } + else { + PrintErrorMessage("Did not found expected angle part",$lc); + next LINE; + } + + s/^,\s*// or s/\s*//; #parse optional comma + my $inout = ""; + if (s/^(internal(?=\W))//i or s/^(external(?=\W))//i) { + $inout = $1; + } + else { + PrintErrorMessage("Did not find expected 'internal' specifier", $lc); + next LINE; + } + s/^,\s*// or s/\s*//; #parse optional comma + my $direction = ""; + if (s/^(clockwise(?=\W))//i or s/^(anticlockwise(?=\W))//i) { + $direction = $1; + } + else { + PrintErrorMessage("Did not find expected 'direction' specifier", $lc); + next LINE; + } + chk_rcb("arguments of $cmd",$lc); + chk_comment($lc); + my $code; + if (lc($cmd) eq "drawanglearc") { + $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction); + } + else { + $code = drawAngleArrow($P1, $P2, $P3, $radius, $inout, $direction); + } + print OUT $code if $code ne ""; + + } + elsif (s/^\s*(drawArrow(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(0,$lc); + } + elsif (s/^\s*(drawcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen("drawcircle",$lc); + my $Point = get_point($lc); + next LINE if $Point eq "_undef_"; + chk_comma($lc); + my $R = expr($lc); + if ($R <= 0) { + PrintErrorMessage("Radius must be greater than zero",$lc); + next LINE; + } + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{lc($Point)}); + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $x+$R, $y, $x, $y; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + + } + elsif (s/^\s*(drawcurve(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(2,$lc); + } + elsif (s/^\s*(drawcircumcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen("drawcircumcircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + my ($xc, $yc,$r) = circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc); + next LINE if $xc == 0 and $yc == 0 and $r == 0; + print OUT "%% circumcircle center = ($xc,$yc), radius = $r\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$r, $yc, $xc, $yc; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + + } + elsif (s/^\s*(drawexcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen("drawexcircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) < 0.0001) { + PrintErrorMessage("Area of triangle is zero!",$lc); + next LINE; + } + chk_comma($lc); + my $point4 = get_point($lc); + if (!memberOf($point4, $point1, $point2, $point3)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + next LINE if $point4 eq "_undef_"; + my $point5 = get_point($lc); + next LINE if $point5 eq "_undef_"; + if (!memberOf($point5, $point1, $point2, $point3)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + if ($point4 eq $point5) { + PrintErrorMessage("Side points are identical",$lc); + next LINE; + } + chk_rparen("arguments of $cmd",$lc); + my ($xc, $yc, $r) = excircle($point1, $point2, $point3, + $point4, $point5); + my $R=$r; + if (s/^\s*\[\s*//) { + $R += expr($lc); + if ($R < 0.0001) { + PrintErrorMessage("Radius has become equal to zero!",$lc); + next LINE; + } + chk_rsb($lc); + } + if ($R > (500 / 2.845)) { + PrintErrorMessage("Radius is greater than 175mm!",$lc); + next LINE; + } + print OUT "%% excircle center = ($xc,$yc) radius = $R\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$R, $yc, $xc, $yc; + chk_comment($lc); + + } + elsif (s/^\s*(drawincircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen("drawincircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) < 0.0001) { + PrintErrorMessage("Area of triangle is zero!",$lc); + next LINE; + } + my ($xc, $yc, $r) = IncircleCenter($x1,$y1,$x2,$y2,$x3,$y3); + my $R=$r; + if (s/^\s*\[\s*//) { + $R += expr($lc); + if ($R < 0.0001) { + PrintErrorMessage("Radius has become equal to zero!",$lc); + next LINE; + } + chk_rsb($lc); + } + if ($R > (500 / 2.845)) { + PrintErrorMessage("Radius is greater than 175mm!",$lc); + next LINE; + } + print OUT "%% incircle center = ($xc,$yc) radius = $R\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$R, $yc, $xc, $yc; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + + } + elsif (s/^\s*(drawline(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(1,$lc); + } + elsif (s/^\s*(drawthickarrow(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n"; + print OUT "{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n"; + print OUT " \\global\\linethickness=0.31\\wd1}%\n"; + DrawLineOrArrow(0,$lc); + print OUT "\\setlength{\\linethickness}{0.4pt}%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + } + elsif (s/^\s*(drawthickline(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n"; + print OUT "{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n"; + print OUT " \\global\\linethickness=0.31\\wd1}%\n"; + DrawLineOrArrow(1,$lc); + print OUT "\\setlength{\\linethickness}{0.4pt}%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + } + elsif (s/^\s*(drawperpendicular(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + + chk_lparen($cmd,$lc); + my $A = get_point($lc); + next LINE if $A eq "_undef_"; + chk_comma($lc); + my $B = get_point($lc); + next LINE if $A eq "_undef_"; + s/\s*//; #ignore white space + my $C = get_point($lc); + next LINE if $A eq "_undef_"; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + # + #start actual computation + # + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$A}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$B}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$C}); + my ($xF, $yF) = perpendicular($x1, $y1, $x2, $y2, $x3, $y3); + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $x1, $y1, $xF, $yF; + + } + elsif (s/^\s*(drawpoint(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + my ($stacklen); + chk_lparen("$cmd",$lc); + if (/^\)/) { + PrintErrorMessage("There are no point to draw",$lc); + next LINE; + } + my(@PP); + DRAWPOINTS:while(1) { + if (s/^([^\W\d_]\d{0,3})//i) { #point name + $P = $1; + if (!exists($PointTable{lc($P)})) { + PrintErrorMessage("Undefined point $P",$lc); + next DRAWPOINTS; + } + else { + push (@PP,$P); + s/\s*//; + } + } + else { + last DRAWPOINTS; + } + } + drawpoints(@PP); + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + + } + elsif (s/^\s*(drawRightAngle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + + chk_lparen("drawRightAngle",lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + chk_comma($lc); + my $dist = expr($lc); + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + # + #actual computation + # + my $lengthAC = Length($x1, $y1, $x3, $y3); + my $angleBAC = Angle($x2, $y2, $x1, $y1, $x3, $y3); + my $line1 = $lengthAC / (1 + tand($angleBAC)); + # + # determine coordinates of point Q + # + my ($xQ, $yQ) = pointOnLine($x1, $y1, $x3, $y3, $line1); + # + # determine coordinates of point S + # + my $deltax = $xQ - $x2; + my $deltay = $yQ - $y2; + my $lengthBQ = sqrt($deltax * $deltax + $deltay * $deltay); + my $xS = $x2 + ($dist * sqrt(2) * $deltax / $lengthBQ); + my $yS = $y2 + ($dist * sqrt(2) * $deltay / $lengthBQ); + # + # determine coordinates of points S1 and S2 + # + my ($xS1, $yS1) = pointOnLine($x2, $y2, $x3, $y3, $dist); + ($xS2, $yS2) = ($xS, $yS); + # + # emit PiCTeX code + # + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $xS1, $yS1, $xS2, $yS2; + ($xS1, $yS1) = pointOnLine($x2, $y2, $x1, $y1, $dist); + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $xS1, $yS1, $xS2, $yS2; + + } + elsif (s/^\s*(drawsquare(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen("drawSquare",$lc); + my $p = get_point($lc); + chk_comma($lc); + my $side = expr($lc); + $side = $side - (1.1 * $LineThickness/$xunits); #Suggested by RWDN + my ($x,$y,$pSV,$pS) = unpack("d3A*",$PointTable{$p}); + printf OUT "\\put {%s} at %.5f %.5f %%drawsquare\n", drawsquare($side), $x, $y; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + + } + elsif (s/^\s*inputfile\*//i) + { + chk_lparen("inputfile*",$lc); + my $row_in = ""; + if (s/^((\w|-|\.)+)//) { + $row_in = $1; + } + else { + PrintErrorMessage("No input file name found",$lc); + next LINE; + } + if (!(-e $row_in)) { + PrintErrorMessage("File $row_in does not exist",$lc); + next LINE; + } + open(ROW, "$row_in")|| die "Can't open file $row_in\n"; + while (defined($in_line=<ROW>)) { print OUT $in_line; } + print OUT "%% ... end of input file <$row_in>\n"; + close ROW; + chk_rparen("input file name",$lc); + chk_comment($lc); + + + } + elsif (s/^\s*(inputfile(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + + chk_lparen("inputfile",$lc); + my $comm_in = ""; + if (s/^((\w|-|\.)+)//) { + $comm_in = $1; + } + else { + PrintErrorMessage("No input file name found",$lc); + next LINE; + } + if (!(-e $comm_in)) { + PrintErrorMessage("File $comm_in does not exist",$lc); + next LINE; + } + chk_rparen("input file name",$lc); + my $input_times = 1; #default value + if (s/^\[//) { + $input_times = expr($lc); + chk_rsb("optional argument",$lc); + } + print OUT "%% ... start of file <$comm_in> loop [$input_times]\n"; + for (my $i=0; $i<int($input_times); $i++) { + open(COMM,"$comm_in") or die "Can't open file $comm_in\n"; + print OUT "%%% Iteration number: ",$i+1,"\n"; + my $old_file_name = $curr_in_file; + process_input(COMM,"File $comm_in, "); + $curr_in_file = $old_file_name; + close COMM; + } + print OUT "%% ... end of file <$comm_in> loop [$input_times]\n"; + chk_comment($lc); + + } + elsif (s/^\s*(linethickness(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lparen("linethickness", $lc); + if (s/^default//i) { + print OUT "\\linethickness=0.4pt\\Linethickness{0.4pt}%%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + $LineThickness = setLineThickness($xunits,"0.4pt"); + } + else { + my $length = expr($lc); + if (s/^\s*($units)//i) { + my $units = $1; + printf OUT "\\linethickness=%.5f%s\\Linethickness{%.5f%s}%%\n", + $length, $units, $length, $units; + $LineThickness = setLineThickness($xunits,"$length$units"); + my $mag; + if ($units eq "pc") { + $mag = $length * 12; + } + elsif ($units eq "in") { + $mag = $length * 72.27; + } + elsif ($units eq "bp") { + $mag = $length * 1.00375; + } + elsif ($units eq "cm") { + $mag = $length * 28.45275; + } + elsif ($units eq "mm") { + $mag = $length * 2.845275; + } + elsif ($units eq "dd") { + $mag = $length * 1.07001; + } + elsif ($units eq "cc") { + $mag = $length * 0.08917; + } + elsif ($units eq "sp") { + $mag = $length * 0.000015259; + } + elsif ($units eq "pt") { + $mag = $length; + } + $mag = 10 * $mag / 1.00278219; + printf OUT "\\font\\CM=cmr10 at %.5fpt%%\n", $mag; + print OUT "\\setplotsymbol ({\\CM .})%\n"; + } + else { + PrintErrorMessage("Did not found expect units part",$lc); + } + } + chk_rparen("linethickness", $lc); + chk_comment($lc); + + + } + elsif (s/^\s*(paper(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + chk_lcb("paper", $lc); + if (s/^units(?=\W)//i) + { + + chk_lparen("units",$lc); + if(s/^\)//) + { + PrintWarningMessage("Missing value in \"units\"--default is 1pt", + $lc); + $xunits = "1pt"; + } + else { + $xunits = expr($lc); + s/\s*//; + if (s/^($units)//i) { + $xunits .= "$1"; + $LineThickness = setLineThickness($xunits,"0.4pt"); + } + elsif(s/^(\w)+//i) { + PrintErrorMessage("$1 is not a valid mathspic unit",$lc); + $xunits = "1pt"; + } + else { + PrintErrorMessage("No x-units found",$lc); + $xunits = "1pt"; + } + s/\s*//; #ignore white space + if (s/^,//) { # there is a comma so expect an y-units + s/\s*//; #ignore white space + $yunits = expr($lc); + s/\s*//; #ignore white space + if (s/^($units)//i) { + $yunits .= "$1"; + } + elsif(s/^(\w)+//i) { + PrintErrorMessage("$1 is not a valid mathspic unit",$lc); + $yunits = "1pt"; + } + else { + PrintErrorMessage("No y-units found",$lc); + $yunits = $xunits; + } + } + else { + $yunits = $xunits; + } + chk_rparen("units",$lc); + } + + $nounits = 0; + } + else + { + $nounits = 1; + } + s/^,\s*// or s/\s*//; + if (s/^xrange//i) + { + + chk_lparen("xrange",$lc); + my $ec; + ($xlow,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($xhigh,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + if ($xlow >= $xhigh) + { + PrintErrorMessage("xlow >= xhigh in xrange",$lc); + next LINE; + } + chk_rparen("$xhigh",$lc); + + $noxrange = 0; + } + else + { + $noxrange = 1; + } + s/^,\s*// or s/\s*//; + if (s/^yrange//i) + { + + chk_lparen("yrange",$lc); + my $ec; + ($ylow,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($yhigh,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + if ($ylow >= $yhigh) + { + PrintErrorMessage("ylow >= yhigh in yrange",$lc); + next LINE; + } + chk_rparen("$yhigh",$lc); + + $noyrange = 0; + } + else + { + $noyrange = 1; + } + + if (!$nounits) + { + printf OUT "\\setcoordinatesystem units <%s,%s>\n", + $xunits,$yunits; + } + if(!$noxrange && !$noyrange) + { + printf OUT "\\setplotarea x from %.5f to %.5f, y from %.5f to %.5f\n", + $xlow, $xhigh, $ylow, $yhigh; + + } + + s/^,\s*// or s/\s*//; + $axis = ""; + if (s/^ax[ei]s(?=\W)//i) + { + + chk_lparen("axis",$lc); + while(/^[^\)]/) + { + if (s/^([lrtbxy]{1}\*?)//i) + { + $axis .= $1; + } + elsif (s/^([^lrtbxy])//i) + { + PrintErrorMessage("Non-valid character \"$1\" in axis()",$lc); + } + s/\s*//; + } + chk_rparen("axis(arguments",$lc); + + } + $axis = uc($axis); + s/^,\s*// or s/\s*//; + if (s/^ticks(?=\W)//i) + { + chk_lparen("ticks",$lc); + my $ec; + ($xticks,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($yticks,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_rparen("ticks(arguments",$lc); + + } + else + { + $xticks = $yticks = 0; + } + chk_rcb("paper", $lc); + YBRANCH: { + if (index($axis, "Y")>-1) + { + if (index($axis, "Y*")>-1) + { + print OUT "\\axis left shiftedto x=0 / \n"; + last YBRANCH; + } + if ($yticks > 0) + { + if (index($axis, "T")>-1 && index($axis, "B")==-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT "$ylow to -$yticks by $yticks\n from $yticks to "; + print OUT $yhigh-$yticks," by $yticks /\n"; + } + elsif (index($axis, "T")==-1 && index($axis, "B")>-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT $ylow+$yticks," to -$yticks by $yticks\n from "; + print OUT "$yticks to $yhigh by $yticks /\n"; + } + elsif (index($axis, "T")>-1 && index($axis, "B")>-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT $ylow+$yticks," to -$yticks by $yticks\n from "; + print OUT "$yticks to ",$yhigh-$yticks," by $yticks /\n"; + } + else + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT "$ylow to -$yticks by $yticks\n from "; + print OUT "$yticks to $yhigh by $yticks /\n"; + } + } + else + { + print OUT "\\axis left shiftedto x=0 /\n"; + } + } + } + XBRANCH: { if (index($axis, "X")>-1) + { + if (index($axis, "X*")>-1) + { + print OUT "\\axis bottom shiftedto y=0 /\n"; + last XBRANCH; + } + if ($xticks > 0) + { + if (index($axis, "L")>-1 && index($axis, "R")==1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT $xlow + $xticks," to -$xticks by $xticks\n from"; + print OUT " $xticks to $xhigh by $xticks /\n"; + } + elsif (index($axis, "L")==-1 && index($axis, "R")>-1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT "$xlow to -$xticks by $xticks\n from "; + print OUT "$xticks to ",$xhigh-$xticks," by $xticks /\n"; + } + elsif (index($axis, "L")>-1 && index($axis, "R")>-1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT $xlow + $xticks," to -$xticks by $xticks\n from "; + print OUT "$xticks to ",$xhigh - $xticks," by $xticks /\n"; + } + else + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT "$xlow to -$xticks by $xticks\n from "; + print OUT "$xticks to $xhigh by $xticks /\n"; + } + } + else + { + print OUT "\\axis bottom shiftedto y=0 /\n"; + } + } } + LBRANCH: {if (index($axis, "L")>-1) + { + if (index($axis, "L")>-1) + { + if (index($axis, "L*")>-1) + { + print OUT "\\axis left /\n"; + last LBRANCH; + } + if ($yticks > 0) + { + print OUT "\\axis left ticks numbered from "; + print OUT "$ylow to $yhigh by $yticks /\n"; + } + else + { + print OUT "\\axis left /\n"; + } + } + } } + RBRANCH: { if (index($axis, "R")>-1) + { + if (index($axis, "R*")>-1) + { + print OUT "\\axis right /\n"; + last RBRANCH; + } + if ($yticks > 0) + { + print OUT "\\axis right ticks numbered from $ylow to $yhigh by "; + print OUT "$yticks /\n"; + } + else + { + print OUT "\\axis right /\n"; + } + } } + TBRANCH: { if (index($axis, "T")>-1) + { + if (index($axis, "T*")>-1) + { + print OUT "\\axis top /\n"; + last TBRANCH; + } + if ($xticks > 0) + { + print OUT "\\axis top ticks numbered from $xlow to $xhigh by "; + print OUT "$xticks /\n"; + } + else + { + print OUT "\\axis top /\n"; + } + } } + BBRANCH: { if (index($axis, "B")>-1) + { + if (index($axis, "B*")>-1) + { + print OUT "\\axis bottom /\n"; + last BBRANCH; + } + if ($xticks > 0) + { + print OUT "\\axis bottom ticks numbered from $xlow to $xhigh by "; + print OUT "$xticks /\n"; + } + else + { + print OUT "\\axis bottom /\n"; + } + } } + + + chk_comment($lc); + + } + elsif (s/^\s*(PointSymbol(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + + chk_lparen("$cmd",$lc); + if (s/^default//i) #default point symbol + { + $defaultsymbol = "\$\\bullet\$"; + } + elsif (s/^(circle|square)//i) { + $defaultsymbol = $1; + chk_lparen($defaultsymbol, $lc); + $GlobalDimOfPoints = expr($lc); + chk_rparen("expression", $lc); + } + elsif (s/^(((\\,){1}|(\\\)){1}|(\\\s){1}|[^\),\s])+)//) #arbitrary LaTeX point + { + $defaultsymbol = $1; + $defaultsymbol=~ s/\\\)/\)/g; + $defaultsymbol=~ s/\\,/,/g; + $defaultsymbol=~ s/\\ / /g; + } + else + { + PrintErrorMessage("unrecognized point symbol",$lc); + } + if (s/\s*,\s*//) { + $defaultLFradius = expr($lc); + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + + } + elsif (s/^\s*point(?=\W)//i) + { + my ($Point_Line); + chomp($Point_Line=$_); + my ($pointStar, $PointName, $origPN); + $pointStar = 0; # default value: he have a point command + $pointStar = 1 if s/^\*//; + chk_lparen("point" . (($pointStar)?"*":""),$lc); + if (s/^([^\W\d_](?![^\W\d_])\d{0,3})//i) { + # + # Note: the regular expression (foo)(?!bar) means that we are + # looking a foo not followed by a bar. Moreover, the regular + # expression [^\W\d_] means that we are looking for letter. + # + $origPN = $1; + $PointName = lc($1); + } + else { + PrintErrorMessage("Invalid point name",$lc); + next LINE; + } + #if ($pointStar and !exists($PointTable{$PointName})) { + # PrintWarningMessage("Point $origPN has not been defined",$lc); + #} + if (!$pointStar and exists($PointTable{$PointName})) { + PrintWarningMessage("Point $origPN has been used already",$lc); + } + chk_rparen("point" . (($pointStar)?"*":""). "($origPN",$lc); + chk_lcb("point" . (($pointStar)?"*":""). "($origPN)",$lc); + my ($Px, $Py); + if (s/^perpendicular(?=\W)//i) { + chk_lparen("perpendicular",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + chk_comma($lc); + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py) = perpendicular($x1,$y1,$x2,$y2,$x3,$y3); + + } + elsif (s/^intersection(?=\W)//i) { + chk_lparen("intersection",$lc); + my $FirstPoint = get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_comma($lc); + my $ThirdPoint = get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + my $ForthPoint = get_point($lc); + next LINE if $ForthPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + my ($x4,$y4,$pSV4,$pS4)=unpack("d3A*",$PointTable{$ForthPoint}); + ($Px, $Py) = intersection4points($x1,$y1,$x2,$y2,$x3,$y3,$x4,$y4); + + + } + elsif (s/^midpoint(?=\W)//i) { + chk_lparen("midpoint",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + $Px = $x1 + ($x2 - $x1)/2; + $Py = $y1 + ($y2 - $y1)/2; + + } + elsif (s/^pointonline(?=\W)//i) { + chk_lparen("pointonline",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_comma($lc); + # now get the distance + my $distance = expr($lc); + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + ($Px, $Py) = pointOnLine($x1,$y1,$x2,$y2,$distance); + + } + elsif (s/^circumcircleCenter(?=\W)//i) { + chk_lparen("circumCircleCenter",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py,$r) = &circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc); + next LINE if $Px == 0 and $Py == 0 and $r == 0; + + } + elsif (s/^IncircleCenter(?=\W)//i) { + chk_lparen("IncircleCenter",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py, $r) = IncircleCenter($x1,$y1,$x2,$y2,$x3,$y3); + + } + elsif (s/^ExcircleCenter(?=\W)//i) { + chk_lparen("ExcircleCenter",$lc); + my $PointA = get_point($lc); + next LINE if $PointA eq "_undef_"; + my $PointB = get_point($lc); + next LINE if $PointB eq "_undef_"; + my $PointC = get_point($lc); + next LINE if $PointC eq "_undef_"; + chk_comma($lc); + my $PointD = &get_point($lc); + next LINE if $PointD eq "_undef_"; + if (!memberOf($PointD, $PointA, $PointB, $PointC)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + my $PointE = get_point($lc); + next LINE if $PointE eq "_undef_"; + if (!memberOf($PointE, $PointA, $PointB, $PointC)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + if ($PointD eq $PointE) { + PrintErrorMessage("Side points are identical",$lc); + next LINE; + } + ($Px, $Py, $r) = excircle($PointA, $PointB, $PointC, + $PointD, $PointE); + chk_rparen("after coordinates part",$lc); + + } + elsif (/^[^\W\d_]\d{0,3}\s*[^,\w]/) { + m/^([^\W\d_]\d{0,3})\s*/i; + if (exists($PointTable{lc($1)})) { + my $Tcoord = get_point($lc); + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{$Tcoord}); + $Px = $x; + $Py = $y; + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + } + elsif (/[^\W\d_]\d{0,3}\s*,\s*shift|polar|rotate|vector/i) { #a point? + s/^([^\W\d_]\d{0,3})//i; + my $PointA = $1; + if (exists($PointTable{lc($PointA)})) { + s/\s*//; + if (s/^,//) { + s/\s*//; + if (s/^shift(?=\W)//i) { + + chk_lparen("shift",$lc); + my $dist1 = expr($lc); + chk_comma($lc); + my $dist2 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $x1 + $dist1; + $Py = $y1 + $dist2; + chk_rparen("shift part",$lc); + + } + elsif (s/^polar(?=\W)//i) { + chk_lparen("polar",$lc); + my ($R1, $Theta1); + $R1 = expr($lc); + chk_comma($lc); + $Theta1 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + s/\s*//; + if (s/^rad(?=\W)//i) { + # do nothing! + } + elsif (s/^deg(?=\W)//i) { + $Theta1 = $Theta1 * PI / 180; + } + else { + #$Theta1 = $Theta1 * PI / 180; + } + $Px = $x1 + $R1 * cos($Theta1); + $Py = $y1 + $R1 * sin($Theta1); + chk_rparen("after polar part",$lc); + + } + elsif (s/^rotate(?=\W)//i) { + chk_lparen("rotate",$lc); + my $Q = lc($PointA); + my $P = get_point($lc); + next LINE if $P eq "_undef_"; + chk_comma($lc); + my $Theta1 = expr($lc); + my ($xP,$yP,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P}); + my ($xQ,$yQ,$pSV2,$pS2)=unpack("d3A*",$PointTable{$Q}); + s/\s*//; + if (s/^rad(?=\W)//i) + { + # do nothing! + } + elsif (s/^deg(?=\W)//i) + { + $Theta1 = $Theta1 * PI / 180; + } + else + { + $Theta1 = $Theta1 * PI / 180; + } + # shift origin to P + $xQ -= $xP; + $yQ -= $yP; + # do the rotation + $Px = $xQ * cos($Theta1) - $yQ * sin($Theta1); + $Py = $xQ * sin($Theta1) + $yQ * cos($Theta1); + # return origin back to original origin + $Px += $xP; + $Py += $yP; + chk_rparen("after rotate part",$lc); + + } + elsif (s/^vector(?=\W)//i) { + chk_lparen("vector",$lc); + my ($x0,$y0,$pSV0,$pS0) = unpack("d3A*",$PointTable{lc($PointA)}); + my $P = get_point($lc); + my $Q = get_point($lc); + my ($x1,$y1,$pSV1,$pS1) = unpack("d3A*",$PointTable{$P}); + my ($x2,$y2,$pSV2,$pS2) = unpack("d3A*",$PointTable{$Q}); + $Px = $x0 + $x2 - $x1; + $Py = $y0 + $y2 - $y1; + chk_rparen("vector part",$lc); + + + } + else { + PrintErrorMessage("unexpected token",$lc); + next LINE; + } + } + else { + my ($xA,$yA,$pSVA,$pSA)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $xA; + $Py = $yA; + } + } + else { + PrintErrorMessage("Undefined point $PointA",$lc); + next LINE; + } + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + + chk_rcb("coordinates part",$lc); + my $sv = $defaultsymbol; + my $sh = $defaultLFradius; + my $side_or_radius = undef; + if (s/^\[\s*//) { # the user has opted to specify the optional part + if (/^(symbol|radius|side)\s*/i) { + my @previous_options = (); + my $number_of_options = 1; + my $symbol_set = 0; + while (s/^(symbol|radius)\s*//i and $number_of_options <= 2) { + my $option = lc($1); + if (s/^=\s*//) { + if (memberOf($option,@previous_options)) { + PrintErrorMessage("Option \"$option\" has been already defined", $lc); + my $dummy = expr($lc); + } + elsif ($option eq "radius") { + $sh = expr($lc); + $sv = $defaultsymbol if ! $symbol_set; + } + elsif ($option eq "symbol") { + if (s/^circle\s*//i) { + $sv = "circle"; + chk_lparen("after token circle",$lc); + $side_or_radius = expr($lc); + chk_rparen("expression",$lc); + } + elsif (s/^square\s*//i) { + $sv = "square"; + chk_lparen("after token square",$lc); + $side_or_radius = expr($lc); + chk_rparen("expression",$lc); + } + elsif (s/^(((\\\]){1}|(\\,){1}|(\\\s){1}|[^\],\s])+)//) { + $sv = $1; + $sv =~ s/\\\]/\]/g; + $sv =~ s/\\,/,/g; + $sv =~ s/\\ / /g; + s/\s*//; + } + $symbol_set = 1; + } + } + else { + PrintErrorMessage("unexpected token", $lc); + next LINE; + } + $number_of_options++; + push (@previous_options, $option); + s/^,\s*//; + } + } + else { + PrintErrorMessage("unexpected token", $lc); + next LINE; + } + + chk_rsb("optional part",$lc); + } + # to avoid truncation problems introduced by the pack function, we + # round each number up to five decimal digits + $Px = sprintf("%.5f", $Px); + $Py = sprintf("%.5f", $Py); + print OUT "%% point$Point_Line \t$origPN = ($Px, $Py)\n" if $comments_on; + chk_comment($lc); + $PointTable{$PointName} = pack("d3A*",$Px,$Py,$sh,$sv); + if (defined($side_or_radius)) { + $DimOfPoint{$PointName} = $side_or_radius; + } + + } + elsif (/^\s*setPointNumber(?=\W)/i) + { + PrintWarningMessage("Command setPointNumber is ignored",$lc); + next LINE; + } + elsif (s/^\s*(showAngle(?=\W))//i) + { + chk_lparen("showangle",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $angle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + $angle = 0 if $angle == -500; + printf OUT "%%%% angle(%s%s%s) = %.5f deg ( %.5f rad)\n", $point_1, + $point_2, $point_3, $angle, $angle*D2R; + chk_rparen("Missing right parenthesis", $lc); + + } + elsif (s/^\s*(showArea(?=\W))//i) + { + chk_lparen("showarea",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + print OUT "%% area($point_1$point_2$point_3) = ", + triangleArea($x1, $y1, $x2, $y2, $x3, $y3), "\n"; + chk_rparen("Missing right parenthesis", $lc); + + } + elsif (s/^\s*(showLength(?=\W))//i) + { + chk_lparen("showlength",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + print OUT "%% length($point_1$point_2) = ", + Length($x1, $y1, $x2, $y2), "\n"; + chk_rparen("Missing right parenthesis", $lc); + + + } + elsif (/^\s*showPoints(?=\W)/i) + { + print OUT "%%-------------------------------------------------\n"; + print OUT "%% L I S T O F P O I N T S \n"; + print OUT "%%-------------------------------------------------\n"; + foreach my $p (keys(%PointTable)) { + my ($x, $y, $pSV, $pS) = unpack("d3A*",$PointTable{$p}); + printf OUT "%%%%\t%s\t= ( %.5f, %.5f ), LF-radius = %.5f, symbol = %s\n", + $p, $x, $y, $pSV, $pS; + } + print OUT "%%-------------------------------------------------\n"; + print OUT "%% E N D O F L I S T O F P O I N T S \n"; + print OUT "%%-------------------------------------------------\n"; + next LINE; + } + elsif (/^\s*showVariables(?=\W)/i) + { + print OUT "%%-------------------------------------------------\n"; + print OUT "%% L I S T O F V A R I A B L E S \n"; + print OUT "%%-------------------------------------------------\n"; + foreach my $var (keys(%VarTable)) { + print OUT "%%\t", $var, "\t=\t", $VarTable{$var}, "\n"; + } + print OUT "%%-------------------------------------------------\n"; + print OUT "%% E N D O F L I S T O F V A R I A B L E S \n"; + print OUT "%%-------------------------------------------------\n"; + next LINE; + } + elsif (s/^\s*(system(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + + chk_lparen("$cmd",$lc); + my ($error, $command, $rest) = get_string($_); + next LINE if $error == 1; + $_ = $rest; + if (! is_tainted($command)) { + system($command); + } + else { + PrintErrorMessage("String \"$command\" has tainted data", $lc); + next LINE; + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + + } + elsif (s/^\s*(text(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + + chk_lparen("text",$lc); + my ($level,$text)=(1,""); + TEXTLOOP: while (1) + { + $level++ if /^\(/; + $level-- if /^\)/; + s/^(.)//; + last TEXTLOOP if $level==0; + $text .= $1; + } + chk_lcb("text part",$lc); + my ($Px, $Py,$dummy,$pos); + $pos=""; + s/\s*//; + + if (/^[^\W\d_]\d{0,3}\s*[^,\w]/) { + my $Tcoord = get_point($lc); + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{$Tcoord}); + $Px = $x; + $Py = $y; + } + elsif (/[^\W\d_]\d{0,3}\s*,\s*shift|polar/i) { + s/^([^\W\d_]\d{0,3})//i; + my $PointA = $1; + if (exists($PointTable{lc($PointA)})) { + s/\s*//; + if (s/^,//) { + s/\s*//; + if (s/^shift(?=\W)//i) { + + chk_lparen("shift",$lc); + my $dist1 = expr($lc); + chk_comma($lc); + my $dist2 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $x1 + $dist1; + $Py = $y1 + $dist2; + chk_rparen("shift part",$lc); + + } + elsif (s/^polar(?=\W)//i) { + chk_lparen("polar",$lc); + my ($R1, $Theta1); + $R1 = expr($lc); + chk_comma($lc); + $Theta1 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + s/\s*//; + if (s/^rad(?=\W)//i) { + # do nothing! + } + elsif (s/^deg(?=\W)//i) { + $Theta1 = $Theta1 * PI / 180; + } + else { + #$Theta1 = $Theta1 * PI / 180; + } + $Px = $x1 + $R1 * cos($Theta1); + $Py = $y1 + $R1 * sin($Theta1); + chk_rparen("after polar part",$lc); + + } + } + } + else { + PrintErrorMessage("undefined point/var",$lc); + next LINE; + } + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + + chk_rcb("coordinates part of text command",$lc); + if (s/^\[//) + { + s/\s*//; + + if (s/^(\w{1})\s*//) { + $pos .= $1; + if (memberOf($pos, "l", "r")) { + if (s/^(\w{1})\s*//) { + my $np = $1; + if (memberOf($np, "t", "b", "B")) { + $pos .= $np; + } + else { + if (memberOf($np, "l", "r")) { + PrintErrorMessage("$np can't follow 'l' or 'r'", $lc); + } + else { + PrintErrorMessage("$np is not a valid positioning option", $lc); + } + next LINE; + } + } + } + elsif (memberOf($pos, "t", "b", "B")) { + if (s/^(\w{1})\s*//) { + my $np = $1; + if (memberOf($np, "l", "r")) { + $pos .= $np; + } + else { + if (memberOf($np, "t", "b", "B")) { + PrintErrorMessage("$np can't follow 't', 'b', or 'B'", $lc); + } + else { + PrintErrorMessage("$np is not a valid positioning option", $lc); + } + next LINE; + } + } + } + else { + PrintErrorMessage("$pos is not a valid positioning option", $lc); + next LINE; + } + } + else { + PrintErrorMessage("illegal token in optional part of text command",$lc); + next LINE; + } + + s/\s*//; + chk_rsb("optional part of text command",$lc); + } + chk_comment($lc); + if ($pos eq "") + { + printf OUT "\\put {%s} at %f %f\n", $text, $Px, $Py; + } + else + { + printf OUT "\\put {%s} [%s] at %f %f\n", $text, $pos, $Px, $Py; + } + + } + elsif (s/^\s*(var(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + do{ + s/\s*//; + PrintErrorMessage("no identifier found after token var",$lc) + if $_ !~ s/^([^\W\d_]\d{0,3})//i; + my $Varname = $1; + my $varname = lc($Varname); + if (exists $ConstTable{$varname}) { + PrintErrorMessage("Redefinition of constant $varname",$lc); + } + s/\s*//; #remove leading white space + PrintErrorMessage("did not find expected = sign",$lc) + if $_ !~ s/^[=]//i; + my $val = expr($lc); + $VarTable{$varname} = $val; + print OUT "%% $Varname = $val\n" if $comments_on; + }while (s/^,//); + chk_comment($lc); + s/\s*//; + if (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } + } + elsif (/^\s*\\(.+)/) + { + my $line = $1; + if ($line =~ /^\s+(.+)/) + { + print OUT " $line\n"; + } + else + { + print OUT "\\$line\n"; + } + next LINE; + } + elsif (0==length) #empty line + { + next LINE; + } + else { + PrintErrorMessage("command not recognized",$lc); + next LINE; + } + + } + } + } + + +our $alarm=""; +our $comments_on=1; +our $out_file="default"; +our $argc=@ARGV; +if ($argc == 0 || $argc > 5 ){ # no command line arguments or more than 4 + # arguments + die "\nmathspic version $version_number\n" . + "Usage: mathspic [-h] [-b] [-c] [-o <out file>] <in file>\n\n"; +} +else { + our $file = ""; + SWITCHES: + while($_ = $ARGV[0]) { + shift; + if (/^-h$/) { + die "\nThis is mathspic version $version_number\n" . + "Type \"man mathspic\" for detailed help\n". + "Usage:\tmathspic [-h] [-b] [-c] [-o <out file>] <in file>\n" . + "\twhere,\n" . + "\t[-b]\tenables bell sound if error exists\n" . + "\t[-c]\tdisables comments in ouput file\n" . + "\t[-h]\tgives this help listing\n" . + "\t[-o]\tcreates specified output file\n\n"; + } + elsif (/^-b$/) { + $alarm = chr(7); + } + elsif (/^-c$/) { + $comments_on = 0; + } + elsif (/^-o$/) { + die "No output file specified!\n" if !@ARGV; + $out_file = $ARGV[0]; + shift; + } + elsif (/^-\w+/) { + die "$_: Illegal command line switch!\n"; + } + else { + $file = $_; + } + } + die "No input file specified!\n" if $file eq ""; + + print "This is mathspic version $version_number\n"; +} + our ($source_file, $log_file); + if (! -e $file) { + die "$file: no such file!\n" if (! (-e "$file.m")); + $source_file = "$file.m"; + } + else { + $source_file = $file; + $file = $1 if $file =~ /(\w[\w-\.]+)\.\w+/; + } + $out_file= "$file.mt" if $out_file eq "default"; + $log_file= "$file.mlg"; + + + open(IN,"$source_file")||die "Can't open source file: $source_file\n"; + open(OUT,">$out_file")||die "Can't open output file: $out_file\n"; + open(LOG,">$log_file")||die "Can't open log file: $log_file\n"; + print_headers; + process_input(IN,""); + +print $alarm if $no_errors > 0; +__END__ + diff --git a/Master/texmf-dist/doc/latex/mathspic/mathsPICa4.pdf b/Master/texmf-dist/doc/latex/mathspic/mathsPICa4.pdf Binary files differnew file mode 100644 index 00000000000..20224849f6f --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/mathsPICa4.pdf diff --git a/Master/texmf-dist/doc/latex/mathspic/mathsPICa5.pdf b/Master/texmf-dist/doc/latex/mathspic/mathsPICa5.pdf Binary files differnew file mode 100644 index 00000000000..88aa80de721 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/mathsPICa5.pdf diff --git a/Master/texmf-dist/doc/latex/mathspic/mathspic.1 b/Master/texmf-dist/doc/latex/mathspic/mathspic.1 new file mode 100644 index 00000000000..a0f9a70fd5b --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/mathspic.1 @@ -0,0 +1,590 @@ +.\" copyright (c) 2005 A Syropoulos and RWD Nickalls +.\" mathspic.1 +.\" place this file in: /usr/share/man/man1/ +.. +.TH mathsPIC 1 "February 2nd, 2005" "mathsPIC perl version" +.SH NAME +.B mathsPIC +.SH AUTHORS +A. Syropoulos and R.W.D. Nickalls (February 2005) + + apostolo[at]<ocean1><ee><duth><gr> + dicknickalls[at]<compuserve><com> + +.SH DESCRIPTION +.B mathsPIC +is a Perl filter program for PiCTeX. mathsPIC has its own macro and macro library capability, and allows use of mathsPIC, PiCTeX, TeX and LaTeX commands. A significant feature of mathsPIC is that it allows access to the command-line, and so allows the user to extend mathsPIC commands by calling Perl and other programs written to perform particular drawing actions. See the package manual for full details and examples. The latest version can be downloaded from +.PP +CTAN: tex-archive/graphics/pictex/mathspic/perl +.PP +Commands which can be used in the mathsPIC script file fall into four main groups (a) mathsPIC macro commands (prefixed with %def), (b) regular mathsPIC commands (do not have a backslash), (c) regular PiCTeX commands (all have a backslash), and (d) regular TeX and LaTeX commands (all have a backslash). +.PP +The following mathematics functions can used (note that decimal fractions having an absolute value less than 1 must have a leading zero). Note also that all the trignometric functions require their argument in radians. + +Trigonometric: sin(), cos(), tan(), asin(), acos(), atan() + +Remainder: rem(); eg var r=12 rem(5) + +Integer: int(); eg var r= int(3.87) --> 3 + +Sign (returns -1, 0, +1): sgn(); eg var s=sgn(-3.27) --> -1 + +Square root: sqrt(); eg var s = sqrt(14) + +Exponentiation: **; eg var j = r**2 + +Pi constant (3.14159...): _Pi_ and _pi_ + +e constant (2.71828...): _E_ and _e_ + +Linethickness: _linethickness_ ; eg var t = _linethickness_ + +.SH COMMAND-LINE USE +perl mathspic.pl [-b] [-c] [-h] [-o <outfile>] <infile> + +.B -b +enables beep if mathsPIC detects an error + +.B -c +disables the writing of comments to output file + +.B -h +displays the help file + +.B -o +defines the output file name +.SH MACRO COMMANDS +macro definition commands are prefixed with %def and can take either 0, 1, or more parameters. Macros will generally be used as part of a +.B var +command as shown below. Macros are deleted using the +.B %undef +command. + + -----syntax: + %def MACRONAME(parameters)<macrodefinition> + %undef MACRONAME(parameters) + + -----notes: + Notes: (a) the () must be used in the definition even if no parameters are used, (b) the name can be any combination of upper and lower case characters and numbers, (c) when the macro is used in a command it is prefixed by a & symbol, (d) it is a good idea to always place a % symbol at the end of the definition, (e) comments (prefixed by a % symbol) can be placed after the macro definition just as in TeX or LaTeX. + + -----examples: + %def d2r()_pi_/180% % degrees2radians + %def AreaOfRectangle(x,y)x*y% % width x, length y + %undef d2r() % delete the macro + + -----use: + var j2= 6*(&d2r(45) + 23) + var a3 = 3*&AreaOfRectangle(5,7) +.SH GENERAL COMMANDS + +.P +.B NUMERICAL EXPRESSIONS + When dealing with commands we will refer frequently to the term `numerical expression' by which is meant either (a) a number (integer or decimal), (b) a numeric variable or constant (defined using the var or const command), (c) any mathsPIC function, macro, or mathematical expression which evaluates to a number, or (d) a pair of point names (e.g. AB) representing the Pythagorean distance between the two points. A leading zero must be used with decimal fractions less than one. + + In general, if a command's argument accepts a number then it will also accept a `numerical expression' (<expr>) as defined above. Sometimes a following <unit> is associated with the number or numerical expression, in which case the number or numerical expression can be delimited by a round bracket (or separated from the unit by a <space>), as shown in the following examples. + + -----examples: + ArrowShape(3mm, 20,40) + var h=4 + ArrowShape(h mm, 20, 40) + ArrowShape((2*h)mm,20,40) + +.P +.B BACKSLASH +\\ + A leading backslash without a following space indicates that it is part of a PiCTeX, TeX or LaTeX command, in which case mathsPIC simply copies the whole line verbatim into the output file. A leading backslash followed by one or more spaces makes mathsPIC copy the whole line verbatim into the output file but without the backslash. + +.P +.B USING THE COLOR PACKAGE + The standard COLOR package can be used with mathsPIC, but note that it is important to load the COLOR package after the mathsPIC package. + + It is best to place a comment symbol % at the end of LaTeX and TeX commands to limit white space at the end. + + In order to prevent color commands in a diagram from influencing any following text (in the document) we recommend that the \\normalcolor command is used as a delimiter within the \\beginpicture...\\endpicture environment as shown in the example below. i.e. use two \\normalcolor commands; one just after the \\beginpicture command, and one just before the \\endpicture command. + + -----example: + \\usepackage{mathspic, color} + ... + \\beginpicture + \\normalcolor + ... + \\color{red}% + drawline{AB} + \\color{blue}% + drawcircle(C,5) + ... + \\normalcolor + \\endpicture + +============================== + +.B ARROWSHAPE + This command defines the shape of an arrowhead, and allows +different arrowheads to be customised. + +The default arrow shape is equivalent to the Arrowshape(2mm,30,40) command. +This default arrowhead shape can be reset using the Arrowshape(default) command, as shown in the following example. + + -----syntax: + arrowshape(<length>[units], <angledeg>, <angledeg>) + + -----examples: + Arrowshape(4mm,30,60) + drawArrow(AB) + Arrowshape(default) + +============================== + +.B beginLOOP...endLOOP + This is an environment which cycles a block of code a specified number of times. + + -----syntax: + beginLoop <expr> + ... + endLoop + + -----notes: + The block of code which lies within the environment is input <expr> times. + + -----example: + beginLoop 5 + ... + endLoop + + +============================== + +.B beginSKIP...endSKIP + This is an `environment' within which commands are not actioned. It is useful in development for testing isolated commands and excluding other commands. + +============================== + +.B CONST + The const command is used to define scalar constants. Note that a constant-name must begin with a single letter (either upper or lower case), and may have up to a maximum of three following digits. Note that constants, variables and points have the same name structure, and a constant could have the same name as a point (and so we suggest points have uppercase letters and variables and constants have lowercase letters). The scalar argument can be any numeric expression. New values cannot be re-allocated to existing constant-names. If this occurs mathsPIC will issue an error message. + + -----syntax: + const name = <expr> + + -----examples: + const r = 20, r4 = r3*tan(0.3) + +============================== + +.B DashArray + The dasharray command takes an arbitrary number of paired arguments that are used to specify a dash pattern. + + -----syntax + dasharray(d1 , g1 , d2 , g2 , ... ) + + -----notes + The ds denotes the length of a dash and the gs denotes the length of the gap between two consecutive dashes. There must be an even number of arguments. If a variable or expression is used then it should be separated from the unit either by a <space> or with round brackets ( ) as shown below. + + -----example + dasharray(6pt, 2pt, 1pt, 2pt) + var d=2 + dasharray(6pt, 2pt, 1pt, d pt) + dasharray(6pt, 2pt, 1pt, (d)pt) + dasharray(6pt, 2pt, 1pt, (3*d)pt) + +============================== + +.B DrawAngleArc + This command draws an arc in the specified angle, a distance <radius> from the angle. The angle is either <internal> (less than 180 deg) or <external> (greater than 180 deg). The direction of the arc is either <clockwise> or <anticlockwise>, and this direction must correspond with the letter sequence specified for the angle. +Strange and unexpected results will be produced if the four parameters are not internally consistent. The option order angle/radius/internal/clockwise is important. The <radius> parameter can be any numerical expression. + + -----syntax: + DrawAngleArc{angle(), radius(), external, clockwise} + + -----example: + DrawAngleArc{angle(ABC), radius(3), external, clockwise} + var r=3 + DrawAngleArc{angle(ABC), radius(r), external, clockwise} + +============================== + +.B DrawAngleArrow + This command draws a curved arrow in the specified angle, a distance <radius> from the angle. The angle is either <internal> (less than 180 deg) or <external> (greater than 180 deg). The direction of the arrow is either <clockwise> or <anticlockwise>, and this direction must correspond with the letter sequence specified for the angle. +Strange and unexpected results will be produced if the four parameters are not internally consistent. The option order angle/radius/internal/clockwise is important. The <radius> parameter can be any numerical expression. + + -----syntax: + DrawAngleArrow{angle(), radius(), external, clockwise} + + -----example: + DrawAngleArrow{angle(ABC), radius(3), external, clockwise} + var r=3 + DrawAngleArrow{angle(ABC), radius(r), external, clockwise} + +============================== + +.B DrawArrow + This command draws an arrow(s) joining two points. The direction of the arrow is in the point order specified. + + -----syntax: + drawArrow(<line> [,<line>] ... ) + + -----notes: + The length option can only refer to one arrow + + -----example: + drawArrow(AB) + drawArrow(FG, HJ) + +============================== + +.B DrawCircle + This command draws a circle defined by its radius and the point-name of its centre. The <radius> can be any numerical expression. If the units of the X and Y axes are different, circles may be drawn strangely, and mathsPIC therefore generates a warning message to this effect. + + -----syntax: + DrawCircle(<center>, <radius>) + + -----examples: + drawCircle(C2,5) + drawCircle(C2,r2) + drawCircle(C2,r2/tan(1.3)) + drawCircle(C2,AB) + +============================== + +.B DrawCircumcircle + This command draws the circumcircle of a triangle. + + -----syntax: + DrawCircumcircle(<triangle>) + + -----example: + drawCircumcircle(ABC) + +============================== + +.B DrawCurve + This command draws a smooth quadratic curve through three points in the point order specified. Note that curves drawn using this command do not break to avoid line-free zones associated with the points. + + -----syntax: + DrawCurve(<point><point><point>) + + -----example: + drawCurve(ABC) + +============================== + +.B DrawExcircle + This command draws the excircle touching one side of a triangle. + + -----syntax: + DrawExcircle(<triangle>, <side>) + + -----example: + drawExcircle(ABC, BC) + +============================== + +.B DrawIncircle + This command draws the incircle of a triangle. + + -----syntax: + DrawIncircle(<triangle>) + + -----example: + drawIncircle(ABC) + +============================== + +.B DrawLine + This command draws a line joining two or more points. Use the Linethickness command to vary thickness. + + -----syntax: + DrawLine( <points> [, <points>] ) + + -----notes: + <points> is any sequence of two or more point names. + <expr> is any numerical expression. + Lines are drawn in the order specified. + Lines are separated by a comma. + + -----examples: + drawline(AB) + drawline(BCDE) + drawline(FG, HJK, PQRST) + +============================== + +.B DrawPerpendicular + This command draws the perpendicular from a point to a line. + + -----syntax: + DrawPerpendicular(<point>, <line) + + -----example: + drawPerpendicular(P,AB) + +============================== + +.B DrawPoint + This command draws the point-symbol at the point-location. Commas must not be used to separate point names. The default point-symbol is \$\\bullet\$, unless an optional point-symbol (or string of characters) is specified in the associated point command. + + -----syntax: + DrawPoint(<point> [<point> ..]) + + -----examples: + drawpoint(T4) + drawpoint(ABCDEF) + drawpoint(P1 P2 P3 P4) + +============================== + +.B DrawRightangle + This command draws the standard right-angle symbol in the internal angle specified at the size specified by <expr>. + + -----syntax: + DrawRightangle(<angle>, <expr>) + + -----notes: + The <expr> can be any numerical expression. + + -----example: + drawRightangle(ABC,3) + drawRightangle(ABC,PQ) + var d=5 + drawRightangle(ABC,d) + +============================== + +.B DrawSquare + This command draws a square defined by its side and the point-name of its centre. The <sidelength> can be any numerical expression. + + -----syntax: + DrawSquare(<centerpoint>, <sidelength>) + + -----examples: + drawSquare(P,5) + var s2=3, j=2 + drawSquare(P,s2) + drawSquare(P, s2*4/(3*j)) + drawSquare(P,AB) + +============================== + +.B DrawThickArrow + This command draws a thick arrow(s) joining two points. The direction of the arrow is in the point order specified. The shape of the arrowhead is controlled by the ArrowShape command. + + -----syntax: + drawThickArrow(<line> [,<line>,...]) + + -----examples: + drawThickarrow(BC) + drawThickarrow(PQ, RS) + +============================== + +.B DrawThickLine + This command draws a thick line(s) joining two points. The direction of the line is in the point order specified. Use the Linethickness command to vary thickness of a line. + + -----syntax: + drawThickLine(<line> [,<line>,...]) + + -----examples: + drawThickline(BC) + drawThickline(PQ, RS) + +============================== + +.B InputFile + This command inputs a plain text file containing mathsPIC commands. Optionally, the file can be input several times, in which case this command functions like a DO--LOOP. +The <loopnumber> can be any numerical expression. If the <loopnumber> is not an integer then mathsPIC will round the value down to the nearest integer. + + -----syntax: + inputFile[*](<filename>)[<loopnumber>] + + -----notes: + The inputfile* command is used to input a file in verbatim, i.e. a file with no mathsPIC commands, for example, a file containing only PiCTeX commands or data-points +for plotting etc. Note that the inputfile* command has no <loopnumber> option. + + -----examples: + inputFile(myfile.dat)[4] + inputFile*(mycurvedata.dat) + +============================== + +.B LineThickness + This command sets a particular linethickness. The command linethickness(default) restores the working linethickness to the default value of 0.4pt. +The current value of the linethickness (in current units) can be accessed using the var command (this can be useful when drawing figures using thick lines) . + + -----syntax: + LineThickness(<expr><units>) + LineThickness(default) + var t = _linethickness_ + + -----notes: + This command also sets the font to \verb!cmr! and plotsymbol to \\CM . and also sets the rule thickness for drawing horizontal and vertical lines. It is important to include a leading zero with decimal fractions less than one. + + -----examples: + linethickness(2pt) + var t=3 + linethickness((t)pt) + lineThickness((2*t)pt) + linethickness(default) + var t = _linethickness_ + + -----caution: + Note that there is a similar PiCTeX command with the same name (but with a different syntax). + +============================== + +.B PAPER + Defines the plotting area in terms of the options units(), xrange(), yrange(), axes(), and ticks(). The units() argument must contain a numeric value and a valid TeX length unit mm, cm, pt, pc(pica), in(inch), bp(big point), dd(didot), cc(cicero), sp(scaled point). The X and Y axes can have different units (see second example below). The axes() arguments XYTBLR refer to the X and Y axes, and the Top, Bottom, Left and Right axes. A * following one of the axes disables ticks on that axis. The X and Y axes pass through the zeros. + + -----examples: + paper{units(1cm),xrange(0,10),yrange(0,10)} + paper{units(2cm,1cm),xrange(0,10),yrange(0,10),axes(LB)} + paper{units(1mm),xrange(0,100),yrange(0,100),axes(XY)} + paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRTBXY),ticks(1,1)} + paper{units(1cm),xrange(-5,5),yrange(-5,5),axes(LRT*B*)} + +============================== + +.B POINT + Defines a new point by allocating coordinates to a new point name. The * option re-allocates coordinates to an existing point name. + + -----syntax: + POINT[*](<name>){<point>}[symbol=<chars>, radius=<expr>] + POINT[*](<name>){<location>}[symbol=<chars>, radius=<expr>] + + -----notes: + <name> one leading letter plus maximum of three trailing digits + <chars> any TeX string allowed in an \\hbox{} + <expr> any numerical expression + The polar(r,theta) option defaults to radians for the angle theta. To work in degrees then must append <deg> eg: polar(r,theta deg). Can use <direction()> and <directiondeg()> to replace theta. + + -----examples: + point(A){5,5} + point(B2){22,46}[symbol=$\\odot$] + point(B2){22,46}[symbol=circle(2),radius=5] + var r=3 + point(B2){22,46}[symbol=square(3),radius=r] + point(B123){22,46}[radius=5] + point(D2){B2, shift(5,5)} + var s = 3 + point(D2){B2, shift(2*s,4*s)} + point(D3){D2, polar(6,32 deg)} + point(D4){D2, polar(6,1.2 rad)} + point(D4){D2, polar(6, direction(AB))} %% radians by default + point(D4){D2, polar(6, directiondeg(AB) deg)} + point(G2){Q, rotate(P, 23 deg)} + point(G2){Q, vector(AB)} + point(D2){intersection(AB,CD)} + point(F){PointOnLine(AB,5.3)} + point(G){perpendicular(P,AB)} + point(H){circumcircleCenter(ABC)} + point(J){incircleCenter(ABC)} + point(K){excircleCenter(ABC,BC)} + point*(A){6,3} + point*(P){Q} + point*(B){B, shift(5,0)} + point*(P){xcoord(J),ycoord(K)} + +============================== + +.B PointSymbol + This command allows the default point-symbol \\bullet (with zero line-free radius) to be changed. The PointSymbol command is particularly useful where a set of points uses the same point-symbol, for example, when drawing graphs. The point-symbol can be reset to the default \\bullet using the command PointSymbol(default). + + -----syntax: + PointSymbol(<symbol>, <line-free-radius>) + PointSymbol(default) + + -----notes: + The PointSymbol command only influences subsequent point commands. + The optional square bracket of the point command overrides the PointSymbol command. + + -----examples: + PointSymbol($\\odot$, 0.7) + PointSymbol(default) + +============================== + +.B SYSTEM + This command allows the user to access the command line and execute standard Linux commands. A important use for this command is to run a Perl program. + + -----syntax: + System("<command>") + + -----notes: + The <command> string must be in inverted commas. + + -----example: + system("dir > mydir-listing.txt") + system("perl myperlprogram.pl") + +============================== + +.B SHOW.... + This command makes mathsPIC return the value of a calculation or specified parameter; for example, the value of a particular angle, or the length of a line. The result is shown in the output-file as a commented line. This allows mathsPIC commands to be adjusted in the light of calculations. There are currently five such commands as follows. + + -----syntax: + showLength(AB) + showAngle(ABC) % returns angle in radians + showAngledeg(ABC) % returns angle in degrees + showArea(ABC) + showPoints + showVariables + +============================== + +.B TEXT + This command places a text-string at a specific location. By default the text is centered vertically and horizontally at the specified point. Optionally, text can be placed relative to a point using appropriate combinations of the PiCTeX `position' options l t r B b to align the (l)eft edge, (r)ight edge, (t)op edge, (B)aseline, (b)ottom edge respectively of the text box with the point-location. + + Remember that the default units for the angle argument of the polar() expression is radians; hence you MUST append `deg' if you want to work in degrees + + -----syntax: + text(<string>){<location>}[<position options>] + text(<string>){<pointname>, shift(<x>,<y>)}[] + text(<string>){<pointname>, polar(<r>,<angle>[rad])}[] + + -----examples: + text(A){5,6} + text($A_1$){A1, shift(2, 2)} + text(Z2){Z2, shift(5, -5)}[tr] + text(Z3){Z2, polar(5, 20 deg)}[Br] + text(Z4){Z2, polar(5, 1.34 rad)} + text(\framebox{Z5}){Z5} + +============================== + +.B VAR + The var command is used to define scalar variables. It can be any numerical expression. A variable-name must begin with a single letter (either upper or lower case), and may have up to a maximum of three following digits. If a more detailed variable name is required, then a simple alternative is to use a mathsPIC macro---as any string can be allocated via macros (see the beginning of this chapter for details on macros). + + Note that variables, constants and points have the same name structure, and a variable can have the same name as a point (and so we suggest points have uppercase letters and variables and constants have lowercase letters). New values can be re-allocated to existing variable-names; however, when this occurs then mathsPIC does not issue a warning message to hightlight this fact. + + If it is important to be warned if a potential variable is accidentally reallocated then one should consider using the const command instead (since mathsPIC does generate an error message if a constant is reallocated). + + -----syntax: + var <name> = <expr> + + -----notes: + In addition to the mathematical functions mathsPIC functions which can be used with the var command are: + + angle(<three-points>) % returns angle in radians + angledeg(<three-points>) % returns angle in degrees + area(<three-points>) + xcoord(<point>) + ycoord(<point>) + direction(<two-points>) % returns angular direction in radians + directiondeg(<two-points>) % returns angular direction in degrees + + -----examples: + var r = 20, r4 = r3*tan(0.3), j = (r*2e3)**2, r5 = AB + var e = _e_, p1 = _Pi_ + var t = _linethickness_ % returns linethickness in current units + var g137 = angle(ABC) %(default: returns in radians) + var g = angledeg(ABC) % angle in degrees + var h = area(ABC) + var x2 = xcoord(A), y2 = ycoord(A) + var m5 = 12 rem 3 % remainder after dividing by 3 + var r1 = direction(PQ) % in radians + var d1 = directiondeg(PQ) + +============================== +.SH SEE ALSO +The mathsPIC package manual and examples +.SH BUGS +Please report bugs to Dick Nickalls (see manual for address) + diff --git a/Master/texmf-dist/doc/latex/mathspic/mathspic.lib b/Master/texmf-dist/doc/latex/mathspic/mathspic.lib new file mode 100644 index 00000000000..0cf4368bd8c --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/mathspic.lib @@ -0,0 +1,11 @@ +%%--- mathspic.lib--- +%% February 2005 +%% example mathsPIC macros +%def bigdots()\setplotsymbol({\large .})\setdots% +%def normaldots()\setplotsymbol({\tiny .})\setdots% +%def log10(a)log(a)/log(10)% +%def loge(a)log(a)% +%def mod(a)rem(a)% +%def d2r() _pi_/180% +%def r2d() 180/_pi_% +%%---end of library--- diff --git a/Master/texmf-dist/doc/latex/mathspic/mathspic.sh b/Master/texmf-dist/doc/latex/mathspic/mathspic.sh new file mode 100644 index 00000000000..6d548a3166e --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/mathspic.sh @@ -0,0 +1,12 @@ +#!/bin/bash +# February 2005 +# mathspic.sh # mathspic script +# put this file in /usr/local/bin +## rename it: mathspic.sh --> mathspic +################# +# format is: +# bash mathspic.sh <options etc> +# mathspic [-b] [-c] [-h] [-o outfile] infile +################# + +perl /usr/local/bin/mpic100.pl $1 $2 $3 $4 $5 diff --git a/Master/texmf-dist/doc/latex/mathspic/sourcecode.html b/Master/texmf-dist/doc/latex/mathspic/sourcecode.html new file mode 100644 index 00000000000..5d963ef76dd --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/sourcecode.html @@ -0,0 +1,5124 @@ +<!-- this file was generated automatically by noweave; better not edit it--> +<html><head><title>sourcecode.nw</title></head><body><center><h1> <tt>mathspic</tt> in Perl </h1></center> +<center><h2> +<table> +<tr><td><address> +<b>Apostolos Syropoulos</b><br> +366, 28th October Str.<br> +GR-671 00 Xanthi<br> +Greece<br> +email: <tt>asyropoulos@yahoo.com</tt> +</address></td> +<td><address> +<b>R.W.D. Nickalls</b><br> + Department of Anaesthesia<br> +Nottingham City Hospital NHS Trust<br> +<a name="NWD21HcNW-1">Hucknall Road</a><br> +Nottingham, NG5-1PB<br> +United Kingdom<br> +email: <tt>dicknickalls@compuserve.com</tt> +</address></td> +</table></h2> +version 1.10 Feb 18, 2007 +</center> + +<h3><b>Introduction</b></h3><p> +<tt>mathspic</tt> is a graphics program which implements a simple +programming notation, <i>mathspic</i>, suitable for the +creation of diagrams or mathematical figures. +<tt>mathspic</tt>'s input is a LaTeX file containing +<tt>mathspic</tt> plotting commands. +<tt>mathspic</tt>'s output is the equivalent LaTeX file +containing PiCTeX plotting commands. +Technically, therefore, <tt>mathspic</tt> +is a preprocessor or `filter' for use with the PiCTeX drawing engine. +<tt>mathspic</tt> was originally written in PowerBASIC 3.5, a +DOS-based programming language. Since, many +potential users are working in rather different programming environments, +the authors thought of porting <tt>mathspic</tt> into another programming +cross-platform language which would be widely available. +The authors decided to rewrite <tt>mathspic</tt> in Perl +since not only is Perl pretty stable, but it has +extensive mathematical support.<p> + +<h3><b>Program Structure</b></h3><p> +<a name="NWD21HcNW-2">Initially, we define a little package that is used to implement the </a><code>loop</code> +command. Then, we must do is to check the possible command line arguments. +Next, we process the input file. +If the user has used the <code>-b</code> (see below), the program will `beep' +if any errors are found during processing. +We need some auxiliary subroutines in order to properly parse the input +file and of course to handle the various commands. We also need a +few global variables. + +<pre><a name="NW21HcNW-1p0Y9w-1" href="#NWD21HcNW-2"><dfn><*>=</dfn></a> +#!/usr/bin/perl +# +#(c) Copyright 2005-2007 +# Apostolos Syropoulos & R.W.D. Nickalls +# asyropoulos@yahoo.com dicknickalls@compuserve.com +# +# This program can be redistributed and/or modified under the terms +# of the LaTeX Project Public License Distributed from CTAN +# archives in directory macros/latex/base/lppl.txt; either +# version 1 of the License, or any later version. +# +<a name="NW21HcNW-1p0Y9w-1-u1" href="#NWD21HcNW-3"><i><package <tt>DummyFH</tt> ></i></a> +package main; +use Math::Trig; +<a name="NW21HcNW-1p0Y9w-1-u2" href="#NWD21HcNW-8"><i><Define global variables></i></a> +<a name="NW21HcNW-1p0Y9w-1-u3" href="#NWD21HcNW-9"><i><subroutine definitions></i></a> +<a name="NW21HcNW-1p0Y9w-1-u4" href="#NWD21HcNW-4"><i><Check for command line arguments></i></a> +<a name="NW21HcNW-1p0Y9w-1-u5" href="#NWD21HcNW-7"><i><process file></i></a> +print $alarm if $no_errors > 0; +__END__ + +</pre><p><a name="NWD21HcNW-3">The package </a><code>DummyFH</code> is used in the implementation of the <code>loop</code> command. +It creates a dummy filehandle that is associated with an array of strings. Since +we only read data from this dummy filehandle, we implement the <code>READLINE</code> subroutine. +When we read a line from this dummy filehandle, we actually requesting the next entry +of the array (if any). That is why we use the package variable <code>$index</code>. When there +are no more entries in the array, subroutine <code>READLINE</code> returns the value <code>undef</code> +so to falsify loop that controls the consumption of input from this dummy filehandle. + +<pre><a name="NW21HcNW-2YwRNH-1" href="#NWD21HcNW-3"><dfn><package <tt>DummyFH</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-2"><-U</a>)</b> +package DummyFH; +my $index = 0; +sub TIEHANDLE { + my $class = shift; + my $self= shift; + bless $self, $class; +} +sub READLINE { + my $self = shift; + #shift @$self; + if ($index > $#$self) { + $index = 0; + return undef; + } + else { + return $self->[$index++]; + } +} + +</pre><p><tt>mathspic</tt> accepts at most four command-line switches, namely +<tt>-b</tt> for enabling the beep, <tt>-s</tt> for automatic +screen viewing of the output-file, +<tt>-c</tt> for cleaning out all comment-lines, +and <tt>-o</tt> with a following file-name +for specifying the output file-name. +<tt><a name="NWD21HcNW-4">mathspic</a></tt> requires the name of an existing input-file +(the so-called <tt>mathspic</tt>-file) containing +<tt>mathspic</tt>commands. +If no command-line arguments are supplied, we print a +suitable usage message indicating the syntax. +For each command-line argument we set a global +variable. The default behavior is that the `bell' does not beep +and comment-lines are not removed from the output-file. + +<pre><a name="NW21HcNW-122Dzz-1" href="#NWD21HcNW-4"><dfn><Check for command line arguments>=</dfn></a> <b>(<a href="#NWD21HcNW-2"><-U</a>)</b> +our $alarm=""; +our $comments_on=1; +our $out_file="default"; +our $argc=@ARGV; +if ($argc == 0 || $argc > 5 ){ # no command line arguments or more than 4 + # arguments + die "\nmathspic version $version_number\n" . + "Usage: mathspic [-h] [-b] [-c] [-o <out file>] <in file>\n\n"; +} +else { + <a name="NW21HcNW-122Dzz-1-u1" href="#NWD21HcNW-5"><i><Process command line arguments></i></a> + print "This is mathspic version $version_number\n"; +} +<a name="NW21HcNW-122Dzz-1-u2" href="#NWD21HcNW-6"><i><Check if .m file exists></i></a> + +</pre><p><a name="NWD21HcNW-5">In order to get the various command-line arguments we use a simple</a> +<code>while</code> loop that checks each element of the array <code>@ARGV</code>. We check +for all the switches, and we get the name of the input-file. + +<pre><a name="NW21HcNW-LnOV9-1" href="#NWD21HcNW-5"><dfn><Process command line arguments>=</dfn></a> <b>(<a href="#NWD21HcNW-4"><-U</a>)</b> + our $file = ""; + SWITCHES: + while($_ = $ARGV[0]) { + shift; + if (/^-h$/) { + die "\nThis is mathspic version $version_number\n" . + "Type \"man mathspic\" for detailed help\n". + "Usage:\tmathspic [-h] [-b] [-c] [-o <out file>] <in file>\n" . + "\twhere,\n" . + "\t[-b]\tenables bell sound if error exists\n" . + "\t[-c]\tdisables comments in ouput file\n" . + "\t[-h]\tgives this help listing\n" . + "\t[-o]\tcreates specified output file\n\n"; + } + elsif (/^-b$/) { + $alarm = chr(7); + } + elsif (/^-c$/) { + $comments_on = 0; + } + elsif (/^-o$/) { + die "No output file specified!\n" if !@ARGV; + $out_file = $ARGV[0]; + shift; + } + elsif (/^-\w+/) { + die "$_: Illegal command line switch!\n"; + } + else { + $file = $_; + } + } + die "No input file specified!\n" if $file eq ""; + +</pre><p><a name="NWD21HcNW-6">In order to check whether the input-file exists, we simply use the</a> +<code>-e</code> operator. First we check to see if <code>$file</code> exits. +If the input-file does exist then the variable <code>$file</code> contains +the file name. In case the user has not specified an output +file, the default output file name is the name of the input file with +extension <code>.mt</code>. Finally, the program outputs all error messages to +the screen and to a log file. The name of the log file consists of +the contents of the variable <code>$file</code> and the extension <code>.mlg</code>. + +<pre><a name="NW21HcNW-2K3CIm-1" href="#NWD21HcNW-6"><dfn><Check if .m file exists>=</dfn></a> <b>(<a href="#NWD21HcNW-4"><-U</a>)</b> + our ($source_file, $log_file); + if (! -e $file) { + die "$file: no such file!\n" if (! (-e "$file.m")); + $source_file = "$file.m"; + } + else { + $source_file = $file; + $file = $1 if $file =~ /(\w[\w-\.]+)\.\w+/; + } + $out_file= "$file.mt" if $out_file eq "default"; + $log_file= "$file.mlg"; + +</pre><p><a name="NWD21HcNW-7">Now that we have all the command line arguments, we can start processing</a> +the input file. This is done by calling the subroutine <code>process_input</code>. +Before that we must open all necessary files. Next, +we print some `header' information to the output file and to the log file. + +<pre><a name="NW21HcNW-EP1QE-1" href="#NWD21HcNW-7"><dfn><process file>=</dfn></a> <b>(<a href="#NWD21HcNW-2"><-U</a>)</b> + open(IN,"$source_file")||die "Can't open source file: $source_file\n"; + open(OUT,">$out_file")||die "Can't open output file: $out_file\n"; + open(LOG,">$log_file")||die "Can't open log file: $log_file\n"; + print_headers; + process_input(IN,""); + +</pre><p>In this section we define a few global variables. More specifically: +the variable <code>$version_number</code> contains the current version number of the +program, the variable <code>$commandLineArgs</code> contains the command line arguments. +These two variables are used in the <code>print_headers</code> subroutine. +The variable <code>$command</code> will contain the whole current input line. +Hash <code>%PointTable</code> is used to store point names and related +information. Hash <code>%VarTable</code> is used to store mathspic variable names +and related information, while the associative array <code>%ConstTable</code> contains the +names of constants. Note that the values of both constants and variables are +kept in <code>%VarTable</code>. +The variable <code>$no_errors</code> is incremented whenever the +program encounters an error in the input file. The variables <code>$xunits</code>, +<code>$yunits</code> and <code>$units</code> are related to the <code>paper</code> command. +In particular, the variable <code>$units</code> is used to parse the unit part of the +<code>unit</code> part of the <code>paper</code> command. The variable <code>$defaultsymbol</code> is used to +set the point shape. The constant <code>PI</code> holds the value of the mathematical + constant pi. +The constant <code>R2D</code> holds the transformation factor to transform radians to +degrees. The constant <code>D2R</code> holds the transformation factor +to transform degrees to radians, i.e., the value <code>1/R2D</code>. The global variables +<code>$arrowLength</code>, <code>$arrowAngleB</code> and <code>$arrowAngleC</code> are actually parameters that +<a name="NWD21HcNW-8">are used by the subroutines that draw arrows. Since </a><code>$arrowLength</code> is actually +a length, variable <code>$arrowLenghtUnits</code> holds the units of measure in which +this length is expressed. The hash table <code>%DimOfPoint</code> contains the side or the +radius of a point whose plot-symbol is a square or a circle, respectively. In case the +default point symbol is a circle or a square, variable <code>$GlobalDimOfPoints</code> is used +to store the length of the radius or the length of the side of default point symbol, +respectively. Variable <code>$LineThickness</code> holds the current line thickness (the +default value is 0.4 pt). + +<pre><a name="NW21HcNW-xIn58-1" href="#NWD21HcNW-8"><dfn><Define global variables>=</dfn></a> <b>(<a href="#NWD21HcNW-2"><-U</a>)</b> +our $version_number = "1.10 Feb 18, 2007"; +our $commandLineArgs = join(" ", @ARGV); +our $command = ""; +our $curr_in_file = ""; +our %PointTable = (); +our %VarTable = (); +our %ConstTable = (); +our $no_errors = 0; +our $xunits = "1pt"; +our $yunits = "1pt"; +our $units = "pt|pc|in|bp|cm|mm|dd|cc|sp"; +our $defaultsymbol = "\$\\bullet\$"; +our $defaultLFradius = 0; +use constant PI => atan2(1,1)*4; +use constant R2D => 180 / PI; +use constant D2R => PI / 180; +our $arrowLength = 2; +our $arrowLengthUnits = "mm"; +our $arrowAngleB = 30; +our $arrowAngleC = 40; +our %DimOfPoint = (); +our $GlobalDimOfPoints = 0; +our @Macros = (); +our $LineThickness = 0.4; + +</pre><p>In this section we define the various subroutines that are needed in order +to process the input file. + +<p> Subroutine <tt>mpp</tt> is a mathspic preprocessor that allows the definition +and use of macros with or without arguments. For the moment it is an experimental +feature and it should be used with care. + +<p> Subroutine <tt>PrintErrorMessage</tt> is used to print error messages +to the screen, to the output file and to the log file. + +<p> Subroutine <tt>PrintWarningMessage</tt> is used to print warning messages +to the screen, to the output file and to the log file. + +<p> Subroutine <tt>PrintFatalError</tt> is used to print an error message +to the screen and to abort execution, where the error is considered fatal +and not recoverable. + +<p>Subroutine <tt>chk_lparen</tt> checks whether the next input +character is a left parenthesis. Subroutine <tt>chk_rparen</tt> +checks whether the next input character is a right parenthesis. Subroutine +<tt>chk_comment</tt> checks whether a given command is followed by a trailing +comment. In the same spirit, we define the subroutines <tt>chk_lcb</tt>, +<tt>chk_rcb</tt>, <tt>chk_lsb</tt>, and <tt>chk_rsb</tt> which check for +opening and closing curly and square brackets respectively. +The subroutine <code>chk_comma</code> checks whether the next token is a comma. + +<p> Subroutine <code>print_headers</code> is used to print a header to the output file, +so a user knows that the file has been generated by <tt>mathspic</tt>. + +<p> Subroutine <code>get_point</code> is used to parse a point name and to +check whether the point exists (i.e whether the point has been defined). + +<p> Subroutine <code>perpendicular</code> is used to compute the coordinates of the +foot of perpendicular line from some point P to a line AB. + +<p> Subroutine <code>Length</code> is used to compute the distance between two +points A and B. + +<p> Subroutine <code>triangleArea</code> computes the area of a triangle defined +by three points. + +<p> Subroutine <code>PointOnLine</code> is used to compute the coordinates of +a point on a line segment AB and a distance d units from A towards B. + +<p> Subroutine <code>circumCircleCenter</code> takes six arguments that are the +coordinates of three points and computes the center of the circle that +passes through the three points which define the triangle. + +<p> Subroutine <code>ComputeDist</code> is used to compute a numeric value that is +specified by either a variable name, a pair of points, or just a number. + +<p> Subroutine <code>intersection4points</code> is used to compute the coordinates +of the point of intersection of two lines specified by the four arguments +(i.e. two arguments for each point). + +<p> Subroutine <code>IncircleCenter</code> is used to compute the center and +the radius of a circle that touches internally the sides of a triangle, +the coordinates of the three points which define the triangle +being the arguments of the subroutine. + +<p> Subroutine <code>Angle</code> determines the opening in degrees of an angle +defined by three points which are the arguments of this subroutine. + +<p> Subroutine <code>excircle</code> computes the center and the radius of +a circle that externally touches a given side (4th and 5th arguments) of +triangle (determined by the 1st, the 2nd and the 3rd argument). + +<p> Subroutine <code>DrawLineOrArrow</code> is used to parse the arguments of the commands + <code>drawline</code>, <code>drawthickline</code>, <code>drawarrow</code>, <code>drawthickarrow</code> and + <code>drawCurve</code>. + +<p> Subroutine <code>drawarrows</code> is used to draw one or more arrows between points. + +<p> Subroutine <code>drawlines</code> is used to draw one or more lines between points. + +<p> Subroutine <code>drawCurve</code> is used to draw a curve between an odd number of points. + +<p> Subroutine <code>drawpoints</code> is used to draw the point symbol of one or more points. + +<p> Subroutine <code>drawAngleArc</code> is used to draw an arc line within an angle. + +<p> Subroutine <code>drawAngleArrow</code> is used to draw an arc line with an arrow on the end, +within an angle. + +<p> Subroutine <code>expr</code> and subroutines <code>term</code>, <code>factor</code> and +<code>primitive</code> are used to parse an expression that follows a variable +declaration. + +<p> Subroutine <code>memberOf</code> is used to determine whether a string is a +member of a list of strings. + +<p> Subroutine <code>tand</code> computes the tangent of an angle, where the +angle is expressed in degrees. + +<p> Subroutine <code>get_string</code> scans a string in order to extract a +valid mathspic string. + +<p> Subroutine <code>is_tainted</code> checks whether a string contains data that +may be proved harmful if used as arguments to a shell escape. + +<p> Subroutine <code>noOfDigits</code> has one argument which is a number and +returns the number of decimal digits it has. + +<p> Subroutine <code>drawsquare</code> has one argument which is the radius of point +and yields LaTeX code that draws a square. + +<p> Subroutine <code>X2sp</code> can be used to transform a length to sp units. + +<p> <a name="NWD21HcNW-9">Subroutine </a><code>sp2X</code> can be used to transform a length expressed in sp units + to any other acceptable unit. + +<p> Subroutine <code>setLineThickness</code> is used to determine the length of the + linethickness in the current paper units. + +<p> Subroutine <code>process_input</code> parses the input file and any other file + being included in the main file, and generates output. + +<pre><a name="NW21HcNW-2AA3uL-1" href="#NWD21HcNW-9"><dfn><subroutine definitions>=</dfn></a> <b>(<a href="#NWD21HcNW-2"><-U</a>)</b> + <a name="NW21HcNW-2AA3uL-1-u1" href="#NWD21HcNW-A"><i><subroutine <tt>mpp</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u2" href="#NWD21HcNW-B"><i><subroutine <tt>PrintErrorMessage</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u3" href="#NWD21HcNW-C"><i><subroutine <tt>PrintWarningMessage</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u4" href="#NWD21HcNW-D"><i><subroutine <tt>PrintFatalError</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u5" href="#NWD21HcNW-E"><i><subroutine <tt>chk_lparen</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u6" href="#NWD21HcNW-F"><i><subroutine <tt>chk_rparen</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u7" href="#NWD21HcNW-G"><i><subroutine <tt>chk_lcb</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u8" href="#NWD21HcNW-H"><i><subroutine <tt>chk_rcb</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u9" href="#NWD21HcNW-I"><i><subroutine <tt>chk_lsb</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u10" href="#NWD21HcNW-J"><i><subroutine <tt>chk_rsb</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u11" href="#NWD21HcNW-K"><i><subroutine <tt>chk_comma</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u12" href="#NWD21HcNW-L"><i><subroutine <tt>chk_comment</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u13" href="#NWD21HcNW-M"><i><subroutine <tt>print_headers</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u14" href="#NWD21HcNW-N"><i><subroutine <tt>get_point</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u15" href="#NWD21HcNW-O"><i><subroutine <tt>perpendicular</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u16" href="#NWD21HcNW-P"><i><subroutine <tt>Length</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u17" href="#NWD21HcNW-Q"><i><subroutine <tt>triangleArea</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u18" href="#NWD21HcNW-R"><i><subroutine <tt>pointOnLine</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u19" href="#NWD21HcNW-S"><i><subroutine <tt>circumCircleCenter</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u20" href="#NWD21HcNW-T"><i><subroutine <tt>ComputeDist</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u21" href="#NWD21HcNW-U"><i><subroutine <tt>intersection4points</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u22" href="#NWD21HcNW-V"><i><subroutine <tt>IncircleCenter</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u23" href="#NWD21HcNW-W"><i><subroutine <tt>Angle</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u24" href="#NWD21HcNW-X"><i><subroutine <tt>excircle</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u25" href="#NWD21HcNW-Y"><i><subroutine <tt>DrawLineOrArrow</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u26" href="#NWD21HcNW-Z"><i><subroutine <tt>drawarrows</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u27" href="#NWD21HcNW-a"><i><subroutine <tt>drawlines</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u28" href="#NWD21HcNW-b"><i><subroutine <tt>drawCurve</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u29" href="#NWD21HcNW-c"><i><subroutine <tt>drawpoints</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u30" href="#NWD21HcNW-d"><i><subroutine <tt>drawAngleArc</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u31" href="#NWD21HcNW-e"><i><subroutine <tt>drawAngleArrow</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u32" href="#NWD21HcNW-f"><i><subroutine <tt>expr</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u33" href="#NWD21HcNW-g"><i><subroutine <tt>memberOf</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u34" href="#NWD21HcNW-h"><i><subroutine <tt>tand</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u35" href="#NWD21HcNW-i"><i><subroutine <tt>get_string</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u36" href="#NWD21HcNW-j"><i><subroutine <tt>is_tainted</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u37" href="#NWD21HcNW-k"><i><subroutine <tt>noOfDigits</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u38" href="#NWD21HcNW-l"><i><subroutine <tt>drawsquare</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u39" href="#NWD21HcNW-m"><i><subroutine <tt>X2sp</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u40" href="#NWD21HcNW-n"><i><subroutine <tt>sp2X</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u41" href="#NWD21HcNW-o"><i><subroutine <tt>setLineThickness</tt> ></i></a> + <a name="NW21HcNW-2AA3uL-1-u42" href="#NWD21HcNW-p"><i><subroutine <tt>process_input</tt> ></i></a> + +</pre><p>Subroutine <tt>mpp</tt> is an implementation of a mathspic preprocessor that allows +the definition of one-line macros with or without arguments. Macro definition has the +following syntax: +<center> + <tt>"%def" macro_name "(" [ parameters ] ")" macro_code +</center> +where parameters is a list of comma separated strings (e.g., x,y,z). Once a macro is +defined it can be used or it can be undefined. To undefine a macro one has to use +the following command: +<center> + <tt>"%undef" [ macro_name ] +</center +This means that an undef command without an accompanying macro name has no effect +at all. In order to use a macro we simply type its name and its arguments in +parentheses. Note that macro arguments should not contain spaces. If a macro has no +argument, there is no need to type any parentheses. We will now describe briefly how +the macro processor operates. +<p> If the current input line starts with <tt>%def</tt>, then we assume that we have +a macro definition. We parse each component of the macro definition and finally we +store the macro name, the macro code and the macro parameters (if any) in an anonymous +hash that eventually becomes part of an array. If we encounter any error, we simply +<a name="NWD21HcNW-A">skip to the next line after printing a suitable error message. Now, if the first tokens</a> +of an input line are <tt>%undef</tt>, we assume the user wants to delete a macro. +In case these tokens are not followed by a macro name or the macro name has not been +defined we simply go on. Otherwise, we delete the corresponding macro data from the +global array <code>@Macros</code> that contains all the macro information. Macro expansion is +more difficult and it will be described in detail in a separate document. At this point +we would like to thank Joachim Schneider <joachim at hal dot rhein-necker dot de> +for a suggestion on improving macro expansion. + +<pre><a name="NW21HcNW-2rq75n-1" href="#NWD21HcNW-A"><dfn><subroutine <tt>mpp</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub mpp { + my $in_line; + chomp($in_line = shift); + my $LC = shift; + my $out_line = $in_line; + my $macro_name = ""; + my @macro_param = (); + my $macro_code = ""; + if ($in_line =~ s/^%def\s*//) { + if ($in_line =~ s/^(\w+)\s*//){ + $macro_name = $1; + } + else { + PrintErrorMessage("No macro name has been found",$LC); + return "" + } + if ($in_line =~ s/^\(\s*//) { + # do nothing + } + else { + PrintErrorMessage("No left parenthesis after macro name has been found",$LC); + return ""; + } + if ($in_line =~ s/^\)//) { + # Macro has no parameters! + } + else { + MACROS: while (1) { + if ($in_line =~ s/^(\w+)\s*//) { + push (@macro_param, $1); + } + else { + PrintErrorMessage("No macro parameter name has been found",$LC); + return ""; + } + if ($in_line =~ s/^,\s*//) { + next MACROS; + } + else { + last MACROS; + } + } + if ($in_line =~ s/^\)//) { + # do nothing! + } + else { + PrintErrorMessage("No closing parenthesis after macro parameters",$LC); + return ""; + } + } + $in_line =~ s/([^%]+)(%.*)/$1/; + $macro_code = $in_line; + push ( @Macros , { 'macro_name' => $macro_name, + 'macro_code' => $macro_code, + 'macro_param' => \@macro_param }); + return $out_line; + } + elsif ($in_line =~ s/^%undef\s*//) { + if ($in_line =~ s/^(\w+)//) { + my $undef_macro = $1; + for(my $i = $#Macros; $i >= 0; $i--) { + if ($Macros[$i]->{'macro_name'} eq $undef_macro) { + splice(@Macros,$i,1); + } + } + } + return $out_line; + } + elsif ($in_line =~ s/^\s*%//) { + return $out_line; + } + else { + my $comment = $2 if $in_line =~ s/([^%]+)(%.+)/$1/; + EXPANSIONLOOP: while () { + my $org_in_line = $in_line; + for(my $i = $#Macros; $i >= 0; $i--) { + my $macro_name = $Macros[$i]->{'macro_name'}; + if ($in_line =~ /&$macro_name\b/) { ############################ + my $num_of_macro_args = @{$Macros[$i]->{'macro_param'}}; + if ( $num_of_macro_args > 0 ) { + # Macro with parameters + my $pattern = "&$macro_name\\("; + foreach my $p ( 1..$num_of_macro_args ) { + my $comma = ($p == $num_of_macro_args) ? "\\s*" : "\\s*,\\s*"; + $pattern .= "\\s*[^\\s\\)]+$comma"; + } + $pattern .= "\\)"; + while($in_line =~ /&$macro_name\b/) { + if ($in_line =~ /$pattern/) { + my $before = $`; + my $after = $'; + my $match = $&; + my $new_code = $Macros[$i]->{'macro_code'}; + $match =~ s/^&$macro_name\(\s*//; + $match =~ s/\)$//; + foreach my $arg ( 0..($num_of_macro_args - 1) ) { + my $old = $Macros[$i]->{'macro_param'}->[$arg]; + my $comma = ($arg == ($num_of_macro_args - 1)) ? "" : ","; + $match =~ s/^\s*([^\s,]+)\s*$comma//; + my $new = $1; + # 'g': Parameter may occur several times + # in $new_code. + # '\b': Substitute only whole words + # not x in xA + $new_code =~ s/\b$old\b/$new/g; + } + $in_line = "$before$new_code$after"; + } + else { + PrintErrorMessage("Usage of macro &$macro_name does not " . + "match its definition", $LC); + return ""; + } + } + } + else { + # Macro without parameters + my $replacement = $Macros[$i]->{'macro_code'}; + # '\b': Substitute only whole words + # not x in xA + $in_line =~ s/&$macro_name\b/$replacement/g; + } + } + } + last EXPANSIONLOOP if ( $org_in_line eq $in_line ); + } + return "$in_line$comment"; + } +} + +</pre><p>Subroutine <tt>PrintErrorMessage</tt> has two parameters: the +error message that will be printed on the screen, the log file and +the output file, and the line number of the line containing the +error was detected. +The general form of the error message is the following: +<pre> +line X: paper{units( + ,mm)xrange(0,20)yrange(0,30)axes(B)ticks(10,10)} + +***Error: Error_Message +</pre> +where <code>X</code> denotes the line number and <code>Error_Message</code> is the +actual error message. Note, that we print the tokens processed so far +and on the text line the unprocessed tokens, so that the user knows +<a name="NWD21HcNW-B">exactly where the error is. In the variable </a><code>$A</code> we store the processed +tokens, while the variable <code>$l</code> holds the length of <code>$A</code> plus the +length of the <code>$error_line</code> (that is the number of the input line where +the error occurred) plus 7, i.e., 4 (the length of the word +<code>line</code>) plus 2 (the two blank spaces) plus 1 (the symbol <code>:</code>). +Finally, we increment the error counter (variable <code>$no_errors</code>). Note, that +in case the user has specified the <code>-c</code> command line switch, we will not +print any messages to the output file. + +<pre><a name="NW21HcNW-1m1522-1" href="#NWD21HcNW-B"><dfn><subroutine <tt>PrintErrorMessage</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub PrintErrorMessage { + my $errormessage = shift; + my $error_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($error_line); + + for my $fh (STDOUT, LOG) { + print $fh "$curr_in_file", "Line $error_line: $A\n"; + print $fh " " x $l ,$_,"***Error: $errormessage\n"; + } + if ($comments_on) { #print to output file file + print OUT "%% *** $curr_in_file", "Line $error_line: $A\n"; + print OUT "%% *** "," " x $l ,$_,"%% ... Error: $errormessage\n"; + } + $no_errors++; + } + +</pre><p><a name="NWD21HcNW-C">Subroutine </a><tt>PrintWarningMessage</tt> behaves exactly like the subroutine +<tt>PrintErrorMessage</tt>. The only difference is that the second +subroutine prints only a warning message. A warning is issued when +the system detects parameters that do nothing. + +<pre><a name="NW21HcNW-3Lpu7M-1" href="#NWD21HcNW-C"><dfn><subroutine <tt>PrintWarningMessage</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub PrintWarningMessage { + my $warningMessage = shift; + my $warning_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($warning_line); + + for my $fh (STDOUT, LOG) { + print $fh "$curr_in_file", "Line $warning_line: $A\n"; + print $fh " " x $l ,$_,"***Warning: $warningMessage\n"; + } + if ($comments_on) { #print to output file file + print OUT "%% *** $curr_in_file", "Line $warning_line: $A\n"; + print OUT "%% *** "," " x $l ,$_,"%% ... Warning: $warningMessage\n"; + } + } + +</pre><p><a name="NWD21HcNW-D">The subroutine </a><tt>PrintFatalError</tt> behaves similarly to the subroutine +<tt>PrintErrorMessage</tt>. It prints an error message to the +screen and aborts execution. + +<pre><a name="NW21HcNW-4RPeBe-1" href="#NWD21HcNW-D"><dfn><subroutine <tt>PrintFatalError</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub PrintFatalError { + my $FatalMessage = shift; + my $fatal_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($fatal_line); + + die "$curr_in_file", "Line $fatal_line: $A\n" . + (" " x $l) . $_ . "***Fatal Error: $FatalMessage\n"; + } + +</pre><p><a name="NWD21HcNW-E">The subroutine </a><tt>chk_lparen</tt> accepts two arguments: the name +of the token that should be immediately before the left parenthesis (variable +<code>$token</code>), and the current line number (variable <code>$lc</code>). First we +skip any leading white space and then check whether the next +input character is a left parenthesis, then the subroutine skips any +trailing white space; otherwise it prints an error message. + +<pre><a name="NW21HcNW-4Y5BUt-1" href="#NWD21HcNW-E"><dfn><subroutine <tt>chk_lparen</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_lparen { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if (/^[^\(]/) { + PrintErrorMessage("Missing ( after $token",$lc); + } + else { + s/^\(\s*//; + } +} + +</pre><p><a name="NWD21HcNW-F">The subroutine </a><tt>chk_rparen</tt> accepts two parameters: the name +of the token that should be immediately after a right parenthesis (variable +<code>$token</code>), and the current line number (variable <code>$lc</code>). Initially, we +skip any leading white space and then we check whether the next input +token is a right parenthesis. If it is not we issue a error message and +return, otherwise we skip the parenthesis and any trailing white space. + +<pre><a name="NW21HcNW-3fTYkz-1" href="#NWD21HcNW-F"><dfn><subroutine <tt>chk_rparen</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_rparen { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if (s/^\)//) { + s/\s*//; + } + else { + PrintErrorMessage("Missing ) after $token",$lc); + } +} + + +</pre><p><a name="NWD21HcNW-G">The subroutine </a><tt>chk_lcb</tt> behaves in a similar way to the subroutine +<tt>chk_lparen</tt>. + +<pre><a name="NW21HcNW-2vMx6j-1" href="#NWD21HcNW-G"><dfn><subroutine <tt>chk_lcb</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_lcb { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if ($_ !~ /^\{/) { + PrintErrorMessage("Missing { after $token",$lc); + } + else { + s/^{\s*//; + } +} + +</pre><p><a name="NWD21HcNW-H">Subroutine </a><tt>chk_rcb</tt> behaves in a similar way to the subroutine +<tt>chk_rparen</tt>. + +<pre><a name="NW21HcNW-FE9Ax-1" href="#NWD21HcNW-H"><dfn><subroutine <tt>chk_rcb</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_rcb { + my $token = $_[0]; + my $lc = $_[1]; + if ($_ !~ /^\s*\}/) { + PrintErrorMessage("Missing } after $token",$lc); + } + else { + s/^\s*}\s*//; + } +} + +</pre><p><a name="NWD21HcNW-I">Subroutine </a><tt>chk_lsb</tt> behaves in a similar way to the subroutine +<tt>chk_lparen</tt>. + +<pre><a name="NW21HcNW-3N30ZF-1" href="#NWD21HcNW-I"><dfn><subroutine <tt>chk_lsb</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_lsb { + my $token = $_[0]; + my $lc = $_[1]; + + s/\s*//; + if ($_ !~ /^\[/) { + PrintErrorMessage("Missing [ after $token",$lc); + } + else { + s/^\[\s*//; + } +} + +</pre><p><a name="NWD21HcNW-J">Subroutine </a><tt>chk_rsb</tt> behaves in a similar way to the subroutine +<tt>chk_rparen</tt>. + +<pre><a name="NW21HcNW-ma6zf-1" href="#NWD21HcNW-J"><dfn><subroutine <tt>chk_rsb</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_rsb { + my $token = $_[0]; + my $lc = $_[1]; + + s/\s*//; + if ($_ !~ /^\]/) { + PrintErrorMessage("Missing ] after $token",$lc); + } + else { + s/^\]\s*//; + } +} + +</pre><p><a name="NWD21HcNW-K">The subroutine </a><code>chk_comma</code> checks whether the next token is a comma. +If it is not then it prints an error message, otherwise it consumes the +comma and any white space that follows the comma. + +<pre><a name="NW21HcNW-UyyUp-1" href="#NWD21HcNW-K"><dfn><subroutine <tt>chk_comma</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_comma { + my $lc = $_[0]; + + s/\s*//; + if (/^[^,]/) { + PrintErrorMessage("Did not find expected comma",$lc); + } + else { + s/^,\s*//; + } +} + +</pre><p><a name="NWD21HcNW-L">The subroutine </a><code>chk_comment</code> has only one parameter which is the current +line number. It checks whether the next input character is a comment +character and in this case it does nothing!. Otherwise, if there is some trailing text +it simply prints a warning to the screen. + +<pre><a name="NW21HcNW-wLKY1-1" href="#NWD21HcNW-L"><dfn><subroutine <tt>chk_comment</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub chk_comment { + my $lc = $_[0]; + + s/\s*//; + if (/^%/) { + # do nothing! + } + elsif (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } +} + +</pre><p><a name="NWD21HcNW-M">The subroutine </a><code>print_headers</code> prints a header to the output file, as +well as a header to the LOG file. +The header contains information regarding the version of the +program, a copyright notice, the command line, date and time information, +and the names of the various files processed/generated. + +<pre><a name="NW21HcNW-3iVliS-1" href="#NWD21HcNW-M"><dfn><subroutine <tt>print_headers</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub print_headers + { + my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localtime; + $year+=1900; + $mon+=1; + $now_string = "$year/" . ($mon>9 ? "$mon/" : "0$mon/") . + ($mday>9 ? "$mday " : "0$mday ") . + ($hour>9 ? "$hour:" : "0$hour:") . + ($min>9 ? "$min:" : "0$min:") . + ($sec>9 ? "$sec" : "0$sec"); + print OUT "%* -----------------------------------------------\n"; + print OUT "%* mathspic (Perl version $version_number)\n"; + print OUT "%* A filter program for use with PiCTeX\n"; + print OUT "%* Copyright (c) 2005 A Syropoulos & RWD Nickalls \n"; + print OUT "%* Command line: $0 $commandLineArgs\n"; + print OUT "%* Input filename : $source_file\n"; + print OUT "%* Output filename: $out_file\n"; + print OUT "%* Date & time: $now_string\n"; + print OUT "%* -----------------------------------------------\n"; + # + print LOG "----\n"; + print LOG "$now_string\n"; + print LOG "mathspic (Perl version $version_number)\n"; + print LOG "Copyright (c) 2005 A Syropoulos & RWD Nickalls \n"; + print LOG "Input file = $source_file\n"; + print LOG "Output file = $out_file\n"; + print LOG "Log file = $log_file\n"; + print LOG "----\n"; + } + +</pre><p><a name="NWD21HcNW-N">The subroutine </a><code>get_point</code> parses an individual point name. +If the next token is also a point name then it returns the point name + (but only if the only if +the point name exists in the PointTable). In all other cases it returns +the string <code>_undef_</code> to indicate that something is wrong. + +<pre><a name="NW21HcNW-1h5ef9-1" href="#NWD21HcNW-N"><dfn><subroutine <tt>get_point</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub get_point { + + my ($lc) = $_[0]; + my ($PointName); + + if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name + $PointName = $1; + if (!exists($PointTable{lc($PointName)})) { + PrintErrorMessage("Undefined point $PointName",$lc); + return "_undef_"; + } + else { + return lc($PointName); + } + } + else { + PrintErrorMessage("Point name expected",$lc); + return "_undef_"; + } + } + +</pre><p>The subroutine <code>perpendicular</code> has 6 parameters that correspond to the +coordinates of some point P and to the coordinates of two points A and +B that define a line. The subroutine returns +a pair of numbers that correspond to the coordinates of a point that lies +at the foot of the perpendicular to the line AB that passes through point P. +The slope of line AB is m<sub>1</sub> and so its equation is +y=m<sub>1</sub>x+c<sub>1</sub>. Similarly, the slope of the line PF is +m<sub>2</sub>=-1/m<sub>1</sub> and its equation is +y=m<sub>2</sub>x+c<sub>2</sub>. Since the line AB passes through A, then +c<sub>1</sub>=y<sub>A</sub>-m<sub>1</sub>x<sub>A</sub>. Similarly, as P is +on line PF, then c<sub>2</sub>=y<sub>P</sub>-m<sub>2</sub>x<sub>P</sub>. +Now point F is on both lines, therefore +<a name="NWD21HcNW-O">y</a><sub>F</sub>=m<sub>2</sub>x<sub>F</sub>+c<sub>2</sub> and +y<sub>F</sub>=m<sub>1</sub>x<sub>F</sub>+c<sub>1</sub>. Solving these +equations for x<sub>F</sub> and y<sub>F</sub> gives: +<center> +x<sub>F</sub>=(c<sub>2</sub>-c<sub>1</sub>)/(m<sub>1</sub>-m<sub>2</sub>)<br> +y<sub>F</sub>=(m<sub>1</sub>c<sub>2</sub>-m<sub>2</sub>c<sub>1</sub>)/ +(m<sub>1</sub>-m<sub>2</sub>) +</center> + +<pre><a name="NW21HcNW-1GxwYt-1" href="#NWD21HcNW-O"><dfn><subroutine <tt>perpendicular</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub perpendicular { + my ($xP, $yP, $xA, $yA, $xB, $yB) = @_; + my ($xF, $yF, $deltax, $deltay, $m1, $m2, $c1, $c2, $factor); + + $deltax = $xA - $xB; + return ($xA, $yP) if abs($deltax) < 0.0000001; + $deltay = $yA - $yB; + return ($xP, $yA) if abs($deltay) < 0.0000001; + $m1 = $deltay / $deltax; + eval { $m2 = (-1) / $m1;}; + PrintFatalError("Division by zero",$lc) if $@; + $c1 = $yA - $m1 * $xA; + $c2 = $yP - $m2 * $xP; + eval { $factor = 1 / ($m1 - $m2)}; + PrintFatalError("Division by zero",$lc) if $@; + return (($c2 - $c1) * $factor, ($m1 * $c2 - $m2 * $c1) * $factor); + } + +</pre><p> <a name="NWD21HcNW-P">The subroutine </a><code>Length</code> computes the distance between two points A and B. +Notice, that the name of the subroutine starts with a capital L, just +to avoid conflict with the predefined Perl function. The subroutine +requires four parameters which are the coordinates of the two points. + +<pre><a name="NW21HcNW-4XEuZg-1" href="#NWD21HcNW-P"><dfn><subroutine <tt>Length</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub Length { + my ($xA, $yA, $xB, $yB)=@_; + return sqrt(($xB - $xA)**2 + ($yB - $yA)**2); + } + +</pre><p><a name="NWD21HcNW-Q">The subroutine </a><code>triangleArea</code> computes the area of a triangle by using +Heron's formula, i.e., given a triangle ABC, we first compute +s=(AB+BC+CA)/2 and then the area of the triangle is equal to the +square root of s times (s-AB) times (s-BC) times (s-BA), where AB, BC, and CA +are the lengths of the three sides of the triangle. The subroutine accepts 6 +parameters, which correspond to the coordinates of three points that define +the triangle. + +<pre><a name="NW21HcNW-4DwBs6-1" href="#NWD21HcNW-Q"><dfn><subroutine <tt>triangleArea</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub triangleArea { + my ($xA, $yA, $xB, $yB, $xC, $yC)=@_; + my ($lenAB, $lenBC, $lenCA, $s); + + $lenAB = Length($xA,$yA,$xB,$yB); + $lenBC = Length($xB,$yB,$xC,$yC); + $lenCA = Length($xC,$yC,$xA,$yA); + $s = ($lenAB + $lenBC + $lenCA) / 2; + return sqrt($s * ($s - $lenAB)*($s - $lenBC)*($s - $lenCA)); + } + +</pre><p><a name="NWD21HcNW-R">The subroutine </a><code>poinOnLine</code> accepts five arguments: the coordinates of two +points and the decimal number which corresponds to the distance from the +first point towards the second one. The way we compute the coordinates of +the point is fairly simple. + +<pre><a name="NW21HcNW-VFnEE-1" href="#NWD21HcNW-R"><dfn><subroutine <tt>pointOnLine</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub pointOnLine { + my ($xA, $yA, $xB, $yB, $dist)=@_; + my ($deltax, $deltay, $xPol, $yPol); + + $deltax = $xB - $xA; + $deltay = $yB - $yA; + $xPol = $xA + ($dist * $deltax / &Length($xA,$yA,$xB,$yB)); + $yPol = $yA + ($dist * $deltay / &Length($xA,$yA,$xB,$yB)); + return ($xPol, $yPol); + } + + +</pre><p>As we have mentioned above the subroutine <code>circumCircleCenter</code> takes six +arguments that correspond to the coordinates of three points that +define a triangle. The subroutine computes the coordinates of +the center of a circle that passes through these three points, and the radius of +the circle. We now describe how the subroutine computes the center +of the circle and its radius. Let the triangle points be <code>t1</code>, <code>t2</code> +and <code>t3</code>. We use the two pairs of points to define two sides, +i.e., <code>t1t2</code> and <code>t2t3</code>. For each +<a name="NWD21HcNW-S">side we locate the midpoints and get the their coordinates. We check</a> +whether either of these two lines is either vertical or horizontal. If this +is true, we know that one of the coordinates of the center of the circumcircle +is the same as that of the midpoints of the horizontal or vertical line. +Next, we determine the slopes of the lines <code>t1t2</code> and <code>t2t3</code>. +We now determine the slope of lines at right-angles to these lines. We solve the +resulting equations and obtain the center of the circumcircle. Now we get the +radius, and then we are done. + +<pre><a name="NW21HcNW-lKNKf-1" href="#NWD21HcNW-S"><dfn><subroutine <tt>circumCircleCenter</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + + sub circumCircleCenter { + my ($xA, $yA, $xB, $yB, $xC, $yC, $lc)=@_; + my ($deltay12, $deltax12, $xs12, $ys12); + my ($deltay23, $deltax23, $xs23, $ys23); + my ($xcc, $ycc); + my ($m23, $mr23, $c23, $m12, $mr12, $c12); + my ($sideA, $sideB, $sideC, $a, $radius); + + if (abs(triangleArea($xA, $yA, $xB, $yB, $xC, $yC)) < 0.0000001) + { + PrintErrorMessage("Area of triangle is zero!",$lc); + return (0,0,0); + } + $deltay12 = $yB - $yA; + $deltax12 = $xB - $xA; + $xs12 = $xA + $deltax12 / 2; + $ys12 = $yA + $deltay12 / 2; + # + $deltay23 = $yC - $yB; + $deltax23 = $xC - $xB; + $xs23 = $xB + $deltax23 / 2; + $ys23 = $yB + $deltay23 / 2; + # + CCXYLINE:{ + if (abs($deltay12) < 0.0000001) + { + $xcc = $xs12; + if (abs($deltax23) < 0.0000001) + { + $ycc = $ys23; + last CCXYLINE; + } + else + { + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $ycc = $mr23 * $xs12 + $c23; + last CCXYLINE; + } + } + if (abs($deltax12) < 0.0000001) + { + $ycc = $ys12; + if (abs($deltay23) < 0.0000001) + { + $xcc = $xs23; + last CCXYLINE; + } + else + { + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $xcc = ($ys12 - $c23) / $mr23; + last CCXYLINE; + } + } + if (abs($deltay23) < 0.0000001) + { + $xcc = $xs23; + if (abs($deltax12) < 0.0000001) + { + $ycc = $ys12; + last CCXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + $ycc = $mr12 * $xcc + $c12; + last CCXYLINE; + } + } + if (abs($deltax23) < 0.0000001) + { + $ycc = $ys23; + if (abs($deltay12) < 0.0000001) + { + $xcc = $xs12; + last CCXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + $xcc = ($ycc - $c12) / $mr12; + last CCXYLINE; + } + } + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + #----- + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $xcc = ($c23 - $c12) / ($mr12 - $mr23); + $ycc = ($c23 * $mr12 - $c12 * $mr23) / ($mr12 - $mr23); + } + # + $sideA = &Length($xA,$yA,$xB,$yB); + $sideB = &Length($xB,$yB,$xC,$yC); + $sideC = &Length($xC,$yC,$xA,$yA); + $a = triangleArea($xA, $yA, $xB, $yB, $xC, $yC); + $radius = ($sideA * $sideB * $sideC) / (4 * $a); + # + return ($xcc, $ycc, $radius); + } + +</pre><p>The subroutine <code>ComputeDist</code> is used to compute a distance that is +specified by either a float number, a pair of points, or a variable +name. In case we have a pair of identifiers, we check whether the first +one is a point. If it isn't a point we assume we have a variable followed +by a keyword. Otherwise, i.e., if it is a point name, we check whether +the second identifier is also a point name. If it is, we simply return +the distance between them, otherwise we issue an error message. +<a name="NWD21HcNW-T">If we have only a single identifier, we check whether it is a</a> +variable that has already been defined, and if so we return its value. + Since, this +subroutine is heavily used, it actually returns a pair of numbers: +the first one being the computed distance and the second one being an +error indicator. If the value of this indicator is 0, then there is no +error. If its value is 1, then there is an error. Moreover, in case there +is an error the distance is assumed to be equal to zero. + +<pre><a name="NW21HcNW-3GSnCT-1" href="#NWD21HcNW-T"><dfn><subroutine <tt>ComputeDist</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub ComputeDist { + my ($lc) = $_[0]; + my ($v1, $v2); + + if (s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//) #is it a number? + { + return ($1, 1); + } + elsif (/^[^\W\d_]\d{0,3}[^\W\d_]\d{0,3}/) #it is a pair of IDs? + { + s/^([^\W\d_]\d{0,3})//i; + $v1 = $1; + if (!exists($PointTable{lc($v1)})) { + if (exists($VarTable{lc($v1)})) { + return ($VarTable{lc($v1)}, 1); + } + PrintErrorMessage("Point $v1 has not been defined", $lc); + s/^\s*[^\W\d_]\d{0,3}//i; + return (0,0); + } + $v1 = lc($v1); + s/^\s*([^\W\d_]\d{0,3})//i; + $v2 = $1; + if (!exists($PointTable{lc($v2)})) + { + PrintErrorMessage("Point $v2 has not been defined", $lc); + return (0,0); + } + $v2 = lc($v2); + my ($x1,$y1,$pSV1,$pS1) = unpack("d3A*",$PointTable{$v1}); + my ($x2,$y2,$pSV2,$pS2) = unpack("d3A*",$PointTable{$v2}); + return (Length($x1,$y1,$x2,$y2), 1); + } + elsif (s/^([^\W\d_]\d{0,3})//i) # it is a single id + { + $v1 = $1; + if (!exists($VarTable{lc($v1)})) #it isn't a variable + { + PrintErrorMessage("Variable $v1 has not been defined", $lc); + return (0,0); + } + return ($VarTable{lc($v1)}, 1); + } + else + { + PrintErrorMessage("Unexpected token", $lc); + return (0,0); + } + } + +</pre><p><a name="NWD21HcNW-U">The subroutine </a><code>intersection4points</code> has 8 parameters that correspond to the +coordinates of four points that uniquely determine two lines, and computes the +the point of intersection of these two lines. + +<pre><a name="NW21HcNW-106ivL-1" href="#NWD21HcNW-U"><dfn><subroutine <tt>intersection4points</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub intersection4points { + my ($x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4) = @_; + my ($deltay12, $deltax12, $deltay34, $deltax34); + my ($xcc, $ycc, $m34, $c34, $m12, $c12); + + $deltay12 = $y2 - $y1; + $deltax12 = $x2 - $x1; + # + $deltay34 = $y4 - $y3; + $deltax34 = $x4 - $x3; + I4PXYLINE:{ + if (abs($deltay12) < 0.0000001) + { + $ycc = $y1; + if (abs($deltax34) < 0.0000001) + { + $xcc = $x3; + last I4PXYLINE; + } + else + { + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $xcc = ($ycc - $c34) / $m34; + last I4PXYLINE; + } + } + if (abs($deltax12) < 0.0000001) + { + $xcc = $x1; + if (abs($deltay34) < 0.0000001) + { + $ycc = $y3; + last I4PXYLINE; + } + else + { + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $ycc = $m34 * $xcc + $c34; + last I4PXYLINE; + } + } + if (abs($deltay34) < 0.0000001) + { + $ycc = $y3; + if (abs($deltax12) < 0.0000001) + { + $xcc = $x1; + last I4PXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $xcc = ($ycc - $c12) / $m12; + last I4PXYLINE; + } + } + if (abs($deltax34) < 0.0000001) + { + $xcc = $x3; + if (abs($deltay12) < 0.0000001) + { + $ycc = $y1; + last I4PXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $ycc = $m12 * $xcc + $c12; + last I4PXYLINE; + } + } + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $xcc = ($c34 - $c12) / ($m12 - $m34); + $ycc = ($c34 * $m12 - $c12 * $m34) / ($m12 - $m34); + } + return ($xcc, $ycc); + } + +</pre><p>The subroutine <code>IncircleCenter</code> computes the center and the +radius of the circle that is inside a triangle and touches the sides of +the triangle. The subroutine has six arguments that correspond to the +coordinates of three points that uniquely determine the triangle. Here are +the details: +<ul> +<li> Let the triangle points be A, B, C and sides a, b, c, where side B +is opposite angle B, etc. </li> +<li> Use angles A and B only.</li> +<li> Let the bisector of angle A meet side a in point A1, and let the +distance of A1 from B be designated BA1</li> +<li> Using the sine rule, one gets: BA1/c = a/(b+c), that is +BA1 = c * a/(b+c).</li> +<li> Now do the same for side b, and determine equivalent point B1. +<a name="NWD21HcNW-V">CB1/a = b/(b+c), that is CB1 = a * b/(b+c).</a></li> +<li> We can now find the intersection of the line from point A to point A1, +and the line from point B to point B1. We have four points, so we use the +mathspic internal <code>intersection4points</code> subroutine to return the +coordinates of the intersection X<sub>i</sub>, Y<sub>i</sub>.</li> +<li> Now get the radius: R=(area of triangle)/(a+b+c)/2</li> +<li>Finally, return the radius and the coordinates of the center. +</ul> + +<pre><a name="NW21HcNW-Kxdzt-1" href="#NWD21HcNW-V"><dfn><subroutine <tt>IncircleCenter</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub IncircleCenter { + my ($Ax, $Ay, $Bx, $By, $Cx, $Cy) = @_; + my ($sideA, $sideB, $sideC); + my ($ba1, $xA1, $yA1, $cb1, $ac1, $xB1, $yB1, $xC1, $yC1, $a, $s, $r); + + #determine the lengths of the sides + $sideA = Length($Bx, $By, $Cx, $Cy); + $sideB = Length($Cx, $Cy, $Ax, $Ay); + $sideC = Length($Ax, $Ay, $Bx, $By); + # + $ba1 = ($sideC * $sideA) / ($sideB + $sideC); + ($xA1, $yA1) = pointOnLine($Bx, $By, $Cx, $Cy, $ba1); + $cb1 = ($sideA * $sideB) / ($sideC + $sideA); + ($xB1, $yB1) = pointOnLine($Cx, $Cy, $Ax, $Ay, $cb1); + $ac1 = ($sideB * $sideC) / ($sideA + $sideB); + ($xC1, $yC1) = pointOnLine($Ax, $Ay, $Bx, $By, $ac1); + ($xcenter, $ycenter) = &intersection4points($Ax, $Ay, $xA1, $yA1, + $Bx, $By, $xB1, $yB1); + # get radius + $a = &triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $s = ($sideA + $sideB +$sideC) / 2; + $r = $a / $s; + return ($xcenter, $ycenter, $r); + } + +</pre><p><a name="NWD21HcNW-W">The subroutine </a><code>Angle</code> takes six arguments which correspond to the +coordinates of three points that define an angle. The subroutine computes +the opening of the angle in degrees. In case there is an error it returns +the number -500. ****EXPLAIN THE ALGORITHM**** + +<pre><a name="NW21HcNW-3xteda-1" href="#NWD21HcNW-W"><dfn><subroutine <tt>Angle</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub Angle { + my ($Ax, $Ay, $Bx, $By, $Cx, $Cy) = @_; + my ($RAx, $RAy, $RBx, $RBy, $RCx, $RCy, $deltax, $deltay); + my ($lineBA, $lineBC, $lineAC, $k, $kk, $angle); + my ($T, $cosT, $sinT) = (0.3, cos(0.3), sin(0.3)); + + $RAx = $Ax * $cosT + $Ay * $sinT; + $RAy = -$Ax * $sinT + $Ay * $cosT; + $RBx = $Bx * $cosT + $By * $sinT; + $RBy = -$Bx * $sinT + $By * $cosT; + $RCx = $Cx * $cosT + $Cy * $sinT; + $RCy = -$Cx * $sinT + $Cy * $cosT; + $deltax = $RBx - $RAx; + $deltay = $RBy - $RAy; + $lineBA = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineBA < 0.0000001) + { + return -500; + } + $deltax = $RBx - $RCx; + $deltay = $RBy - $RCy; + $lineBC = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineBC < 0.0000001) + { + return -500; + } + $deltax = $RAx - $RCx; + $deltay = $RAy - $RCy; + $lineAC = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineAC < 0.0000001) + { + return -500; + } + $k = ($lineBA*$lineBA + $lineBC*$lineBC - $lineAC*$lineAC ) / + (2 * $lineBA * $lineBC); + $k = -1 if $k < -0.99999; + $k = 1 if $k > 0.99999; + $kk = $k * $k; + if (($kk * $kk) == 1) + { + $angle = PI if $k == -1; + $angle = 0 if $k == 1; + } + else + { + $angle = (PI / 2) - atan2($k / sqrt(1 - $kk),1); + } + return $angle * 180 / PI; + } + +</pre><p>The subroutine <code>excircle</code> computes the center and the radius of a circle that +externally touches a given side (4th and 5th arguments) of triangle (determined +by the 1rst, the 2nd and 3rd argument). Here are the details: +<ul> +<li> Let the triangle points be A, B, C, and the given side be BC.</li> +<li> Now calculate the radius of Excircle = (triangle area)/(s - side length), +where s = (a+b+c)/2</li> +<li><a name="NWD21HcNW-X">Calculate the distance from the angle (A) (opposite the given side BC)</a> + to the excircle center = radius/sin(A/2)</li> +<li> Now determine the the Excircle center by locating it on the angle bisector +(i.e., same line that the IncircleCenter is on), but at distance d further +away from angle A. So, we now have the Incircle center (I), + determine deltaX and deltaY from I to A, calculate the distance AI, + and then extend the line from I by distance d to Excenter Xc, Yc.</li> +</ul> + +<pre><a name="NW21HcNW-cchrT-1" href="#NWD21HcNW-X"><dfn><subroutine <tt>excircle</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub excircle { + my ($A, $B, $C, $D, $E) = @_; + my ($Ax,$Ay,$Bx,$By,$Dx,$Dy,$Ex,$Ey,$ASVA,$ASA); + ($Ax,$Ay,$ASVA,$ASA)=unpack("d3A*",$PointTable{$A}); + ($Bx,$By,$ASVA,$ASA)=unpack("d3A*",$PointTable{$B}); + ($Cx,$Cy,$ASVA,$ASA)=unpack("d3A*",$PointTable{$C}); + ($Dx,$Dy,$ASVA,$ASA)=unpack("d3A*",$PointTable{$D}); + ($Ex,$Ey,$ASVA,$ASA)=unpack("d3A*",$PointTable{$E}); + my ($sideA, $sideB, $sideC, $s, $R, $theAdeg, $d); + my ($Xmypoint, $Ymypoint, $deltax, $deltay, $mylength, $xc, $yc); + + $sideA = &Length($Bx, $By, $Cx, $Cy); + $sideB = &Length($Cx, $Cy, $Ax, $Ay); + $sideC = &Length($Ax, $Ay, $Bx, $By); + $s = ($sideA + $sideB + $sideC) / 2; + $R = triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy) / + ($s - &Length($Dx, $Dy, $Ex, $Ey)); + if (($D eq $A && $E eq $B) || ($D eq $B && $E eq $A)) + { + $theAdeg = &Angle($Bx, $By, $Cx, $Cy, $Ax, $Ay); + $Xmypoint = $Cx; + $Ymypoint = $Cy; + } + elsif (($D eq $B && $E eq $C) || ($D eq $C && $E eq $B)) + { + $theAdeg = &Angle($Cx, $Cy, $Ax, $Ay, $Bx, $By); + $Xmypoint = $Ax; + $Ymypoint = $Ay; + } + elsif (($D eq $C && $E eq $A) || ($D eq $A && $E eq $C)) + { + $theAdeg = &Angle($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $Xmypoint = $Bx; + $Ymypoint = $By; + } + else + { + return (0,0,0); + } + $d = $R / sin($theAdeg * PI / 180 / 2); + my ($xIn, $yIn, $rin) = &IncircleCenter($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $deltax = $xIn - $Xmypoint; + $deltay = $yIn - $Ymypoint; + $mylength = sqrt($deltax*$deltax + $deltay*$deltay); + $xc = $Xmypoint + $d * $deltax / $mylength; + $yc = $Ymypoint + $d * $deltay / $mylength; + return ($xc, $yc, $R); + } + +</pre><p>The <code>DrawLineOrArrow</code> subroutine is used to parse the arguments of the commands +<code>drawline</code>, <code>drawthickline</code>, <code>drawarrow</code>, <code>drawthickarrow</code> and +<code>drawCurve</code>. In general, these commands have as arguments a list of points separated by +commas that are used to draw a set of lines. The list of points is +enclosed in parentheses. Here we give only the syntax of the <code>drawline</code> +comma, as the syntax of the other commands is identical: +<pre> + drawline ::= "drawline" "(" Points { "," Points } ")" + Points ::= Point { separator Point} + separator ::= blank | empty +</pre> +<a name="NWD21HcNW-Y">In the following code we</a> +scan a list of points (possibly separated by blanks) and we stop when +we encounter either a comma or some other character. In case we have found +a comma, we check whether we have a <code>drawline</code> command and if this is +the case we plot the list of points. We continue with the next list of points, +until there are no more points. The inner while-loop is used to control the +consumption of point tokens and the external to reset the array <code>PP</code> which +holds the point names. + +<pre><a name="NW21HcNW-cviH2-1" href="#NWD21HcNW-Y"><dfn><subroutine <tt>DrawLineOrArrow</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub DrawLineOrArrow { + my $draw_Line = shift; + my $lc = shift; + my $lineLength = -1; + my $stacklen = 0; + my @PP = (); +# if ($draw_Line != 2) { +# s/\s*//; +# if (s/^\[\s*//) { # optional length specifier +# $lineLength = expr($lc); +# if ($lineLength <= 0) { +# PrintErrorMessage("length must greater than zero",$lc); +# $lineLength = -1; +# } +# chk_rsb("optional part",$lc); +# } +# } + chk_lparen("$cmd",$lc); + DRAWLINES:while(1) { + @PP = () ; + while(1) { + if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name + $P = $1; + if (!exists($PointTable{lc($P)})) { + PrintErrorMessage("Undefined point $P",$lc); + } + else { + push (@PP,$P); + } + } + else { + $stacklen = @PP; + if ($draw_Line != 2) { + if ($stacklen <= 1) { + PrintErrorMessage("Wrong number of points",$lc); + } + else { + push(@PP,$lc); + if ($draw_Line == 0) { + drawarrows(@PP); + } + elsif ($draw_Line == 1) { + drawlines(@PP); + } + } + } + if (s/^,\s*// and $draw_Line != 2) { + next DRAWLINES; + } + else { + last DRAWLINES; + } + } + } + } + if ($draw_Line == 2) { + $stacklen = @PP; + if ($stacklen < 2) { + PrintErrorMessage("Wrong number of points",$lc); + } + elsif ($stacklen % 2 == 0) { + PrintErrorMessage("Number of points must be odd",$lc); + } + else { + drawCurve(@PP); + } + } + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + } + +</pre><p>The subroutine <code>drawarrows</code> is used to draw one or more lines. The subroutine +accepts as argument an array which contains the names of the points which +<a name="NWD21HcNW-Z">define the lines, plus the current program line number. Each arrow is printed</a> +using the following code: +<center> +<tt>\arrow < </tt>ArrowLength <tt> mm> [</tt> beta <tt>,</tt> gamma <tt>] from +x1 y1 to x2 y2 </tt> +</center> +where beta is equal to tan(<code>$arrowAngleB</code> * <code>d2r</code> /2) and gamma is equal to +2*tan(<code>$arrowAngleC</code> * <code>d2r</code> / 2). + +<pre><a name="NW21HcNW-4STZZz-1" href="#NWD21HcNW-Z"><dfn><subroutine <tt>drawarrows</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub drawarrows { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p, $q, $r12, $d12); + my ($px,$py,$pSV,$pS, $qx,$qy,$qSV,$qS); + + $NumberOfPoints = $NoArgs - 1; + LOOP: for(my $i=0; $i < $NumberOfPoints - 1; $i++) + { + $p = $_[$i]; + $q = $_[$i+1]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + ($qx,$qy,$qSV,$qS) = unpack("d3A*",$PointTable{lc($q)}); + $pSV = $defaultLFradius if $pSV == 0; + $qSV = $defaultLFradius if $qSV == 0; + $r12 = $pSV + $qSV; + $d12 = Length($px,$py,$qx,$qy); + if ($d12 <= $r12) + { + if($d12 == 0) + { + PrintErrorMessage("points $p and $q are the same", $lc); + next LOOP; + } + PrintWarningMessage("arrow $p$q not drawn: points too close or ". + "radii too big", $lc); + next LOOP; + } + ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV > 0; + ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV > 0; + my ($beta, $gamma); + $beta = tan($arrowAngleB * D2R / 2); + $gamma = 2 * tan($arrowAngleC * D2R / 2); + printf OUT "\\arrow <%.5f%s> [%.5f,%.5f] from %.5f %.5f to %.5f %.5f\n", + $arrowLength, $arrowLengthUnits, $beta, $gamma, $px, $py, $qx, $qy; + } + } + +</pre><p>The subroutine <code>drawlines</code> is used to draw one or more lines. The subroutine +accepts as argument an array which contains the names of the points which +define the lines, plus the current program line number. If there are only +two points (i.e., only one line), then we output the following PiCTeX code: +<center> +<tt> \plot x1 y1 x2 y2 / %% pointname1 pointname2</tt> +</center> +If there are more than two points, then we need to write the PiCTeX code in +pairs with two points on each line (just to keep things simple) as follows: +<center> +<tt> \plot x1 y1 x2 y2 / %% pointname1 pointname2</tt> +<tt> \plot x2 y2 x3 y3 / %% pointname2 pointname3</tt> +<tt> \plot x3 y3 x4 y4 / %% pointname3 pointname4</tt> +</center> +<a name="NWD21HcNW-a">An important part of the subroutine is devoted to checking whether either</a> +or both of the pairs of points are associated with a line-free zone, and if +so, then we must take care not to draw the line inside the line-free zone. If +a point does have a line-free zone, then we use the <code>pointOnLine</code> +subroutine to determine the point on the line which is just on the line-free +boundary, and draw the line to the that point instead of to the exact +point-location. + +<pre><a name="NW21HcNW-3KtTfB-1" href="#NWD21HcNW-a"><dfn><subroutine <tt>drawlines</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub drawlines { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p, $q, $r12, $d12); + my ($px,$py,$pSV,$pS, $qx,$qy,$qSV,$qS); + + $NumberOfPoints = $NoArgs - 1; + LOOP: for(my $i=0; $i < $NumberOfPoints - 1; $i++) + { + $p = $_[$i]; + $q = $_[$i+1]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + ($qx,$qy,$qSV,$qS) = unpack("d3A*",$PointTable{lc($q)}); + $pSV = $defaultLFradius if $pSV == 0; + $qSV = $defaultLFradius if $qSV == 0; + $r12 = $pSV + $qSV; + $d12 = Length($px,$py,$qx,$qy); + if ($d12 <= $r12) + { + if($d12 == 0) + { + PrintErrorMessage("points $p and $q are the same", $lc); + next LOOP; + } + PrintWarningMessage("line $p$q not drawn: points too close or ". + "radii too big", $lc); + next LOOP; + } + ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV > 0; + ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV > 0; + if ($px == $qx || $py == $qy) + { + printf OUT "\\putrule from %.5f %.5f to %.5f %.5f %%%% %s%s\n", + $px,$py,$qx,$qy,$p,$q; + } + else + { + printf OUT "\\plot %.5f %.5f\t%.5f %.5f / %%%% %s%s\n", + $px, $py,$qx,$qy,$p,$q; + } + } + } + +</pre><p>The subroutine <code>drawCurve</code> is used to draw a curve that passes through an odd +number of points. The subroutine has as argument an array which contains the names of the +points which define the lines plus the current program line number. The subroutine +emits code that has the following general form: +<pre> + <a name="NWD21HcNW-b">\setquadratic</a> + \plot + X1 Y1 + X2 Y2 + X3 Y3 + \setlinear +</pre> + + +<pre><a name="NW21HcNW-3c2Tgd-1" href="#NWD21HcNW-b"><dfn><subroutine <tt>drawCurve</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub drawCurve { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p); + + $NumberOfPoints = $NoArgs - 1; + print OUT "\\setquadratic\n\\plot\n"; + for(my $i=0; $i <= $NumberOfPoints; $i++) + { + $p = $_[$i]; + my ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + printf OUT "\t%0.5f %0.5f", $px, $py; + print OUT (($i == $NumberOfPoints) ? " / %$p\n" : " %$p\n"); + } + print OUT "\\setlinear\n"; + } + +</pre><p>The subroutine <code>drawpoints</code> is used to draw one or more points. The subroutine +<a name="NWD21HcNW-c">has as arguments a list of points. For each point we produce code that has</a> +the following general form: +<center> +<tt> \put {SYMBOL} at Px PY</tt> +</center> +where <code>SYMBOL</code> is either the default plot symbol, i.e., <code>$\bullet$</code>, +whatever the user has set with the <code>PointSymbol</code> command, or the plot +symbol specified in the definition of the point. + +<pre><a name="NW21HcNW-1NgToL-1" href="#NWD21HcNW-c"><dfn><subroutine <tt>drawpoints</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub drawpoints { + my ($NumberOfPoints,$p); + $NumberOfPoints = @_; + my ($px,$py,$pSV,$pS); + + for($i=0; $i < $NumberOfPoints; $i++) + { + $p = $_[$i]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + if ($pS eq "" and $defaultsymbol =~ /circle|square/) { + $pS = $defaultsymbol; + } + POINTSWITCH: { + if ($pS eq "") # no plot symbol specified + { + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", + $defaultsymbol, $px, $py, $p; + last POINTSWITCH; + } + if ($pS eq "circle") # plot symbol is a circle + { + my $radius = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} : + $GlobalDimOfPoints; + if ($radius > 0) # draw a circle using the current units + { + if ($radius == 1.5) # use \bigcirc + { + printf OUT "\\put {\$\\bigcirc\$} at %.5f %.5f %%%% %s\n", + $px, $py, $p; + } + else + { + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f %%%% %s\n", + $px+$radius, $py, $px, $py, $p; + } + } + else #use \circ symbol + { + printf OUT "\\put {\$\\circ\$} at %.5f %.5f %%%% %s\n", + $px,$py,$p; + } + last POINTSWITCH; + } + if ($pS eq "square") + { + my $side = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} : + $GlobalDimOfPoints; + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", + drawsquare($side), $px, $py, $p; + last POINTSWITCH; + } + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", $pS,$px,$py,$p; + } + } + } + +</pre><p>The subroutine <code>drawAngleArc</code> gets six arguments which correspond to +three points defining an angle (variables <code>$P1</code>, <code>$P2</code> and <code>$P3</code>), +the radius, the internal/external specification and the direction +specification (clockwise or anticlockwise). +Depending on the values of these arguments, the subroutine +returns the corresponding PiCTeX code, the general format of +which is <pre> + \circulararc Angle degrees from x y center at x2 y2 +</pre> +<a name="NWD21HcNW-d">where </a><code>Angle</code> is the angle that the three points P1 P2 P3 define +(computed by subroutine <code>Angle</code>), +and <code>x</code> and <code>y</code> are the coordinates of a point +residing on line P2P1 at distance equal to a <code>$radius</code> from +point <code>$P2</code>; and <code>x2</code>, <code>y2</code> are the coordinates of the +center of the circle about which the arc is drawn, +i.e., point <code>$P2</code>. + +<pre><a name="NW21HcNW-497AQD-1" href="#NWD21HcNW-d"><dfn><subroutine <tt>drawAngleArc</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub drawAngleArc { + my ($P1, $P2, $P3, $radius, $inout, $direction) = @_; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + + my $internalAngle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + my $externalAngle = 360 - $internalAngle; + my ($x, $y) = pointOnLine($x2, $y2, $x1, $y1, $radius); + my $code = ""; + if ($inout eq "internal" and $direction eq "clockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + -1 * $internalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "internal" and $direction eq "anticlockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + $internalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "external" and $direction eq "clockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + -1 * $externalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "external" and $direction eq "anticlockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + $externalAngle, $x, $y, $x2, $y2; + } + return $code; +} + +</pre><p><a name="NWD21HcNW-e">The subroutine </a><code>drawAngleArrow</code> gets six arguments which correspond to +three points defining an angle (variables <code>$P1</code>, <code>$P2</code> and <code>$P3</code>), +the radius, the internal/external specification and the direction +specification. The subroutine mainly draws the arrowhead, and +calls the subroutine <code>drawAngleArc</code> to draw the +arc part of the arrow. + +<pre><a name="NW21HcNW-4UPwva-1" href="#NWD21HcNW-e"><dfn><subroutine <tt>drawAngleArrow</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub drawAngleArrow { + my ($P1, $P2, $P3, $radius, $inout, $direction) = @_; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + + my $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction); + + my ($xqp, $yqp) = pointOnLine($x2, $y2, $x1, $y1, $radius); + my ($deltax, $deltay) = ($x1 - $x2, $y1 - $y2); + my $AL; + + if ($xunits =~ /mm/) { + $AL = 1; + } + elsif ($xunits =~ /cm/) { + $AL = 0.1; + } + elsif ($xunits =~ /pt/) { + $AL = 2.845; + } + elsif ($xunits =~ /bp/) { + $AL = 2.835; + } + elsif ($xunits =~ /pc/) { + $AL = 0.2371; + } + elsif ($xunits =~ /in/) { + $AL = 0.03937; + } + elsif ($xunits =~ /dd/) { + $AL = 2.659; + } + elsif ($xunits =~ /cc/) { + $AL = 0.2216; + } + elsif ($xunits =~ /sp/) { + $AL = 186467.98; + } + my $halfAL = $AL / 2; + my $d = sqrt($radius * $radius - $halfAL * $halfAL); + my $alpha = atan2($d / $halfAL, 1) * R2D; + my $beta = 2 * (90 - $alpha); + my $thetaqr; + if (abs($deltay) < 0.00001) { + if ($deltax > 0 ) {$thetaqr = 0 } + elsif ($deltax < 0) {$thetaqr = -180} + } + else { + if (abs($deltax) < 0.00001) { + $thetaqr = 90; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + } + my ($xqr, $yqr) = pointOnLine($x2, $y2, $x3, $y3, $radius); + $deltax = $x3 - $x2; + $deltay = $y3 - $y2; + $alpha = atan2(sqrt($radius * $radius - $halfAL * $halfAL) / $halfAL, 1) / + D2R; + $beta = 2 * (90 - $alpha); + LINE2 : { + if (abs($deltax) < 0.00001) { + if ($deltay > 0) { $thetaqr = 90 } + elsif ($deltay < 0) { $thetaqr = - 90 } + last LINE2; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + if (abs($deltay) < 0.00001) { + if ($deltax > 0) { $thetaqr = 0 } + elsif ($deltax < 0) { $thetaqr = -180 } + last LINE2; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + if ($deltax < 0 and $deltay > 0) { $thetaqr += 180 } + elsif ($deltax < 0 and $deltay < 0) { $thetaqr += 180 } + elsif ($deltax > 0 and $deltay < 0) { $thetaqr += 360 } + } + my $xqrleft = $x2 + $radius * cos(($thetaqr + $beta) * D2R); + my $yqrleft = $y2 + $radius * sin(($thetaqr + $beta) * D2R); + my $xqrright = $x2 + $radius * cos(($thetaqr - $beta) * D2R); + my $yqrright = $y2 + $radius * sin(($thetaqr - $beta) * D2R); + if ($inout eq "internal" and $direction eq "clockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrleft, $yqrleft, $xqr, $yqr; + } + elsif ($inout eq "internal" and $direction eq "anticlockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrright, $yqrright, $xqr, $yqr; + } + elsif ($inout eq "external" and $direction eq "clockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrleft, $yqrleft, $xqr, $yqr; + } + elsif ($inout eq "external" and $direction eq "anticlockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrright, $yqrright, $xqr, $yqr; + } + return $code; +} + +</pre><p>The subroutine <code>expr</code> is used to parse an expression. We are using a +recursive descent parser to parse and evaluate an expression. The +general syntax of an expression is as follows: +<pre> +expr ::= term { addop term } +addop ::= "+" | "-" +term ::= factor { mulop factor } +mulop ::= "*" | "/" | "rem" +factor ::= primitive [ ** factor ] +primitive ::= [ "+" | "-"] primitive | number | variable | + pair-of-points | "(" expr ")" | + "sin (" expr ")" | "cos (" expr ")" | "area (" ThreePoints ")" | + "tan (" expr ")" | "exp (" expr ")" | "int" "(" expr ")" | + "log (" expr ")" | "atan (" expr ")" | "sgn" "(" expr ")" | + <a name="NWD21HcNW-f">"sqrt (" expr ")" | "acos (" expr ")" | "asin (" expr ")" |</a> + "atan (" expr ")" | "_pi_" | "_e_" | + "xcoord (" point ")" | "ycoord (" point ")" | "angle "(" ThreePoints ")"| + "angledeg" "(" ThreePoints ")" | "direction" "(" TwoPoints ")" | + "directiondeg" "(" TwoPoints ")" | "_linethickness_" +</pre> +Note that <code>_pi_</code> and <code>_e_</code> can be used to access the value of the constants +Pi and e. + +<pre><a name="NW21HcNW-1aVxdI-1" href="#NWD21HcNW-f"><dfn><subroutine <tt>expr</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub expr { + my $lc = $_[0]; + my($left,$op,$right); + + $left = term($lc); + while ($op = addop()) { + $right = term($lc); + if ($op eq '+') + { $left += $right } + else + { $left -= $right } + } + return $left; +} + +sub addop { + s/^([+-])// && $1; +} + +sub term { + my $lc = $_[0]; + my ($left, $op, $right); + $left = factor($lc); + while ($op = mulop()) { + $right = factor($lc); + if ($op eq '*') + { $left *= $right } + elsif ($op =~ /rem/i) { + eval {$left %= $right}; + PrintFatalError("Division by zero", $lc) if $@; + } + else { + eval {$left /= $right}; + PrintFatalError("Division by zero", $lc) if $@; + } + } + return $left; +} + +sub mulop { + (s#^([*/])## || s/^(rem)//i) && lc($1); +} + +sub factor { + my $lc = $_[0]; + my ($left); + + $left = primitive($lc); + if (s/^\*\*//) { + $left **= factor($lc); + } + return $left; +} + +sub primitive { + my $lc = $_[0]; + my $val; + s/\s*//; + if (s/^\(//) { #is it an expr in parentheses + $val = expr($lc); + s/^\)// || PrintErrorMessage("Missing right parenthesis", $lc); + } + elsif (s/^-//) { # is it a negated primitive + $val = - primitive(); + } + elsif (s/^\+//) { # is it a positive primitive + $val = primitive(); + } + elsif (s/^angledeg//i) { + chk_lparen("angledeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $d12 = Length($x1, $y1, $x2, $y2); + my $d23 = Length($x2, $y2, $x3, $y3); + my $d31 = Length($x3, $y3, $x1, $y1); + if ( $d12 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_2' are the same", $lc); + $val = 0; + } + elsif ( $d23 == 0 ) { + PrintErrorMessage("points `$point_2' and `$point_3' are the same", $lc); + $val = 0; + } + elsif ( $d31 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_3' are the same", $lc); + $val = 0; + } + else { + $val = Angle($x1, $y1, $x2, $y2, $x3, $y3); + $val = 0 if $val == -500; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^angle//i) { + chk_lparen("angle".$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $d12 = Length($x1, $y1, $x2, $y2); + my $d23 = Length($x2, $y2, $x3, $y3); + my $d31 = Length($x3, $y3, $x1, $y1); + if ( $d12 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_2' are the same", $lc); + $val = 0; + } + elsif ( $d23 == 0 ) { + PrintErrorMessage("points `$point_2' and `$point_3' are the same", $lc); + $val = 0; + } + elsif ( $d31 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_3' are the same", $lc); + $val = 0; + } + else { + $val = Angle($x1, $y1, $x2, $y2, $x3, $y3); + if ($val == -500) { + $val = 0; + } + else { + $val = D2R * $val; + } + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^area//i) { + chk_lparen("angledeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + $val = triangleArea($x1, $y1, $x2, $y2, $x3, $y3); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^asin//i) { + chk_lparen("asin"); + $val = expr(); + PrintFatalError("Can't take asin of $val", $lc) if $val < -1 || $val > 1; + $val = asin($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^acos//i) { + chk_lparen("acos"); + $val = expr(); + PrintFatalError("Can't take acos of $val", $lc) if $val < -1 || $val > 1 ; + $val = acos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^atan//i) { + chk_lparen("atan"); + $val = expr(); + $val = atan($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^cos//i) { + chk_lparen("cos"); + $val = expr(); + $val = cos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^directiondeg//i) { + chk_lparen("directiondeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $x3 = $x1+1; + if ( ($y2 - $y1) >= 0) { + $val = Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + } + else { + $val = 360 - Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^direction//i) { + chk_lparen("direction",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $x3 = $x1+1; + if ( ($y2 - $y1) >= 0) { + $val = Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + $val = D2R * $val; + } + else { + $val = 360 - Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + $val = D2R * $val; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^exp//i) { + chk_lparen("exp"); + $val = expr(); + $val = exp($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^int//i) { + chk_lparen("int"); + $val = expr(); + $val = int($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^log//i) { + chk_lparen("log"); + $val = expr(); + PrintFatalError("Can't take log of $val", $lc) if $val <= 0; + $val = log($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sin//i) { + chk_lparen("sin"); + $val = expr(); + $val = sin($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sgn//i) { + chk_lparen("sgn"); + $val = expr(); + if ($val > 0) { + $val = 1; + } + elsif ($val == 0) { + $val = 0; + } + else { + $val = -1; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sqrt//i) { + chk_lparen("sqrt"); + $val = expr(); + $val = sqrt($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^tan//i) { + chk_lparen("tan"); + $val = expr(); + $val = sin($val)/cos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^xcoord//i) { + chk_lparen("xcoord"); + my $point_name = get_point; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_name}); + $val = $x1; + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^ycoord//i) { + chk_lparen("ycoord"); + my $point_name = get_point; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_name}); + $val = $y1; + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^_pi_//i) { + $val = PI; + } + elsif (s/^_e_//i) { + $val = 2.71828182845905; + } + elsif (s/^_linethickness_//i) { + $val = $LineThickness / $xunits; + } + else { + my $err_code; + ($val,$err_code) = ComputeDist($lc); + } + s/\s*//; + return $val; +} + +</pre><p><a name="NWD21HcNW-g">The subroutine </a><code>memberOf</code> is used to check whether a string is part of +a list of strings. We assume that the first argument is the string in +question. We compare each list element against the string in question and +if we find it we stop and return the value <code>1</code> (denoting truth). Otherwise, +we simply return the value <code>0</code> (denoting false). + +<pre><a name="NW21HcNW-2tc9Fr-1" href="#NWD21HcNW-g"><dfn><subroutine <tt>memberOf</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub memberOf { + my $elem = shift(@_); + + my $found = 0; + foreach $item (@_){ + if ($item eq $elem){ + $found = 1; + last; + } + } + return $found; +} + +</pre><p><a name="NWD21HcNW-h">The subroutine </a><code>tand</code> computes the tangent of an angle. The angle is +supposed to be in degrees. We simply transform it into radians and then +compute the actual result. + +<pre><a name="NW21HcNW-22jtMr-1" href="#NWD21HcNW-h"><dfn><subroutine <tt>tand</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub tand { + my $d = $_[0]; + $d = $d * PI / 180; + return sin($d)/cos($d); +} + +</pre><p>The subroutine <code>get_string</code> is used to extract a leading valid mathspic string +from the input line. A string must start with a quotation mark, i.e., <code>"</code>, +and must end with the same symbol. A string may contain quotation marks which +must be escaped with a backslash, i.e., <code>\</code>. Initially, we remove all +leading white space. If the next character of the string is not a quotation +mark we print an error message and stop. Otherwise, we split the string into +an array of characters and store the characters up to the next quotation +mark to the array <code>@cmd</code>. In case the next character is a backslash and +we aren't at the end of the input string and the next character is a +quotation mark, we have an escape sequence. This means that we store these +two characters in the <code>@cmd</code> array and skip to characters after the quotation +mark. Otherwise, we simply store the character in the <code>@cmd</code> array and +<a name="NWD21HcNW-i">skip to the next character. This process is repeated until either we consume</a> +all the characters of the string or until we find a sole quotation mark. +Since we are not sure what has forced the loop to exit, we check whether +there are still characters in the input string and we check whether this +is a quotation mark. If these tests fail we have a string without a +closing quotation mark. In all cases we return a triplet consisting of +a number denoting success (1) or failure (0) and what we have consumed +from the input string, and what is left from the input string. + +<pre><a name="NW21HcNW-ufkvF-1" href="#NWD21HcNW-i"><dfn><subroutine <tt>get_string</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub get_string { + my $string = shift; + my $lc = shift; + + $string =~ s/^\s+//; + if ($string !~ s/^\"//) { + PrintErrorMessage("No starting \" found",$lc); + return (1,$string,$string); + } + my @ch = split //,$string; + my @cmd; + while (@ch and $ch[0] ne "\"") { + if ($ch[0] eq "\\" and (defined $ch[1]) and $ch[1] eq "\"") { + shift @ch; + push @cmd, $ch[0]; + shift @ch; + } + else { + push @cmd, $ch[0]; + shift @ch; + } + } + if (! defined $ch[0]) { + PrintErrorMessage("No closing \" found",$lc); + return (1,join("",@cmd), join("",@ch)) + } + else { + shift @ch; + return (0, join("",@cmd), join("",@ch)) + } +} + +</pre><p><a name="NWD21HcNW-j">The definition as well as an explanation of the functionality of the</a> +following subroutine can be found in "Programming Perl", 3rd edition. + +<pre><a name="NW21HcNW-1MGdDt-1" href="#NWD21HcNW-j"><dfn><subroutine <tt>is_tainted</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub is_tainted { + my $arg = shift; + my $nada = substr($arg,0,0); + local $@; + eval { eval "# $nada"}; + return length($@) != 0; +} + +</pre><p><a name="NWD21HcNW-k">The subroutine </a><code>noOfDigits</code> has one argument which is a number and returns +the number of decimal digits it has. If the number matches the regular +expression <code>^\d+(?!\.)</code> (a series of digits <i>not</i> followed by a +period), then the number of decimal digits is zero. If the +number matches the +regular expression <code>^\d+\.(\d+)?</code>, then number of decimal digits equals +<code>length($1)</code>. Naturally, it maybe zero! + +<pre><a name="NW21HcNW-3mBo7s-1" href="#NWD21HcNW-k"><dfn><subroutine <tt>noOfDigits</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub noOfDigits { + my $num = $_[0]; + + if ($num =~ /^[\+-]?\d+(?!\.)/) { + return 0; + } + elsif ($num =~ /^[\+-]\d+\.(\d+)?/) { + return length($1); + } +} + +</pre><p><a name="NWD21HcNW-l">Subroutine </a><code>drawsquare</code> is use by the <code>drawpoints</code> routine to plot a +point whose point symbol is a square. The subroutine has one argument, which is +equal to the radius of the point. From this argument it computes the side of +the square. + +<pre><a name="NW21HcNW-3ywJ89-1" href="#NWD21HcNW-l"><dfn><subroutine <tt>drawsquare</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub drawsquare { + my $s = $_[0]; + #$s *= sqrt(2); + $s = sprintf "%.5f", $s; + my $code = "\\setlength{\\unitlength}{$xunits}%\n"; + $code .= "\\begin{picture}($s,$s)\\put(0,0)" . + "{\\framebox($s,$s){}}\\end{picture}"; + return $code; +} + +</pre><p><a name="NWD21HcNW-m">Subroutine </a><code>X2sp</code> has two arguments: a number and a length unit. It returns +the length expresssed in sp units. + +<pre><a name="NW21HcNW-39f7o8-1" href="#NWD21HcNW-m"><dfn><subroutine <tt>X2sp</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub X2sp { + my $LT = shift; + my $units = shift; + + if ($units eq "pc") { + return $LT * 786432; + } + elsif ($units eq "pt") { + return $LT * 65536; + } + elsif ($units eq "in") { + return $LT * 4736286.72; + } + elsif ($units eq "bp") { + return $LT * 65781.76; + } + elsif ($units eq "cm") { + return $LT * 1864679.811023622; + } + elsif ($units eq "mm") { + return $LT * 186467.981102362; + } + elsif ($units eq "dd") { + return $LT * 70124.086430424; + } + elsif ($units eq "cc") { + return $LT * 841489.037165082; + } + elsif ($units eq "sp") { + return $LT; + } +} + + +</pre><p><a name="NWD21HcNW-n">Subroutine </a><code>sp2X</code> has two arguments: a number that denotes a length in sp units + and a length unit. It returns the length expresssed in units that are specified by + the second argument. + +<pre><a name="NW21HcNW-3wV39i-1" href="#NWD21HcNW-n"><dfn><subroutine <tt>sp2X</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub sp2X { + my $LT = shift; + my $units = shift; + + if ($units eq "pc") { + return $LT / 786432; + } + elsif ($units eq "pt") { + return $LT / 65536; + } + elsif ($units eq "in") { + return $LT / 4736286.72; + } + elsif ($units eq "bp") { + return $LT / 65781.76; + } + elsif ($units eq "cm") { + return $LT / 1864679.811023622; + } + elsif ($units eq "mm") { + return $LT / 186467.981102362; + } + elsif ($units eq "dd") { + return $LT / 70124.086430424; + } + elsif ($units eq "cc") { + return $LT / 841489.037165082; + } + elsif ($units eq "sp") { + return $LT; + } +} + +</pre><p><a name="NWD21HcNW-o">Subroutine </a><code>setLineThickness</code> takes two arguments: the value of the variable + <code>$xunits</code> and a string denoting the linethickness. It returns the linthickness + expressed in the units of the <code>$xunits</code>. + +<pre><a name="NW21HcNW-4XWBBY-1" href="#NWD21HcNW-o"><dfn><subroutine <tt>setLineThickness</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> +sub setLineThickness { + my $Xunits = shift; + my $LT = shift; + $Xunits =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//; + my $xlength = "$1"; + $Xunits =~ s/^\s*($units)//; + my $x_in_units = $1; + $LT =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//; + my $LTlength = "$1"; + $LT =~ s/^\s*($units)//; + my $LT_in_units = $1; + $LTlength = X2sp($LTlength,$LT_in_units); + $LTlength = sp2X($LTlength,$x_in_units); + return $LTlength; +} + +</pre><p>The subroutine <code>process_input</code> accepts one argument which is a file handle +that corresponds to the file that the subroutine is supposed to process. +The processing cycle is fairly simple: we input one line at the time, remove +any leading space characters and the trailing new line character, and then +start the actual processing. The variable <code>$INFILE</code> contains the name of +the input file and the variable <code>$lc</code> is the local line counter. The +commands <code>beginSkip</code> and <code>endSkip</code> can be used to ignore blocks +of code and so we need to process them here. The variable <code>$no_output</code> +is used as a switch to toggle from process mode to no-precess mode. +<a name="NWD21HcNW-p">If the first token is </a><code>beginSkip</code>, we set the variable <code>$no_output</code> to 1, +print a comment to the output file and continue with the next input line. +If the first token is <code>endSkip</code>, we check whether we are in a no-process +mode. If this is the case, we revert to process mode; otherwise we print +an error message. Finally, depending on whether we are in process or no-process +mode we process the input text or simply printed commented out to the output +file. Note, that we don't allow nested comment blocks, as this makes really +no sense! + +<pre><a name="NW21HcNW-1RrLPF-1" href="#NWD21HcNW-p"><dfn><subroutine <tt>process_input</tt> >=</dfn></a> <b>(<a href="#NWD21HcNW-9"><-U</a>)</b> + sub process_input { + my ($INFILE,$currInFile) = @_; + my $lc = 0; + my $no_output = 0; + $curr_in_file = $currInFile; + LINE: while(<$INFILE>) { + $lc++; + chomp($command = $_); + s/^\s+//; + if (/^beginSkip\s*/i) { + $no_output = 1; + print OUT "%%$_" if $comments_on; + next LINE; + } + elsif (/^endSkip\s*/i) { + if ($no_output == 0) { + PrintErrorMessage("endSkip without beginSkip",$lc); + } + else { + $no_output = 0; + } + print OUT "%%$_" if $comments_on and !$no_output; + next LINE; + } + elsif ($no_output == 1) { + next LINE; + } + else { + if (/^[^\\]/) { + my $out_line = mpp($command,$lc) unless /^\\/; #call macro pre-processor + $_ = "$out_line\n"; + } + <a name="NW21HcNW-1RrLPF-1-u1" href="#NWD21HcNW-q"><i><process input line></i></a> + } + } + } + +</pre><p>Each command line starts with a particular <i>token</i> and depending on +which one we have we perform different actions. If the first character +is <code>%</code> we have a comment line, and depending on the value of the variable +<code>$comments_on</code> we either output the comment on the output file (default +action) or just ignore it and continue with the next input line. In case the +first token is the name of a valid command we process the command and +output the corresponding code. Otherwise, we print an error message to +the screen and to the log file and continue with the next input line. +Note that the input language is case-insensitive and so one is free to write a +command name using any combination of upper and lower case +letters, e.g., the tokens <code>lAtEx</code>, +<code>LaTeX</code>, and <code>latex</code> are considered exactly the same. +The valid <i>MathsPIC</i> commands are the following (don't pay attention +to the case!): +<ul> +<li> +Commands <code>drawAngleArc</code> and <code>drawAngleArrow</code> are used to draw an arc and an +arrow, respectively. Since, their user interface is identical, we process +them as if they were identical commands. +</li> +<li> +Command <code>drawcircle</code> is used to draw a circle with a specified radius. +</li> +<li> +Command <code>drawCircumCircle</code> is used to draw the circumcircle of triangle +specified by three points. +</li> +<li> +Command <code>drawexcircle</code> is used to draw the excircle of triangle +relative to a given side of the triangle. +</li> +<li> +Command <code>drawincircle</code> is used to draw the incircle of triangle. +</li> +<li> +Command <code>drawincurve</code> is used to draw a curve that passes through a number of points. +</li> +<li> Command <code>drawline</code> is used to draw either +a line (not necessarily a straight one) or a number of lines from a list +or lists of points. The lines are specified as pairs of points that can +be separated by blank spaces. +<li> Command <code>drawthickline</code> is used to draw either +a thick line (not necessarily a straight one) or a number of lines from a list +or lists of points. The lines are specified as pairs of points that can +be separated by blank spaces. +</li> +<li> +Command <code>drawPerpendicular</code> draws a perpendicular line from point A to +line BC. +</li> +<li> Command <code>drawpoint</code> is used to draw one, two or more points. +The point names can be separated by blanks. +</li> +<li> +Command <code>drawRightAngle</code> draws an angle, specified by three points, +of a size specified by a side length. +</li> +<li> +Command <code>drawsquare</code> draws a square, centered at the coordinates of the +first arguments, which is assumed to be a point, with side equal to the +second argument. +</li> +<li> +Command <code>inputfile*</code> is used to verbatim include a file into the output +file. +</li> +<li> +Command <code>inputfile</code> is used to include a <i>MathsPIC</i> program file +into the main file. +</li> +<li> +Command <code>linethickness</code> should be used to set the thickness of lines. +</li> +<li> +The <code>paper</code> command sets the paper scale, size, axes, etc. The most +general format of the command follows: +<center> +<tt>paper{units(mm), xrange(0,120), yrange(0,100),axes(LRTB)}</tt> +</center> +Note, that one may opt not to write the commas between the different +parts of command. +</li> +<li> +Command <code>point*</code> allocates <i>new</i> co-ordinates and optionally +a T<sub>E</sub>X point-name, to an existing point-name. +Command <code>point</code> allocates co-ordinates and, optionally a T<sub>E</sub>X +point character, to a <i>new</i> point-name. Since, both commands have +identical syntax, we handle them together. +</li> +<li> Command <code>PointSymbol</code> is used to set or reset the default +point symbol, i.e., when one plots a point this is the symbol that will +appear on the final DVI/PostScript file. +</li> +<li> +In the original DOS version of <tt>mathspic</tt> the command +<code>setPointNumber</code> was used to set the length of the arrays that keep the +various point related information. Since, in Perl arrays are dynamic objects +and one can push as many objects as he/she wants, the command is implemented +as an no-op. For reasons of compatibility, we only check the syntax of the +command. +</li> +<li> +Commands <code>showAngle</code> and <code>showArea</code> can be used to get +the angle or the area determined by three points. In addition, the command +<code>showLenght</code> can be used to get the length between two points. These three +commands produce a comment to the output file. +</li> +<li> The <code>system</code> command provides a shell escape. +</li> +<li> +The <code>text</code> command is used to put a symbol/text at a +particular point location. +</li> +<li> +Command <code>var</code> is used to store a numeric value into a comma separated +list of variables. +</li> +<li> +Command <code>const</code> is used to store a numeric value into a comma separated +list of variables, whose value cannot be altered. +</li> +<li> +<a name="NWD21HcNW-q">If a line starts with a backslash, </a><code>\</code>, then we copy verbatim this +line to the output file. In case the second character is a space character, +then we simply output a copy of the line without the leading backslash. +</li> +</ul> +Empty lines are always ignored. + +<pre><a name="NW21HcNW-RKDir-1" href="#NWD21HcNW-q"><dfn><process input line>=</dfn></a> <b>(<a href="#NWD21HcNW-p"><-U</a>)</b> + + if (/^\s*%/) + { + print OUT "$_" if $comments_on; + } + elsif (s/^\s*(beginloop(?=\W))//i) { + s/\s+//; + my $times = expr($lc); + print OUT "%% BEGINLOOP $times\n" if $comments_on; + my @C = (); + REPEATCOMMS: while (<$INFILE>) { + if (/^\s*endloop/i) { + last REPEATCOMMS; + } + else { + push @C, $_; + } + } + if (! /^\s*endloop/i) { + PrintFatalError("unexpected end of file",$lc); + } + else { + s/^\s*endloop//i; + for(my $i=1; $i<=$times; $i++) { + tie *DUMMY, 'DummyFH', \@C; + process_input(DUMMY, $currInFile); + untie *DUMMY; + } + print OUT "%% ENDLOOP\n" if $comments_on; + } + } + elsif (s/^\s*(ArrowShape(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u1" href="#NWD21HcNW-1V"><i><process <tt>ArrowShape</tt> command></i></a> + } + elsif (s/^\s*(const(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u2" href="#NWD21HcNW-1b"><i><process <tt>const</tt> command></i></a> + } + elsif (s/^\s*(dasharray(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u3" href="#NWD21HcNW-r"><i><process <tt>dasharray</tt> command></i></a> + } + elsif (s/^\s*(drawAngleArc(?=\W))//i or s/^\s*(drawAngleArrow(?=\W))//i ) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u4" href="#NWD21HcNW-s"><i><process <tt>drawAngleArcOrArrow</tt> command></i></a> + } + elsif (s/^\s*(drawArrow(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(0,$lc); + } + elsif (s/^\s*(drawcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u5" href="#NWD21HcNW-v"><i><process <tt>drawcircle</tt> command></i></a> + } + elsif (s/^\s*(drawcurve(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(2,$lc); + } + elsif (s/^\s*(drawcircumcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u6" href="#NWD21HcNW-w"><i><process <tt>drawcircumcircle</tt> command></i></a> + } + elsif (s/^\s*(drawexcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u7" href="#NWD21HcNW-x"><i><process <tt>drawexcircle</tt> command></i></a> + } + elsif (s/^\s*(drawincircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u8" href="#NWD21HcNW-y"><i><process <tt>drawincircle</tt> command></i></a> + } + elsif (s/^\s*(drawline(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(1,$lc); + } + elsif (s/^\s*(drawthickarrow(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n"; + print OUT "{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n"; + print OUT " \\global\\linethickness=0.31\\wd1}%\n"; + DrawLineOrArrow(0,$lc); + print OUT "\\setlength{\\linethickness}{0.4pt}%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + } + elsif (s/^\s*(drawthickline(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n"; + print OUT "{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n"; + print OUT " \\global\\linethickness=0.31\\wd1}%\n"; + DrawLineOrArrow(1,$lc); + print OUT "\\setlength{\\linethickness}{0.4pt}%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + } + elsif (s/^\s*(drawperpendicular(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u9" href="#NWD21HcNW-z"><i><process <tt>drawPerpendicular</tt> command></i></a> + } + elsif (s/^\s*(drawpoint(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u10" href="#NWD21HcNW-10"><i><process <tt>drawpoint</tt> command></i></a> + } + elsif (s/^\s*(drawRightAngle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u11" href="#NWD21HcNW-11"><i><process <tt>drawRightAngle</tt> command></i></a> + } + elsif (s/^\s*(drawsquare(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u12" href="#NWD21HcNW-12"><i><process <tt>drawsquare</tt> command></i></a> + } + elsif (s/^\s*inputfile\*//i) + { + <a name="NW21HcNW-RKDir-1-u13" href="#NWD21HcNW-13"><i><process <tt>inputfile*</tt> command></i></a> + } + elsif (s/^\s*(inputfile(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u14" href="#NWD21HcNW-14"><i><process <tt>inputfile</tt> command></i></a> + } + elsif (s/^\s*(linethickness(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u15" href="#NWD21HcNW-15"><i><process <tt>linethickness</tt> command></i></a> + } + elsif (s/^\s*(paper(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u16" href="#NWD21HcNW-16"><i><process <tt>paper</tt> command></i></a> + } + elsif (s/^\s*(PointSymbol(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u17" href="#NWD21HcNW-1W"><i><process <tt>PointSymbol</tt> command></i></a> + } + elsif (s/^\s*point(?=\W)//i) + { + my ($Point_Line); + chomp($Point_Line=$_); + <a name="NW21HcNW-RKDir-1-u18" href="#NWD21HcNW-1H"><i><process <tt>point/point*</tt> commands></i></a> + } + elsif (/^\s*setPointNumber(?=\W)/i) + { + PrintWarningMessage("Command setPointNumber is ignored",$lc); + next LINE; + } + elsif (s/^\s*(showAngle(?=\W))//i) + { + <a name="NW21HcNW-RKDir-1-u19" href="#NWD21HcNW-1A"><i><process <tt>showAngle</tt> command></i></a> + } + elsif (s/^\s*(showArea(?=\W))//i) + { + <a name="NW21HcNW-RKDir-1-u20" href="#NWD21HcNW-1B"><i><process <tt>showArea</tt> command></i></a> + } + elsif (s/^\s*(showLength(?=\W))//i) + { + <a name="NW21HcNW-RKDir-1-u21" href="#NWD21HcNW-1C"><i><process <tt>showLength</tt> command></i></a> + } + elsif (/^\s*showPoints(?=\W)/i) + { + print OUT "%%-------------------------------------------------\n"; + print OUT "%% L I S T O F P O I N T S \n"; + print OUT "%%-------------------------------------------------\n"; + foreach my $p (keys(%PointTable)) { + my ($x, $y, $pSV, $pS) = unpack("d3A*",$PointTable{$p}); + printf OUT "%%%%\t%s\t= ( %.5f, %.5f ), LF-radius = %.5f, symbol = %s\n", + $p, $x, $y, $pSV, $pS; + } + print OUT "%%-------------------------------------------------\n"; + print OUT "%% E N D O F L I S T O F P O I N T S \n"; + print OUT "%%-------------------------------------------------\n"; + next LINE; + } + elsif (/^\s*showVariables(?=\W)/i) + { + print OUT "%%-------------------------------------------------\n"; + print OUT "%% L I S T O F V A R I A B L E S \n"; + print OUT "%%-------------------------------------------------\n"; + foreach my $var (keys(%VarTable)) { + print OUT "%%\t", $var, "\t=\t", $VarTable{$var}, "\n"; + } + print OUT "%%-------------------------------------------------\n"; + print OUT "%% E N D O F L I S T O F V A R I A B L E S \n"; + print OUT "%%-------------------------------------------------\n"; + next LINE; + } + elsif (s/^\s*(system(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u22" href="#NWD21HcNW-1X"><i><process <tt>system</tt> command></i></a> + } + elsif (s/^\s*(text(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u23" href="#NWD21HcNW-1Y"><i><process <tt>text</tt> command></i></a> + } + elsif (s/^\s*(var(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <a name="NW21HcNW-RKDir-1-u24" href="#NWD21HcNW-1c"><i><process <tt>var</tt> command></i></a> + } + elsif (/^\s*\\(.+)/) + { + my $line = $1; + if ($line =~ /^\s+(.+)/) + { + print OUT " $line\n"; + } + else + { + print OUT "\\$line\n"; + } + next LINE; + } + elsif (0==length) #empty line + { + next LINE; + } + else { + PrintErrorMessage("command not recognized",$lc); + next LINE; + } + +</pre><p>Command <code>dasharray</code> takes an arbitrary number of arguments that are used to +specify a dash pattern. Its general syntax follows: +<center> + <tt> "dasharray" "(" d<sub>1</sub> "," g<sub>1</sub> "," d<sub>2</sub> "," + g<sub>2</sub> "," ... ")"</tt> +</center> +where <tt>d<sub>i</sub></tt> denotes the length of a dash and <tt>g<sub>i</sub></tt> +<a name="NWD21HcNW-r">denotes the length of gap between two consecutive dashes. Each </a><tt>d<sub>i</sub></tt> +and <tt>g<sub>i</sub></tt> is a length (i.e., a number accompanied by a length of unit). +Since we do not a priori know the number of arguments, we push them onto a stack and +then we produce a command of the form +<center> + <tt> \setdashpattern < d<sub>1</sub>, g<sub>1</sub>, d<sub>2</sub>, + g<sub>2</sub>, ...></tt> +</center> + +<pre><a name="NW21HcNW-19jqyn-1" href="#NWD21HcNW-r"><dfn><process <tt>dasharray</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen($cmd,$lc); + my @DashArray = (); + my $dash = ""; + my $dashpattern = ""; + PATTERN: while (1) { + $dash = sprintf("%.5f", expr($lc)); + if (s/^\s*($units)//i) { + push (@DashArray, "$dash$1"); + } + else { + PrintErrorMessage("Did not found unit after expression", $lc); + } + s/\s*//; + if (/^[^,]/) { + last PATTERN; + } + else { + s/^,\s*//; + } + } + print OUT "\\setdashpattern <"; + while (@DashArray) { + $dashpattern .= shift @DashArray; + $dashpattern .= ","; + } + $dashpattern =~ s/,$//; + print OUT $dashpattern, ">\n"; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +</pre><p>The command <code>drawAngleArc</code> draws an arc in the specified angle, a +distance <i>radius</i> from the angle. The angle is either <i>internal</i> +(<= 180 degrees) or <i>external</i> (>180 degrees). The direction of the +arc is either <i>clockwise</i> or <i>anticlockwise</i>. The command +<code>drawAngleArrow</code> draws an arrow just like the command <code>drawAngleArc</code> +draws an arc. The syntax of these commands is as follows: +<pre> + cmds ::= ( "drawAngleArc" | "drawAngleArrow" ) args + args ::= "{" angle comma radius comma internal comma clockwise "}" + angle ::= "angle" "(" three-points ")" + radius ::= "radius" "(" distance ")" + distance ::= expression + internal ::= "internal" | "external" + clockwise ::= "clockwise" | "anticlockwise" + comma ::= "," | empty +</pre> +We first collect all relevant information by parsing the <code>args</code> and then +call the either the subroutine <code>drawAngleArc</code> or the subroutine +<code>drawAngleArrow</code> to produce the actual code +which is then printed into the output file. In order to be able to distinguish +which command we are dealing with we simply use the variable <code>$cmd</code>. +<a name="NWD21HcNW-s">We now start parsing the input line. We first check whether there is a</a> +left curly bracket. Next, we parse the <code>angle</code>, the <code>distance</code>, the +<code>internal</code> and the <code>clockwise</code> parts of the command. Finally, we check +for right curly bracket and a trailing comment. Depending on +the value of +the variable <code>$cmd</code> we call either the subroutine <code>drawAngleArc</code> or the +subroutine <code>drawAngleArrow</code>. These subroutines return the code that will be +finally output to the output file. + +<pre><a name="NW21HcNW-12lwO-1" href="#NWD21HcNW-s"><dfn><process <tt>drawAngleArcOrArrow</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lcb($cmd,$lc); + <a name="NW21HcNW-12lwO-1-u1" href="#NWD21HcNW-t"><i><process <tt>angle</tt> part of command></i></a> + s/^,\s*// or s/\s*//; #parse optional comma + <a name="NW21HcNW-12lwO-1-u2" href="#NWD21HcNW-u"><i><process <tt>radius</tt> part of command></i></a> + s/^,\s*// or s/\s*//; #parse optional comma + my $inout = ""; + if (s/^(internal(?=\W))//i or s/^(external(?=\W))//i) { + $inout = $1; + } + else { + PrintErrorMessage("Did not find expected 'internal' specifier", $lc); + next LINE; + } + s/^,\s*// or s/\s*//; #parse optional comma + my $direction = ""; + if (s/^(clockwise(?=\W))//i or s/^(anticlockwise(?=\W))//i) { + $direction = $1; + } + else { + PrintErrorMessage("Did not find expected 'direction' specifier", $lc); + next LINE; + } + chk_rcb("arguments of $cmd",$lc); + chk_comment($lc); + my $code; + if (lc($cmd) eq "drawanglearc") { + $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction); + } + else { + $code = drawAngleArrow($P1, $P2, $P3, $radius, $inout, $direction); + } + print OUT $code if $code ne ""; + +</pre><p><a name="NWD21HcNW-t">We first check whether the first token is the word </a><code>angle</code>. In case it +isn't, this yields an unrecoverable error. In case the expected word is +there, we check for a left parenthesis. Next, we parse the three points that +must follow. For this purpose we use the user-defined subroutine +<code>get_point</code>. Now we check that the angle has a reasonable value, i.e., if +it is less than -400 or equal to zero, the value yields an unrecoverable error. +We finish by checking whether there is a right parenthesis. + +<pre><a name="NW21HcNW-4X9wPg-1" href="#NWD21HcNW-t"><dfn><process <tt>angle</tt> part of command>=</dfn></a> <b>(<a href="#NWD21HcNW-s"><-U</a>)</b> + my ($P1, $P2, $P3); + if (s/^angle(?=\W)//i) { + chk_lparen("token angle of command $cmd",$lc); + $P1 = get_point($lc); + next LINE if $P1 eq "_undef_"; + $P2 = get_point($lc); + next LINE if $P2 eq "_undef_"; + $P3 = get_point($lc); + next LINE if $P3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + my $Angle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + if ($Angle <= 0) { + if ($Angle == 0) { + PrintErrorMessage("Angle is equal to zero",$lc); + next LINE; + } + elsif ($Angle < -400) { + PrintErrorMessage("Something is wrong with the points",$lc); + next LINE; + } + } + chk_rparen("angle part of command $cmd",$lc); + } + else { + PrintErrorMessage("Did not find expected angle part",$lc); + next LINE; + } + +</pre><p><a name="NWD21HcNW-u">In this section we parse the </a><code>radius</code> part of the <code>drawAngleArc</code> or the +<code>drawAngleArrow</code> command. We first check whether the next token is the word +<code>radius</code>. If it is not, then we continue with the next line. + +<pre><a name="NW21HcNW-2mAaDL-1" href="#NWD21HcNW-u"><dfn><process <tt>radius</tt> part of command>=</dfn></a> <b>(<a href="#NWD21HcNW-s"><-U</a>)</b> + + my $radius; + if (s/^radius(?=\W)//i) { + chk_lparen("token radius of command $cmd",$lc); + $radius = expr($lc); + chk_rparen("radius part of command $cmd",$lc); + } + else { + PrintErrorMessage("Did not found expected angle part",$lc); + next LINE; + } + +</pre><p>Command <code>drawcircle</code> accepts two arguments--a point name that is +used to specify the center of the circle and the radius of the circle. +The radius is simply an expression, whose value must be greater than zero. +Otherwise, we print an error message and continue with the next input line. +The general syntax of the command is as follows: +<pre> + "drawcircle" "(" point-name "," rad ")" +</pre> +The code we emit for a point with coordinates <code>x</code> and <code>y</code> and for radius +equal to <code>R</code> is: +<pre> + \circulararc 360 degrees from X y center at x y +</pre> +where <code>X = x+R</code>.<p> +<a name="NWD21HcNW-v">Initially, we check whether there is an opening left parenthesis. Next,</a> +we get the point name by using the subroutine <code>get_point</code> which +issues an error message if the point hasn't been defined. In this +case we stop processing the command, as there is absolutely no reason to +do otherwise. Next, we parse the comma and then the radius by using +the subroutine <code>ComputeDist</code>. If there is no problem, we emit the code +and finally we check for a closing right parenthesis and for +possible garbage that may follow the command. + +<pre><a name="NW21HcNW-EIAAh-1" href="#NWD21HcNW-v"><dfn><process <tt>drawcircle</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("drawcircle",$lc); + my $Point = get_point($lc); + next LINE if $Point eq "_undef_"; + chk_comma($lc); + my $R = expr($lc); + if ($R <= 0) { + PrintErrorMessage("Radius must be greater than zero",$lc); + next LINE; + } + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{lc($Point)}); + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $x+$R, $y, $x, $y; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +</pre><p>Command <code>drawcircumcircle</code> is used to draw the circumcircle of triangle +specified by three points which are the arguments of the command. We start +by parsing the opening left parenthesis. Next, we get the three points +that define the triangle. We are now able to compute the center and +the radius of the circumcircle by calling the subroutine <code>circumCircleCenter</code>. +If the triangle area is equal to zero, then this subroutine will return +the array <code>(0,0,0)</code> to indicate this fact. +We now have all necessary information to draw the circumcircle. We use the +<a name="NWD21HcNW-w">following code to do the job:</a> +<pre> + \circulararc 360 degrees from X y center x y +</pre> +where <code>x</code> and <code>y</code> are the coordinates of the center, <code>R</code> its +radius and <code>X=x+R</code>. What is left is to check whether there is a +closing right parenthesis and any trailing garbage. + + +<pre><a name="NW21HcNW-1HqG4z-1" href="#NWD21HcNW-w"><dfn><process <tt>drawcircumcircle</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("drawcircumcircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + my ($xc, $yc,$r) = circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc); + next LINE if $xc == 0 and $yc == 0 and $r == 0; + print OUT "%% circumcircle center = ($xc,$yc), radius = $r\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$r, $yc, $xc, $yc; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +</pre><p>The syntax of the <code>drawexcircle</code> command is as follows: +<pre> + drawexcircle ::= "drawexcircle" "(" ThreePoints "," TwoPoints ")" + [ modifier ] + modifier ::= "[" expr "]" + +</pre> +The <code>modifier</code> is an expression that is used to modify the radius of the +excicle. We start by checking whether there is a left parenthesis. Then we +get names of the three points. In case any of the points is not defined +we issue an error message and continue with the next input line. Next, we +check whether there is a comma that separates the three points defining the +triangle from the two points defining a side of the triangle (variables +<code>$point1</code>, <code>$point2</code>, and <code>$point3</code>). Moreover, we must ensure that +the area of the area defined by these points is not equal to +zero. If it is we issue an error message and we continue with the next +input line. Now, we are ready to get the two +point names that define the side of the triangle (variables <code>$point3</code> and +<code>$point5</code>). At this point we must make sure that these points are different +points and that they are members of the list of points that define the triangle. +We make this check by calling the subroutine <code>memberOf</code>. Next, we check +whether there is a closing right parenthesis. We now compute the center +and the radius of the excircle by calling the subroutine <code>excircle</code>. The +coordinates of the center are stored in the variables <code>$xc</code> and <code>$yc</code>, +while the radius is stored in the variable <code>$r</code>. If the next +non-blank input character is a left square bracket, then we know the user has +specified the optional part. We use the subroutine <code>expr</code> to get the value of +the optional part. The value of the optional part is stored in the variable <code>$R</code>. +At this point we check whether the sum of the radius +plus the optional part is equal to zero and if it is we continue with the +next input line. Next, we check for a closing right square bracket. We are +<a name="NWD21HcNW-x">now ready to emit the source code. The first thing we must check is that</a> +the radius is not too big for PiCTeX, i.e., not greater than 500/2.845. +Then we print some informative text to the output file and of course the +actual code. We use the following code to do the job: +<pre> + \circulararc 360 degrees from (xc+R) yc center xc yc +</pre> +The last thing we check is whether there is some trailing garbage. + +<pre><a name="NW21HcNW-Wbuba-1" href="#NWD21HcNW-x"><dfn><process <tt>drawexcircle</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("drawexcircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) < 0.0001) { + PrintErrorMessage("Area of triangle is zero!",$lc); + next LINE; + } + chk_comma($lc); + my $point4 = get_point($lc); + if (!memberOf($point4, $point1, $point2, $point3)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + next LINE if $point4 eq "_undef_"; + my $point5 = get_point($lc); + next LINE if $point5 eq "_undef_"; + if (!memberOf($point5, $point1, $point2, $point3)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + if ($point4 eq $point5) { + PrintErrorMessage("Side points are identical",$lc); + next LINE; + } + chk_rparen("arguments of $cmd",$lc); + my ($xc, $yc, $r) = excircle($point1, $point2, $point3, + $point4, $point5); + my $R=$r; + if (s/^\s*\[\s*//) { + $R += expr($lc); + if ($R < 0.0001) { + PrintErrorMessage("Radius has become equal to zero!",$lc); + next LINE; + } + chk_rsb($lc); + } + if ($R > (500 / 2.845)) { + PrintErrorMessage("Radius is greater than 175mm!",$lc); + next LINE; + } + print OUT "%% excircle center = ($xc,$yc) radius = $R\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$R, $yc, $xc, $yc; + chk_comment($lc); + +</pre><p>The syntax of the <code>drawincircle</code> command is as follows: +<pre> + drawincircle ::= "drawincircle" "(" ThreePoints ")" [ modifier] + modifier ::= "[" expr "]" +</pre> +where <code>ThreePoints</code> correspond to the points defining the triangle and +<code>modifier</code> is an optional modification factor. +The first thing we do is to check whether +there is an opening left parenthesis. Then we get the names of the three +points that define the triangle (variables <code>$point1</code>, <code>$point2</code>, +and <code>$point3</code>). Next, we make sure that the area of the +triangle defined by these three points is not equal to zero. If it is, then +we issue an error message and continue with the next input line. Now, we +compute the center and the radius of the incircle (variables <code>$xc</code>, <code>$yc</code>, +and <code>$r</code>). If the next non-blank input character is a left square bracket, +then we now the user has specified the optional part. We use subroutine +<code>expr</code> to get the value of the optional part. The value of +the optional part +is stored in the variable <code>$R</code>. At this point we check whether the sum of the +radius plus the optional part is equal to zero and if it is we continue with +the next input line. Next, we check for a closing right square bracket. +<a name="NWD21HcNW-y">We are now ready to emit the source code. The first thing we must check is</a> +that the radius is not too big for PiCTeX, i.e., not greater than 500/2.845. +Then we print some informative text to the output file and of course the +actual code. We use the following code to do the job: +<pre> + \circulararc 360 degrees from (xc+R) yc center xc yc +</pre> +The last thing we check is whether there is some trailing garbage. + +<pre><a name="NW21HcNW-3GJ2p7-1" href="#NWD21HcNW-y"><dfn><process <tt>drawincircle</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("drawincircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) < 0.0001) { + PrintErrorMessage("Area of triangle is zero!",$lc); + next LINE; + } + my ($xc, $yc, $r) = IncircleCenter($x1,$y1,$x2,$y2,$x3,$y3); + my $R=$r; + if (s/^\s*\[\s*//) { + $R += expr($lc); + if ($R < 0.0001) { + PrintErrorMessage("Radius has become equal to zero!",$lc); + next LINE; + } + chk_rsb($lc); + } + if ($R > (500 / 2.845)) { + PrintErrorMessage("Radius is greater than 175mm!",$lc); + next LINE; + } + print OUT "%% incircle center = ($xc,$yc) radius = $R\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$R, $yc, $xc, $yc; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +</pre><p>The command <code>drawPerpendicular</code> command draws a line from point A to line +BC, such that it is perpendicular to line BC. The general syntax of the +command is as follows: +<pre> + drawPenpedicular ::= "drawPenpedicular" "(" Point "," TwoPoints ")" +</pre> +The first thing we do is to parse the left parenthesis. Then we parse +the name of the first point, namely <code>$A$</code>. If this point is undefined +we print an error message and continue with the next line. Next, we parse +the expected leading comma and the names of the other two points. Certainly, +in case either of these two points has not been defined, we simply print an +error message and continue with the next input line. Finally, we check for +a closing right parenthesis and a possible trailing comment. Now we are +ready to compute the coordinates of the foot of the +perpendicular line. We do so my calling subroutine +<code><a name="NWD21HcNW-z">perpendicular</a></code>. Certainly, before we do this we have to get the +coordinates of the points that we have parsed. Finally, we output the +PiCTeX code: +<pre> + \plot x1 y1 xF xY / +</pre> +where <code>x1</code> and <code>y1</code> are coordinates of the point A and <code>xF</code> and <code>yF</code> +the coordinates of the foot. + +<pre><a name="NW21HcNW-4OiWfi-1" href="#NWD21HcNW-z"><dfn><process <tt>drawPerpendicular</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen($cmd,$lc); + my $A = get_point($lc); + next LINE if $A eq "_undef_"; + chk_comma($lc); + my $B = get_point($lc); + next LINE if $A eq "_undef_"; + s/\s*//; #ignore white space + my $C = get_point($lc); + next LINE if $A eq "_undef_"; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + # + #start actual computation + # + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$A}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$B}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$C}); + my ($xF, $yF) = perpendicular($x1, $y1, $x2, $y2, $x3, $y3); + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $x1, $y1, $xF, $yF; + +</pre><p>The <code>drawpoint</code> command has a number of points as arguments and produces +PiCTeX code that draws a plot symbol at the coordinates of each point. The +syntax of the command is as follows: +<pre> + drawpoint ::= "drawpoint" "(" Point { separator Point } ")" +</pre> +The <code>while</code> loop is used to consume all points that are +<a name="NWD21HcNW-10">between an opening left parenthesis and a closing right parenthesis. All</a> +points are pushed on the local array <code>PP</code>. When we have parsed the lists +of points, we call the subroutine <code>drawpoints</code> to emit the actual PiCTeX code. +Finally, we check whether there is a closing parenthesis +parenthesis, and whether +there is some trailing text that makes no sense. In case there are no points +between the parentheses, then we issue an appropriate error message and +we continue with the next input line. + +<pre><a name="NW21HcNW-2EC5Ei-1" href="#NWD21HcNW-10"><dfn><process <tt>drawpoint</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + my ($stacklen); + chk_lparen("$cmd",$lc); + if (/^\)/) { + PrintErrorMessage("There are no point to draw",$lc); + next LINE; + } + my(@PP); + DRAWPOINTS:while(1) { + if (s/^([^\W\d_]\d{0,3})//i) { #point name + $P = $1; + if (!exists($PointTable{lc($P)})) { + PrintErrorMessage("Undefined point $P",$lc); + next DRAWPOINTS; + } + else { + push (@PP,$P); + s/\s*//; + } + } + else { + last DRAWPOINTS; + } + } + drawpoints(@PP); + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +</pre><p>The syntax of the <code>drawRightAngle</code> command is as follows: +<pre> + drawRightAngle "(" ThreePoints "," dist ")" + dist ::= expr | TwoPoints +</pre> +Before we proceed with the actual computation we parse the left parenthesis, +the three points, the comma, the <code>dist</code>, and the right parenthesis. In case +we have neither three points nor a <code>dist</code> we print an error message and +continue with the next input line, i.e., these errors are irrecoverable. +The names of the three points are stored in variables <code>$point1</code>, +<code>$point2</code>, and <code>$point3</code>. The value of the distance is stored +in the variable <code>$dist</code>. +Let's now explain the semantics of this command.<p> + +Our aim is to draw lines S<sub>1</sub>-S, S<sub>2</sub>-S (S<sub>1</sub> +and S<sub>2</sub> are at distance d from B). All the relevant points are +depicted in the following figure: +<center> +<img src="fig1.jpg"> +</center> +Some notes are in order: +<ol> +<li> BS bisects angle ABC, and meets AC in Q, so start by determining point +Q, then determine S, and then S<sub>1</sub> and S<sub>2</sub>, and then +draw S<sub>1</sub>-S and S<sub>2</sub>-S.</li> +<li> Distance AQ is given by AC/(1+tan(BCA))</li> +<li> The coordinates of Q are computed using the subroutine <code>pointOnLine</code>.</li> +<li> Now we compute the coordinates of S on line BQ.</li> +<li> We compute the coordinates of S<sub>1</sub> and S<sub>2</sub> by using +The subroutine <code>pointOnLine</code>.</li> +</ol> +<a name="NWD21HcNW-11">In order to implement the above steps we first compute the length of the line</a> +AB. Note that A is <code>$point1</code>, etc. Next we compute the angle BAC. Now +we compute the distance AQ (variable <code>$line1</code>). The coordinates of point +Q are stored in variables <code>$xQ</code> and <code>$yQ</code>. The coordinates of point +S are stored in variables <code>$xS</code> and <code>$yS</code>. Now we have to determine the +coordinates of points S<sub>1</sub> and S<sub>2</sub>. These coordinates +are stored in variables <code>$xS1</code>, <code>$yS1</code> and <code>$xS2</code>, <code>$yS2</code>, +respectively. Finally, we emit the PiCTeX target code. + +<pre><a name="NW21HcNW-2KJKP6-1" href="#NWD21HcNW-11"><dfn><process <tt>drawRightAngle</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen("drawRightAngle",lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + chk_comma($lc); + my $dist = expr($lc); + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + # + #actual computation + # + my $lengthAC = Length($x1, $y1, $x3, $y3); + my $angleBAC = Angle($x2, $y2, $x1, $y1, $x3, $y3); + my $line1 = $lengthAC / (1 + tand($angleBAC)); + # + # determine coordinates of point Q + # + my ($xQ, $yQ) = pointOnLine($x1, $y1, $x3, $y3, $line1); + # + # determine coordinates of point S + # + my $deltax = $xQ - $x2; + my $deltay = $yQ - $y2; + my $lengthBQ = sqrt($deltax * $deltax + $deltay * $deltay); + my $xS = $x2 + ($dist * sqrt(2) * $deltax / $lengthBQ); + my $yS = $y2 + ($dist * sqrt(2) * $deltay / $lengthBQ); + # + # determine coordinates of points S1 and S2 + # + my ($xS1, $yS1) = pointOnLine($x2, $y2, $x3, $y3, $dist); + ($xS2, $yS2) = ($xS, $yS); + # + # emit PiCTeX code + # + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $xS1, $yS1, $xS2, $yS2; + ($xS1, $yS1) = pointOnLine($x2, $y2, $x1, $y1, $dist); + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $xS1, $yS1, $xS2, $yS2; + +</pre><p><a name="NWD21HcNW-12">The command </a><code>drawsquare</code> has two arguments: a point, which specifies the +coordinates of the point where the square will be placed, and a number, which +specifies the length of the side of the square. The syntax of the command is as follows: +<center> + <tt> "drawSquare" "(" Point "," expression ")" </tt> +</center> +Note that RWDN has suggested to alter the value of the <code>$side</code> variable (see the +line with <code>RWDN</code> comment). + +<pre><a name="NW21HcNW-2lxjRF-1" href="#NWD21HcNW-12"><dfn><process <tt>drawsquare</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("drawSquare",$lc); + my $p = get_point($lc); + chk_comma($lc); + my $side = expr($lc); + $side = $side - (1.1 * $LineThickness/$xunits); #Suggested by RWDN + my ($x,$y,$pSV,$pS) = unpack("d3A*",$PointTable{$p}); + printf OUT "\\put {%s} at %.5f %.5f %%drawsquare\n", drawsquare($side), $x, $y; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +</pre><p>The argument of the <code>inputfile*</code> command is a file name that is always +enclosed in parentheses: +<pre> + starred-input-file ::= "inputfile*" "(" file-name ")" + file-name ::= (alpha | period) { alpha | period } + alpha ::= letter | digit | "_" | "-" +</pre> +<a name="NWD21HcNW-13">Note, that the input file is assumed to contain TeX code.</a> +We first check to see if there is a left parenthesis. Then we consume +the file name. We check if the file exists and then we copy verbatim the +input file to the output file. Next, we check for the closing parenthesis. +Now, if there is a trailing comment we copy it to the output file depending +on the value of the variable <code>$comments_on</code>, else if there is some other +text we simply ignore it and issue a warning message. + +<pre><a name="NW21HcNW-fJuCf-1" href="#NWD21HcNW-13"><dfn><process <tt>inputfile*</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("inputfile*",$lc); + my $row_in = ""; + if (s/^((\w|-|\.)+)//) { + $row_in = $1; + } + else { + PrintErrorMessage("No input file name found",$lc); + next LINE; + } + if (!(-e $row_in)) { + PrintErrorMessage("File $row_in does not exist",$lc); + next LINE; + } + open(ROW, "$row_in")|| die "Can't open file $row_in\n"; + while (defined($in_line=<ROW>)) { print OUT $in_line; } + print OUT "%% ... end of input file <$row_in>\n"; + close ROW; + chk_rparen("input file name",$lc); + chk_comment($lc); + + +</pre><p>The <code>inputfile</code> command has at most two arguments, second being +optional: a file name enclosed in curly brackets and the number of +times this file should be included in square brackets: +<pre> + inputfile ::= "inputfile" "(" file-name ")" [ Times ] + <a name="NWD21HcNW-14">Times ::= "[" expr "]"</a> +</pre> +Note that the input file is assumed to contain mathspic commands. In addition, if +the expression is equal to a decimal number, it is truncated. +As in the case of the <code>inputfile*</code> command we parse the left parenthesis, +the file name, the right parenthesis and the optional argument if it exists. +In order to process the commands contained in the input file, we call +The subroutine <code>process_input</code>. + +<pre><a name="NW21HcNW-2EQO3c-1" href="#NWD21HcNW-14"><dfn><process <tt>inputfile</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen("inputfile",$lc); + my $comm_in = ""; + if (s/^((\w|-|\.)+)//) { + $comm_in = $1; + } + else { + PrintErrorMessage("No input file name found",$lc); + next LINE; + } + if (!(-e $comm_in)) { + PrintErrorMessage("File $comm_in does not exist",$lc); + next LINE; + } + chk_rparen("input file name",$lc); + my $input_times = 1; #default value + if (s/^\[//) { + $input_times = expr($lc); + chk_rsb("optional argument",$lc); + } + print OUT "%% ... start of file <$comm_in> loop [$input_times]\n"; + for (my $i=0; $i<int($input_times); $i++) { + open(COMM,"$comm_in") or die "Can't open file $comm_in\n"; + print OUT "%%% Iteration number: ",$i+1,"\n"; + my $old_file_name = $curr_in_file; + process_input(COMM,"File $comm_in, "); + $curr_in_file = $old_file_name; + close COMM; + } + print OUT "%% ... end of file <$comm_in> loop [$input_times]\n"; + chk_comment($lc); + +</pre><p><a name="NWD21HcNW-15">The </a><code>linethickness</code> command should be used to set the thickness of lines. +The command has one argument, which is a length or the word <code>default</code>. +The default line thickness is 0.4 pt. + +<pre><a name="NW21HcNW-1t58ZF-1" href="#NWD21HcNW-15"><dfn><process <tt>linethickness</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("linethickness", $lc); + if (s/^default//i) { + print OUT "\\linethickness=0.4pt\\Linethickness{0.4pt}%%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + $LineThickness = setLineThickness($xunits,"0.4pt"); + } + else { + my $length = expr($lc); + if (s/^\s*($units)//i) { + my $units = $1; + printf OUT "\\linethickness=%.5f%s\\Linethickness{%.5f%s}%%\n", + $length, $units, $length, $units; + $LineThickness = setLineThickness($xunits,"$length$units"); + my $mag; + if ($units eq "pc") { + $mag = $length * 12; + } + elsif ($units eq "in") { + $mag = $length * 72.27; + } + elsif ($units eq "bp") { + $mag = $length * 1.00375; + } + elsif ($units eq "cm") { + $mag = $length * 28.45275; + } + elsif ($units eq "mm") { + $mag = $length * 2.845275; + } + elsif ($units eq "dd") { + $mag = $length * 1.07001; + } + elsif ($units eq "cc") { + $mag = $length * 0.08917; + } + elsif ($units eq "sp") { + $mag = $length * 0.000015259; + } + elsif ($units eq "pt") { + $mag = $length; + } + $mag = 10 * $mag / 1.00278219; + printf OUT "\\font\\CM=cmr10 at %.5fpt%%\n", $mag; + print OUT "\\setplotsymbol ({\\CM .})%\n"; + } + else { + PrintErrorMessage("Did not found expect units part",$lc); + } + } + chk_rparen("linethickness", $lc); + chk_comment($lc); + + +</pre><p>We first output the input line as a comment into the output file. Now, +after the <code>paper</code> token we look for an opening brace. Then we process +the <code>units</code> part of the command, if the token <code>units</code> is present. Note +that the <code>units</code> part is optional. Next we process the <code>xrange</code> and the +<code>yrange</code> part of the command, which are also optional parts of the command. +We are now ready to process the <code>axis</code> part. Note, that the user is allowed +to alternatively specify this part with the word <code>axes</code>. +<a name="NWD21HcNW-16">The variable </a><code>$axis</code> +is supposed to hold the various data relate to the <code>axis</code> part. The last +thing we check is the <code>ticks</code> part. In case the user has not specified +this part we assume that both ticks are equal to zero. If everything is +according to the language syntax, we expect a closing right curly bracket. +Now, that we have all relevant information we can output the rest of the code, +as some parts of it have already been output during parsing. The last thing we +do is to check whether there is any trailing comment. + +<pre><a name="NW21HcNW-1Pby5X-1" href="#NWD21HcNW-16"><dfn><process <tt>paper</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lcb("paper", $lc); + if (s/^units(?=\W)//i) + { + <a name="NW21HcNW-1Pby5X-1-u1" href="#NWD21HcNW-17"><i><process <tt>unit</tt> part></i></a> + $nounits = 0; + } + else + { + $nounits = 1; + } + s/^,\s*// or s/\s*//; + if (s/^xrange//i) + { + <a name="NW21HcNW-1Pby5X-1-u2" href="#NWD21HcNW-18"><i><process <tt>xrange</tt> part></i></a> + $noxrange = 0; + } + else + { + $noxrange = 1; + } + s/^,\s*// or s/\s*//; + if (s/^yrange//i) + { + <a name="NW21HcNW-1Pby5X-1-u3" href="#NWD21HcNW-19"><i><process <tt>yrange</tt> part></i></a> + $noyrange = 0; + } + else + { + $noyrange = 1; + } + <a name="NW21HcNW-1Pby5X-1-u4" href="#NWD21HcNW-1D"><i><generate plot area related commands></i></a> + s/^,\s*// or s/\s*//; + $axis = ""; + if (s/^ax[ei]s(?=\W)//i) + { + <a name="NW21HcNW-1Pby5X-1-u5" href="#NWD21HcNW-1E"><i><process <tt>axis</tt> part></i></a> + } + $axis = uc($axis); + s/^,\s*// or s/\s*//; + if (s/^ticks(?=\W)//i) + { + <a name="NW21HcNW-1Pby5X-1-u6" href="#NWD21HcNW-1F"><i><process <tt>ticks</tt> part></i></a> + } + else + { + $xticks = $yticks = 0; + } + chk_rcb("paper", $lc); + <a name="NW21HcNW-1Pby5X-1-u7" href="#NWD21HcNW-1G"><i><generate the rest of the code for the <tt>paper</tt> command></i></a> + chk_comment($lc); + +</pre><p><a name="NWD21HcNW-17">We first check whether there is a left parenthesis. Next, we check</a> +whether there is decimal number or a variable name. In case there isn't one we assume it +is the number 1. Now, we get the units. If there is no valid unit, we issue +an error and the x-unit is set to its default value. In case, there is +a trailing comma, we assume the user wants also to specify the y-unit and +we process this part just like we did with the x-unit part. Finally, we +output the corresponding PiCTeX command. In case there is no y-unit +we assume it is equal to the x-unit. + +<pre><a name="NW21HcNW-15UlOC-1" href="#NWD21HcNW-17"><dfn><process <tt>unit</tt> part>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> + + chk_lparen("units",$lc); + if(s/^\)//) + { + PrintWarningMessage("Missing value in \"units\"--default is 1pt", + $lc); + $xunits = "1pt"; + } + else { + $xunits = expr($lc); + s/\s*//; + if (s/^($units)//i) { + $xunits .= "$1"; + $LineThickness = setLineThickness($xunits,"0.4pt"); + } + elsif(s/^(\w)+//i) { + PrintErrorMessage("$1 is not a valid mathspic unit",$lc); + $xunits = "1pt"; + } + else { + PrintErrorMessage("No x-units found",$lc); + $xunits = "1pt"; + } + s/\s*//; #ignore white space + if (s/^,//) { # there is a comma so expect an y-units + s/\s*//; #ignore white space + $yunits = expr($lc); + s/\s*//; #ignore white space + if (s/^($units)//i) { + $yunits .= "$1"; + } + elsif(s/^(\w)+//i) { + PrintErrorMessage("$1 is not a valid mathspic unit",$lc); + $yunits = "1pt"; + } + else { + PrintErrorMessage("No y-units found",$lc); + $yunits = $xunits; + } + } + else { + $yunits = $xunits; + } + chk_rparen("units",$lc); + } + +</pre><p><a name="NWD21HcNW-18">The </a><code>xrange</code> token must be followed by a left parenthesis, so we +check whether the next token is a left parenthesis. We store in the variables +<code>$xlow</code> and <code>$xhigh</code> the values of the range. The range is specified +as pair of decimal numbers/variable/pair of points, separated by a +comma. We use the subroutine <code>ComputeDist</code> to get the value of the lower +end and the upper end of the range. The last thing we check is whether +the lower end is less than the upper end. If this isn't the case we +issue an error message and we skip into the next input line. + +<pre><a name="NW21HcNW-39noUt-1" href="#NWD21HcNW-18"><dfn><process <tt>xrange</tt> part>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> + + chk_lparen("xrange",$lc); + my $ec; + ($xlow,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($xhigh,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + if ($xlow >= $xhigh) + { + PrintErrorMessage("xlow >= xhigh in xrange",$lc); + next LINE; + } + chk_rparen("$xhigh",$lc); + +</pre><p><a name="NWD21HcNW-19">The </a><code>yrange</code> token must be followed by a left parenthesis, so we +check whether the next token is a left parenthesis. We store in the variables +<code>$ylow</code> and <code>$yhigh</code> the values of the range. The range is specified +as pair of decimal numbers/variable/pair of points, separated by a +comma. We use the subroutine <code>ComputeDist</code> to get the value of the lower +end and the upper end of the range. The last thing we check is whether +the lower end is less than the upper end. If this isn't the case we +issue an error message and we skip into the next input line. + +<pre><a name="NW21HcNW-3SApmu-1" href="#NWD21HcNW-19"><dfn><process <tt>yrange</tt> part>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> + + chk_lparen("yrange",$lc); + my $ec; + ($ylow,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($yhigh,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + if ($ylow >= $yhigh) + { + PrintErrorMessage("ylow >= yhigh in yrange",$lc); + next LINE; + } + chk_rparen("$yhigh",$lc); + +</pre><p><a name="NWD21HcNW-1A">The </a><code>showAngle</code> command has three arguments that correspond to three distinct +points and emits a comment of the form: +<center> +<tt>%% angle(ABC) = 45</tt> +</center> +Note that the computed angle is expressed in degrees. + +<pre><a name="NW21HcNW-2ObcXb-1" href="#NWD21HcNW-1A"><dfn><process <tt>showAngle</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("showangle",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $angle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + $angle = 0 if $angle == -500; + printf OUT "%%%% angle(%s%s%s) = %.5f deg ( %.5f rad)\n", $point_1, + $point_2, $point_3, $angle, $angle*D2R; + chk_rparen("Missing right parenthesis", $lc); + +</pre><p><a name="NWD21HcNW-1B">The </a><code>showArea</code> command has three arguments that correspond to three distinct +points and emits a comment of the form: +<center> +<tt>%% area(ABC) = 45</tt> +</center> +Note that the computed angle is expressed in degrees. + +<pre><a name="NW21HcNW-2THNRJ-1" href="#NWD21HcNW-1B"><dfn><process <tt>showArea</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("showarea",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + print OUT "%% area($point_1$point_2$point_3) = ", + triangleArea($x1, $y1, $x2, $y2, $x3, $y3), "\n"; + chk_rparen("Missing right parenthesis", $lc); + +</pre><p><a name="NWD21HcNW-1C">The </a><code>showLength</code> command has two arguments that correspond to two distinct +points and emits a comment of the form: +<center> +<tt>%% length(AB) = 45</tt> +</center> +Note that the computed angle is expressed in degrees. + +<pre><a name="NW21HcNW-Ofe1b-1" href="#NWD21HcNW-1C"><dfn><process <tt>showLength</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + chk_lparen("showlength",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + print OUT "%% length($point_1$point_2) = ", + Length($x1, $y1, $x2, $y2), "\n"; + chk_rparen("Missing right parenthesis", $lc); + + +</pre><p><a name="NWD21HcNW-1D">If the user hasn't specified units then we use the previous values to</a> +set the coordinate system. If the user hasn't specified either the +<code>xunits</code> part or the <code>yunits</code>, then we don't emit code. In case he/she +has specified both parts we generate the command that sets the plot area. + +<pre><a name="NW21HcNW-2SitZA-1" href="#NWD21HcNW-1D"><dfn><generate plot area related commands>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> + + if (!$nounits) + { + printf OUT "\\setcoordinatesystem units <%s,%s>\n", + $xunits,$yunits; + } + if(!$noxrange && !$noyrange) + { + printf OUT "\\setplotarea x from %.5f to %.5f, y from %.5f to %.5f\n", + $xlow, $xhigh, $ylow, $yhigh; + + } + +</pre><p>We first check to see whether there is an opening left parenthesis. Next +<a name="NWD21HcNW-1E">we get the various options the user may have entered. The valid options</a> +are the letters L, R, T, B, X, and Y. These letters may be followed by +an optional star <code>*</code> with space characters between the letter and the star. +We use a loop, that stops when a right parenthesis is found, to +go through all +possible arguments and append each argument in the string <code>$axis</code>. Note +one can have blank space between different arguments. The last thing we do is +to check for the closing right parenthesis. + +<pre><a name="NW21HcNW-19Hy2D-1" href="#NWD21HcNW-1E"><dfn><process <tt>axis</tt> part>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> + + chk_lparen("axis",$lc); + while(/^[^\)]/) + { + if (s/^([lrtbxy]{1}\*?)//i) + { + $axis .= $1; + } + elsif (s/^([^lrtbxy])//i) + { + PrintErrorMessage("Non-valid character \"$1\" in axis()",$lc); + } + s/\s*//; + } + chk_rparen("axis(arguments",$lc); + +</pre><p>As usual we start by skipping white space. Next we check whether there is +<a name="NWD21HcNW-1F">an opening left parenthesis. Now, we expect two numbers/variables/pair of</a> +point representing the <code>ticks</code> increment value. These <code>ticks</code> increment +values must be separated by a comma (and possibly some white space around +them). We use the subroutine <code>ComputeDist</code> to get the value of the <code>ticks</code> +increment value and we assign to the variables <code>$xticks</code> and <code>$yticks</code> +the value of x-ticks and y-ticks increment value. In case there is a +problem we issue an error message and continue with the next line. The last +thing we check is whether there is a closing right parenthesis. + +<pre><a name="NW21HcNW-1isLLJ-1" href="#NWD21HcNW-1F"><dfn><process <tt>ticks</tt> part>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> + chk_lparen("ticks",$lc); + my $ec; + ($xticks,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($yticks,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_rparen("ticks(arguments",$lc); + +</pre><p><a name="NWD21HcNW-1G">We actually emit code if the user has specified either the </a><code>X</code> or +<code>Y</code> option in the <code>axis</code> part. If the user has specified the +<code>Y*</code> or the <code>X*</code> option in the axis part, we just emit the commands +<code>\axis left shiftedto x=0</code> or <code>\axis bottom shiftedto y=0</code> respectively +and exit. If the use has specified ticks, then, depending on the options +he had supplied with the <code>axis</code> part, we emit code that +implements the user's wishes. +**** HERE WE MUST EXPLAIN THE MEANING OF THE CODE EMITTED!!! ***** + +<pre><a name="NW21HcNW-2gFm3I-1" href="#NWD21HcNW-1G"><dfn><generate the rest of the code for the <tt>paper</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-16"><-U</a>)</b> +YBRANCH: { + if (index($axis, "Y")>-1) + { + if (index($axis, "Y*")>-1) + { + print OUT "\\axis left shiftedto x=0 / \n"; + last YBRANCH; + } + if ($yticks > 0) + { + if (index($axis, "T")>-1 && index($axis, "B")==-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT "$ylow to -$yticks by $yticks\n from $yticks to "; + print OUT $yhigh-$yticks," by $yticks /\n"; + } + elsif (index($axis, "T")==-1 && index($axis, "B")>-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT $ylow+$yticks," to -$yticks by $yticks\n from "; + print OUT "$yticks to $yhigh by $yticks /\n"; + } + elsif (index($axis, "T")>-1 && index($axis, "B")>-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT $ylow+$yticks," to -$yticks by $yticks\n from "; + print OUT "$yticks to ",$yhigh-$yticks," by $yticks /\n"; + } + else + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT "$ylow to -$yticks by $yticks\n from "; + print OUT "$yticks to $yhigh by $yticks /\n"; + } + } + else + { + print OUT "\\axis left shiftedto x=0 /\n"; + } + } + } + XBRANCH: { if (index($axis, "X")>-1) + { + if (index($axis, "X*")>-1) + { + print OUT "\\axis bottom shiftedto y=0 /\n"; + last XBRANCH; + } + if ($xticks > 0) + { + if (index($axis, "L")>-1 && index($axis, "R")==1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT $xlow + $xticks," to -$xticks by $xticks\n from"; + print OUT " $xticks to $xhigh by $xticks /\n"; + } + elsif (index($axis, "L")==-1 && index($axis, "R")>-1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT "$xlow to -$xticks by $xticks\n from "; + print OUT "$xticks to ",$xhigh-$xticks," by $xticks /\n"; + } + elsif (index($axis, "L")>-1 && index($axis, "R")>-1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT $xlow + $xticks," to -$xticks by $xticks\n from "; + print OUT "$xticks to ",$xhigh - $xticks," by $xticks /\n"; + } + else + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT "$xlow to -$xticks by $xticks\n from "; + print OUT "$xticks to $xhigh by $xticks /\n"; + } + } + else + { + print OUT "\\axis bottom shiftedto y=0 /\n"; + } + } } + LBRANCH: {if (index($axis, "L")>-1) + { + if (index($axis, "L")>-1) + { + if (index($axis, "L*")>-1) + { + print OUT "\\axis left /\n"; + last LBRANCH; + } + if ($yticks > 0) + { + print OUT "\\axis left ticks numbered from "; + print OUT "$ylow to $yhigh by $yticks /\n"; + } + else + { + print OUT "\\axis left /\n"; + } + } + } } + RBRANCH: { if (index($axis, "R")>-1) + { + if (index($axis, "R*")>-1) + { + print OUT "\\axis right /\n"; + last RBRANCH; + } + if ($yticks > 0) + { + print OUT "\\axis right ticks numbered from $ylow to $yhigh by "; + print OUT "$yticks /\n"; + } + else + { + print OUT "\\axis right /\n"; + } + } } + TBRANCH: { if (index($axis, "T")>-1) + { + if (index($axis, "T*")>-1) + { + print OUT "\\axis top /\n"; + last TBRANCH; + } + if ($xticks > 0) + { + print OUT "\\axis top ticks numbered from $xlow to $xhigh by "; + print OUT "$xticks /\n"; + } + else + { + print OUT "\\axis top /\n"; + } + } } + BBRANCH: { if (index($axis, "B")>-1) + { + if (index($axis, "B*")>-1) + { + print OUT "\\axis bottom /\n"; + last BBRANCH; + } + if ($xticks > 0) + { + print OUT "\\axis bottom ticks numbered from $xlow to $xhigh by "; + print OUT "$xticks /\n"; + } + else + { + print OUT "\\axis bottom /\n"; + } + } } + + +</pre><p>The syntax of the <code>point</code> commands follows: +<pre> +point[*](PointName){Coordinates}[PointSymbol] +</pre> +where <code>PointName</code> is valid point name, <code>Coordinates</code> is either a +pair of numbers denoting the coordinates of the point or an expression +by means of which the system computes the coordinates of the point, and +the <code>PointSymbol</code> is a valid T<sub><font size=+1>E</font></sub>X +command denoting a point symbol. A valid point name consists of a +letter and at most two trailing digits. That is, the names <code>a11</code>, +<code>b2</code> and <code>c</code> are valid names while <code>qw</code> and <code>s123</code> are not. +The first thing we do is to set the point shape to the default symbol +(this has been initialized in the main program). Next, we check whether +we have a <code>point</code>command or a <code>point*</code> simply by inspecting the very +next token. Note that there must be no blank spaces between the token +<code>point</code> and the star symbol. Next, we get the point name: remember that +<a name="NWD21HcNW-1H">the point name is surrounded by parentheses. In case we don't find a valid</a> +point name we issue an error message and continue with the next line of +input. Suppose the point name was a valid one. If we have a <code>point*</code> +command we must ensure that the this particular point name has been defined. +If we have a <code>point</code> command we must ensure that this particular point +name has not been defined. Point names are stored in the hash <code>%PointTable</code>. +We are now ready to process the coordinates part and the optional +plot symbol part. + +<pre><a name="NW21HcNW-2bvYBY-1" href="#NWD21HcNW-1H"><dfn><process <tt>point/point*</tt> commands>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + my ($pointStar, $PointName, $origPN); + $pointStar = 0; # default value: he have a point command + $pointStar = 1 if s/^\*//; + chk_lparen("point" . (($pointStar)?"*":""),$lc); + if (s/^([^\W\d_](?![^\W\d_])\d{0,3})//i) { + # + # Note: the regular expression (foo)(?!bar) means that we are + # looking a foo not followed by a bar. Moreover, the regular + # expression [^\W\d_] means that we are looking for letter. + # + $origPN = $1; + $PointName = lc($1); + } + else { + PrintErrorMessage("Invalid point name",$lc); + next LINE; + } + #if ($pointStar and !exists($PointTable{$PointName})) { + # PrintWarningMessage("Point $origPN has not been defined",$lc); + #} + if (!$pointStar and exists($PointTable{$PointName})) { + PrintWarningMessage("Point $origPN has been used already",$lc); + } + chk_rparen("point" . (($pointStar)?"*":""). "($origPN",$lc); + chk_lcb("point" . (($pointStar)?"*":""). "($origPN)",$lc); + my ($Px, $Py); + <a name="NW21HcNW-2bvYBY-1-u1" href="#NWD21HcNW-1I"><i><process coordinates></i></a> + chk_rcb("coordinates part",$lc); + my $sv = $defaultsymbol; + my $sh = $defaultLFradius; + my $side_or_radius = undef; + if (s/^\[\s*//) { # the user has opted to specify the optional part + <a name="NW21HcNW-2bvYBY-1-u2" href="#NWD21HcNW-1U"><i><process optional point shape part></i></a> + chk_rsb("optional part",$lc); + } + # to avoid truncation problems introduced by the pack function, we + # round each number up to five decimal digits + $Px = sprintf("%.5f", $Px); + $Py = sprintf("%.5f", $Py); + print OUT "%% point$Point_Line \t$origPN = ($Px, $Py)\n" if $comments_on; + chk_comment($lc); + $PointTable{$PointName} = pack("d3A*",$Px,$Py,$sh,$sv); + if (defined($side_or_radius)) { + $DimOfPoint{$PointName} = $side_or_radius; + } + +</pre><p>In this section we parse the <code>Coordinates</code> part of the <code>point</code> command. +The complete syntax of the <code>Coordinates</code> part follows: +<pre> +Coordinates ::= Variable | + Distance "," Distance | + "midpoint" "(" Point-Name Point-Name ")" | + "pointOnLine" "(" Two-Points "," Distance ")" | + "intersection" "(" Two-Points "," Two-Points ")" | + "perpendicular" "(" Point-Name "," Two-Points ")" | + "circumCircleCenter" "(" Three-Points ") | + "incircleCenter" "(" Three-Points ")" | + "excircleCenter" "(" Three-Points "," Two-Points ")" | + Point-Name [ "," Modifier ] + +Modifier ::= "shift" "(" Distance "," Distance ")" | + "polar" "(" Distance, Distance [ "deg" | "rad" ] ")" | + "rotate" "(" Point-Name, Distance [ "deg" | "rad" ] ")" | + "vector" "(" Two-Points ")" + +Distance ::= expression + +Two-Points ::= Point-Name Point-Name + +Three-Points ::= Point-Name Two-Points +</pre> +We now briefly explain the functionality of each option: +<ul> +<li>midpoint(AB): the midpoint between points A and B</li> +<li>pointOnLine(AB,d): point at distance d from A towards B</li> +<li>intersection(AB,CD): intersection of lines defined by AB and CD</li> +<li>perpendicular(A,BC): point of the foot of the perpendicular from A to line BC</li> +<li>circumCircleCenter(ABC): center of circumcircle of triangle ABC</li> +<li>incircleCenter(ABC):center of incircle of triangle ABC</li> +<li>excircleCenter(ABC,BC): center of excircle of triangle ABC, touching +side BC</li> +<li>A, shift(x,y): Point displaced from A by x and y along the X and Y +axes</li> +<li>A, polar(r,d): Point displaced from A by distance r in direction d</li> +<li>A, rotate(B,d): Rotate A about B by d</li> +</ul> +We now explain how the following piece of code operates. In case the first +token is a number, we assume that the coordinates are specified by a +number and another number, a variable or a pair of points. So, we check +whether there is a comma and use the subroutine <code>ComputeDist</code> to get the +second coordinate. In case the next token is one of the words +<code>perpendicular</code>, <code>intersection</code>, <code>midpoint</code>, <code>pointonline</code>, +<code>circumcircleCenter</code>, <code>IncircleCenter</code>, or <code>ExcircleCenter</code> +we consume the corresponding token and process the corresponding case. +In case the first two tokens are two identifiers, then we assume that we +have a pair of numbers. We compute their distance, check whether there is +a leading comma and compute the y-coordinate by calling subroutine +<code>ComputeDist</code>. In case the next token is a single identifier, we store +its name in the variable <code>$PointA</code>. If this identifier is a defined point name, +we check whether the next token is a comma. In case it is, we check whether +he token after the comma is either the token <code>shift</code>, <code>polar</code>, or +<code>rotate</code> and process each case accordingly. If it is +<a name="NWD21HcNW-1I">none of these tokens we issue an error message and continue with the next</a> +input line. Now, if the token after the identifier isn't a comma, we assume +that the coordinates of the point will be identical to those of the point +whose name has been stored in the variable <code>$PointA</code>. If the identifier is a +variable name, we assume that the x-coordinate is the value of this variable. +We check whether the next token is a comma, and compute the y-coordinate by +calling the subroutine <code>ComputeDist</code>. The x-coordinate is stored in the variable +<code>$Px</code> and the y-coordinate in the variable <code>$Py</code>. + +<pre><a name="NW21HcNW-3bnmlP-1" href="#NWD21HcNW-1I"><dfn><process coordinates>=</dfn></a> <b>(<a href="#NWD21HcNW-1H"><-U</a>)</b> + if (s/^perpendicular(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u1" href="#NWD21HcNW-1J"><i><process <tt>perpendicular</tt> case></i></a> + } + elsif (s/^intersection(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u2" href="#NWD21HcNW-1K"><i><process <tt>intersection</tt> case></i></a> + } + elsif (s/^midpoint(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u3" href="#NWD21HcNW-1L"><i><process <tt>midpoint</tt> case></i></a> + } + elsif (s/^pointonline(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u4" href="#NWD21HcNW-1M"><i><process <tt>pointonline</tt> case></i></a> + } + elsif (s/^circumcircleCenter(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u5" href="#NWD21HcNW-1N"><i><process <tt>circumcircleCenter</tt> case></i></a> + } + elsif (s/^IncircleCenter(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u6" href="#NWD21HcNW-1O"><i><process <tt>IncircleCenter</tt> case></i></a> + } + elsif (s/^ExcircleCenter(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u7" href="#NWD21HcNW-1P"><i><process <tt>ExcircleCenter</tt> case></i></a> + } + elsif (/^[^\W\d_]\d{0,3}\s*[^,\w]/) { + m/^([^\W\d_]\d{0,3})\s*/i; + if (exists($PointTable{lc($1)})) { + my $Tcoord = get_point($lc); + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{$Tcoord}); + $Px = $x; + $Py = $y; + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + } + elsif (/[^\W\d_]\d{0,3}\s*,\s*shift|polar|rotate|vector/i) { #a point? + s/^([^\W\d_]\d{0,3})//i; + my $PointA = $1; + if (exists($PointTable{lc($PointA)})) { + s/\s*//; + if (s/^,//) { + s/\s*//; + if (s/^shift(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u8" href="#NWD21HcNW-1Q"><i><process <tt>shift</tt> case></i></a> + } + elsif (s/^polar(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u9" href="#NWD21HcNW-1R"><i><process <tt>polar</tt> case></i></a> + } + elsif (s/^rotate(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u10" href="#NWD21HcNW-1S"><i><process <tt>rotate</tt> case></i></a> + } + elsif (s/^vector(?=\W)//i) { + <a name="NW21HcNW-3bnmlP-1-u11" href="#NWD21HcNW-1T"><i><process <tt>vector</tt> case></i></a> + } + else { + PrintErrorMessage("unexpected token",$lc); + next LINE; + } + } + else { + my ($xA,$yA,$pSVA,$pSA)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $xA; + $Py = $yA; + } + } + else { + PrintErrorMessage("Undefined point $PointA",$lc); + next LINE; + } + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + +</pre><p>In the following piece of code we process the <code>perpendicular</code> +case of the <code>point</code> specification. We first check whether there is an +<a name="NWD21HcNW-1J">opening left parenthesis. Next, we get the first point name. In case</a> +there is no point name, we simply abandon the processing of this +line and continue with the next one. Then we see whether there is +a trailing comma. Omitting this token yields a non-fatal error. +Then we get two more points. As before, if we can't find any of these +points this yields a fatal-error. Note, that each time we check that the +point names correspond to existing point names. Then, we call subroutine +<code>perpendicular</code> to calculate the coordinates of the point. + +<pre><a name="NW21HcNW-s2gHc-1" href="#NWD21HcNW-1J"><dfn><process <tt>perpendicular</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("perpendicular",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + chk_comma($lc); + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py) = perpendicular($x1,$y1,$x2,$y2,$x3,$y3); + +</pre><p><a name="NWD21HcNW-1K">In the following piece of code we process the </a><code>intersection</code> case of the +<code>point</code> specification. We get the four point names and if there is +no error we compute the intersection point by calling subroutine +<code>intersection</code>. + +<pre><a name="NW21HcNW-1uJA3A-1" href="#NWD21HcNW-1K"><dfn><process <tt>intersection</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("intersection",$lc); + my $FirstPoint = get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_comma($lc); + my $ThirdPoint = get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + my $ForthPoint = get_point($lc); + next LINE if $ForthPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + my ($x4,$y4,$pSV4,$pS4)=unpack("d3A*",$PointTable{$ForthPoint}); + ($Px, $Py) = intersection4points($x1,$y1,$x2,$y2,$x3,$y3,$x4,$y4); + + +</pre><p><a name="NWD21HcNW-1L">Given two points A and B, the midpoint option computes the coordinates</a> +of a third point that lies on the middle of the line segment defined by +these two points. We get the the two points, and then we compute the +coordinates of the midpoint by means of the simple formula: +<center> +m<sub>x</sub>=x<sub>1</sub>+(y<sub>2</sub> - y<sub>1</sub>)/2 <br> +m<sub>y</sub>=y<sub>1</sub>+(x<sub>2</sub> - x<sub>1</sub>)/2 +</center> + +<pre><a name="NW21HcNW-3udkns-1" href="#NWD21HcNW-1L"><dfn><process <tt>midpoint</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("midpoint",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + $Px = $x1 + ($x2 - $x1)/2; + $Py = $y1 + ($y2 - $y1)/2; + +</pre><p><a name="NWD21HcNW-1M">Given two points A and B and length d, the </a><code>PointOnLine</code> option +computes the coordinates of a point that lies d units in the direction from +A towards B. We first get the coordinates of the two points that define +the line and then we get the distance, which can be a number, a variable, +or a pair of points. + +<pre><a name="NW21HcNW-2ahy6i-1" href="#NWD21HcNW-1M"><dfn><process <tt>pointonline</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("pointonline",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_comma($lc); + # now get the distance + my $distance = expr($lc); + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + ($Px, $Py) = pointOnLine($x1,$y1,$x2,$y2,$distance); + +</pre><p><a name="NWD21HcNW-1N">The </a><code>circumcircleCenter</code> is used when one wants to compute the coordinates +of the center of circle that passes through the three points +of a triangle defined +by the three arguments of the option. All we do is get the coordinates +of the three points and then we call the subroutine <code>circumCircleCenter</code> +to compute the center. + +<pre><a name="NW21HcNW-2TpCLC-1" href="#NWD21HcNW-1N"><dfn><process <tt>circumcircleCenter</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("circumCircleCenter",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py,$r) = &circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc); + next LINE if $Px == 0 and $Py == 0 and $r == 0; + +</pre><p><a name="NWD21HcNW-1O">The </a><code>IncircleCenter</code> option is to determine the coordinates of a point +that is the center of circle that internally touches the sides +of a triangle defined by three given points. +The coordinates are computed by the subroutine <code>IncircleCenter</code>. + +<pre><a name="NW21HcNW-4fhWIW-1" href="#NWD21HcNW-1O"><dfn><process <tt>IncircleCenter</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("IncircleCenter",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py, $r) = IncircleCenter($x1,$y1,$x2,$y2,$x3,$y3); + +</pre><p>The <code>ExcircleCenter</code> option is used to define the coordinates of point +that is the center of an excircle of a triangle. We first check +whether there is an opening left parenthesis. Next, we get the names of the +<a name="NWD21HcNW-1P">three points that define the triangle. Then, we</a> +check whether there is a comma. Now we get the names of the two points that +define one side of the triangle. We check whether the two points we +get are of the set of the triangle points. If not we issue +an error message and continue with the next input line. Then we make sure +that these two points are not identical. We compute the actual +coordinates by calling the subroutine <code>excircle</code>. Finally, we +make sure there is a closing right parenthesis. + +<pre><a name="NW21HcNW-13KcO0-1" href="#NWD21HcNW-1P"><dfn><process <tt>ExcircleCenter</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("ExcircleCenter",$lc); + my $PointA = get_point($lc); + next LINE if $PointA eq "_undef_"; + my $PointB = get_point($lc); + next LINE if $PointB eq "_undef_"; + my $PointC = get_point($lc); + next LINE if $PointC eq "_undef_"; + chk_comma($lc); + my $PointD = &get_point($lc); + next LINE if $PointD eq "_undef_"; + if (!memberOf($PointD, $PointA, $PointB, $PointC)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + my $PointE = get_point($lc); + next LINE if $PointE eq "_undef_"; + if (!memberOf($PointE, $PointA, $PointB, $PointC)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + if ($PointD eq $PointE) { + PrintErrorMessage("Side points are identical",$lc); + next LINE; + } + ($Px, $Py, $r) = excircle($PointA, $PointB, $PointC, + $PointD, $PointE); + chk_rparen("after coordinates part",$lc); + +</pre><p> <a name="NWD21HcNW-1Q">The </a><code>shift</code> option allows us to define a point's coordinates relative +to the coordinates of an existing point by using two shift parameters. Each +parameter can be either a float, a variable name, or a pair of points. + +<pre><a name="NW21HcNW-aOKf8-1" href="#NWD21HcNW-1Q"><dfn><process <tt>shift</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a> <a href="#NWD21HcNW-1Z">U-></a>)</b> + + chk_lparen("shift",$lc); + my $dist1 = expr($lc); + chk_comma($lc); + my $dist2 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $x1 + $dist1; + $Py = $y1 + $dist2; + chk_rparen("shift part",$lc); + +</pre><p><a name="NWD21HcNW-1R">The </a><code>polar</code> option allows us to define a point's coordinates relative +to the coordinates of an existing point using the polar coordinates of some +other point. We first check whether there is a left parenthesis, +Then we parse the various parts of the <code>polar</code> option. +In case the user has specified the angle in degrees, we have +to transform it into radians, as all trigonometric function expect their +arguments to be radians. Next, we compute the coordinates of the point. +We conclude by checking whether there is a closing parenthesis. + +<pre><a name="NW21HcNW-2GUwzc-1" href="#NWD21HcNW-1R"><dfn><process <tt>polar</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a> <a href="#NWD21HcNW-1Z">U-></a>)</b> + chk_lparen("polar",$lc); + my ($R1, $Theta1); + $R1 = expr($lc); + chk_comma($lc); + $Theta1 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + s/\s*//; + if (s/^rad(?=\W)//i) { + # do nothing! + } + elsif (s/^deg(?=\W)//i) { + $Theta1 = $Theta1 * PI / 180; + } + else { + #$Theta1 = $Theta1 * PI / 180; + } + $Px = $x1 + $R1 * cos($Theta1); + $Py = $y1 + $R1 * sin($Theta1); + chk_rparen("after polar part",$lc); + +</pre><p>The <code>rotate</code> option allows us to define a point's coordinates by +rotating an existing point, Q, about a third point, P, by a +specified angle. +The method to achieve this is to first get the coordinates of points +P and Q and then +<ol> +<li> <a name="NWD21HcNW-1S">translate origin to P</a></li> +<li> rotate about P</li> +<li> translate from P back to origin, etc</li> +</ol> +As in the case of the <code>polar</code> option, we check for an opening parenthesis. +Next, we parse the point name and the angle. At this point we are able to +compute the coordinates of the rotated point. We conclude by checking +whether there is a closing parenthesis. + +<pre><a name="NW21HcNW-42YuKP-1" href="#NWD21HcNW-1S"><dfn><process <tt>rotate</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("rotate",$lc); + my $Q = lc($PointA); + my $P = get_point($lc); + next LINE if $P eq "_undef_"; + chk_comma($lc); + my $Theta1 = expr($lc); + my ($xP,$yP,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P}); + my ($xQ,$yQ,$pSV2,$pS2)=unpack("d3A*",$PointTable{$Q}); + s/\s*//; + if (s/^rad(?=\W)//i) + { + # do nothing! + } + elsif (s/^deg(?=\W)//i) + { + $Theta1 = $Theta1 * PI / 180; + } + else + { + $Theta1 = $Theta1 * PI / 180; + } + # shift origin to P + $xQ -= $xP; + $yQ -= $yP; + # do the rotation + $Px = $xQ * cos($Theta1) - $yQ * sin($Theta1); + $Py = $xQ * sin($Theta1) + $yQ * cos($Theta1); + # return origin back to original origin + $Px += $xP; + $Py += $yP; + chk_rparen("after rotate part",$lc); + +</pre><p> <code><a name="NWD21HcNW-1T">vector(PQ)</a></code> is actually is a shorthand of <code>shift(xQ-xP,yQ-yP)</code>. Thus, it +is implemented by borrowing code from the <code>shift</code> modifier. + +<pre><a name="NW21HcNW-3FiNXu-1" href="#NWD21HcNW-1T"><dfn><process <tt>vector</tt> case>=</dfn></a> <b>(<a href="#NWD21HcNW-1I"><-U</a>)</b> + chk_lparen("vector",$lc); + my ($x0,$y0,$pSV0,$pS0) = unpack("d3A*",$PointTable{lc($PointA)}); + my $P = get_point($lc); + my $Q = get_point($lc); + my ($x1,$y1,$pSV1,$pS1) = unpack("d3A*",$PointTable{$P}); + my ($x2,$y2,$pSV2,$pS2) = unpack("d3A*",$PointTable{$Q}); + $Px = $x0 + $x2 - $x1; + $Py = $y0 + $y2 - $y1; + chk_rparen("vector part",$lc); + + +</pre><p> When lines are drawn to a point, the line will (unless otherwise +specified) extend to the point location. However, this can be prevented by +allocating an optional circular line-free zone to a point by specifying the +radius (in square brackets) of the optional point shape part. Currently, in this part +we are allowed to describe the point shape and the radius value. If only the +radius is specified, e.g., <tt>[radius=5]</tt>, then the line-free zone will be +applied to the default point character, i.e., <tt>$\bullet$</tt> or whatever it +has been set to. Here is the syntax we employ: +<pre> +Optional_point_shape_part ::= "[" [ symbol_part ] [","] [ radius_part ]" +<a name="NWD21HcNW-1U">symbol_part ::= "symbol" "=" symbol</a> +symbol ::= "circle" "(" expression ")" | + "square" "(" expression ")" | + LaTeX_Code +radius_part ::= "radius" "=" expression +</pre> +Note that it is possible to have right square bracket in the <tt>LaTeX_Code</tt> but it +has to be escaped (i.e., <tt>\]</tt>). + +<pre><a name="NW21HcNW-48J1W6-1" href="#NWD21HcNW-1U"><dfn><process optional point shape part>=</dfn></a> <b>(<a href="#NWD21HcNW-1H"><-U</a>)</b> + if (/^(symbol|radius|side)\s*/i) { + my @previous_options = (); + my $number_of_options = 1; + my $symbol_set = 0; + while (s/^(symbol|radius)\s*//i and $number_of_options <= 2) { + my $option = lc($1); + if (s/^=\s*//) { + if (memberOf($option,@previous_options)) { + PrintErrorMessage("Option \"$option\" has been already defined", $lc); + my $dummy = expr($lc); + } + elsif ($option eq "radius") { + $sh = expr($lc); + $sv = $defaultsymbol if ! $symbol_set; + } + elsif ($option eq "symbol") { + if (s/^circle\s*//i) { + $sv = "circle"; + chk_lparen("after token circle",$lc); + $side_or_radius = expr($lc); + chk_rparen("expression",$lc); + } + elsif (s/^square\s*//i) { + $sv = "square"; + chk_lparen("after token square",$lc); + $side_or_radius = expr($lc); + chk_rparen("expression",$lc); + } + elsif (s/^(((\\\]){1}|(\\,){1}|(\\\s){1}|[^\],\s])+)//) { + $sv = $1; + $sv =~ s/\\\]/\]/g; + $sv =~ s/\\,/,/g; + $sv =~ s/\\ / /g; + s/\s*//; + } + $symbol_set = 1; + } + } + else { + PrintErrorMessage("unexpected token", $lc); + next LINE; + } + $number_of_options++; + push (@previous_options, $option); + s/^,\s*//; + } + } + else { + PrintErrorMessage("unexpected token", $lc); + next LINE; + } + +</pre><p>The <code>ArrowShape</code> command has either one or three arguments. If the only argument of +the command is the token <code>default</code>, then the parameters associated with the +arrow shape resume their default values. Now, if there are three arguments, these are +used to specify the shape of an arrow. The command actually sets the three global variables +<code>$arrowLength</code>, <code>$arrowAngleB</code> and <code>$arrowAngleC</code>. Arguments whose value is equal +to zero, do not affect the value of the corresponding global variables. To reset the +values of the global variables one should use the commane with <code>default</code> as it +only argument. The syntax of the command is as follows: +<center> +<tt><a name="NWD21HcNW-1V">"ArrowShape" "(" expr [ units ] "," expr "," expr ")"</a></tt> or<br> +<tt>"ArrowShape" "(" "default" ")" </tt> +</center>> +Here <code>units</code> is any valid TeX unit (e.g., "mm", "cm", etc.). Note that if +any of the three expressions is equal to zero, the default value is taken +instead. As direct consequence, if the value of the first expression is zero, +the units part is actually ignored. + +<pre><a name="NW21HcNW-4T61Ms-1" href="#NWD21HcNW-1V"><dfn><process <tt>ArrowShape</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen("$cmd",$lc); + if (s/^default//i) { + $arrowLength = 2; + $arrowLengthUnits = "mm"; + $arrowAngleB = 30; + $arrowAngleC = 40; + } + else { + my ($LocalArrowLength, $LocalArrowAngleB ,$LocalArrowAngleC) = (0,0,0); + $LocalArrowLength = expr($lc); + if (s/^\s*($units)//i) { + $arrowLengthUnits = "$1"; + } + else { + $xunits =~ /(\d+(\.\d+)?)\s*($units)/; + $LocalArrowLength *= $1; + $arrowLengthUnits = "$3"; + } + chk_comma($lc); + $LocalArrowAngleB = expr($lc); + chk_comma($lc); + $LocalArrowAngleC = expr($lc); + $arrowLength = ($LocalArrowLength == 0 ? 2 : $LocalArrowLength); + $arrowLengthUnits = ($LocalArrowLength == 0 ? "mm" : $arrowLengthUnits); + $arrowAngleB = ($LocalArrowAngleB == 0 ? 30 : $LocalArrowAngleB); + $arrowAngleC = ($LocalArrowAngleC == 0 ? 40 : $LocalArrowAngleC); + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + print OUT "%% arrowLength = $arrowLength$arrowLengthUnits, ", + "arrowAngleB = $arrowAngleB ", + "and arrowAngleC = $arrowAngleC\n" if $comments_on; + +</pre><p>The <code>PointSymbol</code> command is used to set the point symbol and possibly its +line-free radius. The point symbol can be either a LaTeX symbol or the word <code>default</code> +which corresponds to the default point symbol, i.e., <tt>$\bullet$</tt>. The line-free +radius can be an expression. Here is the complete syntax: +<pre> + <a name="NWD21HcNW-1W">pointsymbol ::= "pointsymbol" ( symbol [ "," radius])</a> + symbol ::= "default" | circle | square | LaTeX_Code + circle ::= "circle" "(" expression ")" + square ::= "square" "(" expression ")" + radius ::= expression +</pre> +Note that the <tt>LaTeX_Code</tt> can contain the symbols <tt>\,</tt> and +<tt>\)</tt> which are escape sequences for a comma and right parenthesis, respectively. + +<pre><a name="NW21HcNW-iKtUD-1" href="#NWD21HcNW-1W"><dfn><process <tt>PointSymbol</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen("$cmd",$lc); + if (s/^default//i) #default point symbol + { + $defaultsymbol = "\$\\bullet\$"; + } + elsif (s/^(circle|square)//i) { + $defaultsymbol = $1; + chk_lparen($defaultsymbol, $lc); + $GlobalDimOfPoints = expr($lc); + chk_rparen("expression", $lc); + } + elsif (s/^(((\\,){1}|(\\\)){1}|(\\\s){1}|[^\),\s])+)//) #arbitrary LaTeX point + { + $defaultsymbol = $1; + $defaultsymbol=~ s/\\\)/\)/g; + $defaultsymbol=~ s/\\,/,/g; + $defaultsymbol=~ s/\\ / /g; + } + else + { + PrintErrorMessage("unrecognized point symbol",$lc); + } + if (s/\s*,\s*//) { + $defaultLFradius = expr($lc); + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + +</pre><p>The <code>system</code> command provides a shell escape. However, we use a subroutine +to check whether the argument of the command contains tainted data. If this +is the case, then we simply ignore this command. The syntax of the command +is as follows: +<pre> + system-cmd ::= "system" "(" string ")" +</pre> +<a name="NWD21HcNW-1X">where string is just a sequence of characters enclosed in quotation marks.</a> +We start by parsing a left parenthesis and then we get the command by +calling the subroutine <code>get_string</code>. If there is an error we skip this +command. Otherwise, we assign to the variable <code>$_</code> what is left. Now we check +if the variable <code>$command</code> contains any tainted data. If it doesn't, we +execute the command, otherwise we print an error message and skip to the +next input line. Next, we check for closing right parenthesis and a possible +trailing comment. + +<pre><a name="NW21HcNW-4C0pFV-1" href="#NWD21HcNW-1X"><dfn><process <tt>system</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen("$cmd",$lc); + my ($error, $command, $rest) = get_string($_); + next LINE if $error == 1; + $_ = $rest; + if (! is_tainted($command)) { + system($command); + } + else { + PrintErrorMessage("String \"$command\" has tainted data", $lc); + next LINE; + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + +</pre><p>The <code>text</code> command is used to put a piece of text or a symbol on +a particular point of the resulting graph. The syntax of the command is +as follows: +<pre> + text-comm ::= "text" "(" text ")" "{"coords"} "[" pos-code "]" + text ::= ascii string + coords ::= Coord "," Coord | + Point-Name "," "shift" "(" Coord "," Coord ")" | + Point-Name "," "polar" "(" Coord "," Coord [angle-unit] ")" + Coord ::= decimal number | variable | pair-of-Point-Names + pair-of-Point-Names ::= Point-Name Point-Name + angle-unit ::= "deg" | "rad" + pos-code ::= lr-code [tb-code] | tb-code [lr-code] + lr-code ::= "l" | "r" + tb-code ::= "t" | "b" | "B" +</pre> +Initially, we parse the <code>text</code>. Since the text may contain parentheses +we assume that the user enters pairs of matching parentheses. Note, that +this is a flaw in the original design of the language, which may be remedied +in future releases of the software. Then, we check the <code>coords</code> part. Next, +<a name="NWD21HcNW-1Y">if there is a left square bracket, we assume the user has specified the</a> +<code>pos-code</code>. We conclude by checking a possible trailing comment. +The next thing we do is to generate the PiCTeX code. The two possible +forms follow: +<center> +<tt>\put {TEXT} [POS] at Px Py</tt><br> +<tt>\put {TEXT} at Px Py</tt><br> +</center> + +<pre><a name="NW21HcNW-z25eX-1" href="#NWD21HcNW-1Y"><dfn><process <tt>text</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + + chk_lparen("text",$lc); + my ($level,$text)=(1,""); + TEXTLOOP: while (1) + { + $level++ if /^\(/; + $level-- if /^\)/; + s/^(.)//; + last TEXTLOOP if $level==0; + $text .= $1; + } + chk_lcb("text part",$lc); + my ($Px, $Py,$dummy,$pos); + $pos=""; + s/\s*//; + <a name="NW21HcNW-z25eX-1-u1" href="#NWD21HcNW-1Z"><i><process coordinates part of text command></i></a> + chk_rcb("coordinates part of text command",$lc); + if (s/^\[//) + { + s/\s*//; + <a name="NW21HcNW-z25eX-1-u2" href="#NWD21HcNW-1a"><i><process optional part of text command></i></a> + s/\s*//; + chk_rsb("optional part of text command",$lc); + } + chk_comment($lc); + if ($pos eq "") + { + printf OUT "\\put {%s} at %f %f\n", $text, $Px, $Py; + } + else + { + printf OUT "\\put {%s} [%s] at %f %f\n", $text, $pos, $Px, $Py; + } + +</pre><p> In this section we define the code that handles the coordinates part +<a name="NWD21HcNW-1Z">of the </a><code>text</code> command. The code just implements the grammar given above. +If the first token is a number, we assume this is the x-coordinate. If +it is a variable, we assume its value is the x-coordinate. However, if +it is a point name, we check whether the next token is another point name. +In this case we compute the distance between the two points. In case we +have a single point followed by a comma, we expect to have either a polar +or a shift part, which we process the same we processed them in the point +command. + +<pre><a name="NW21HcNW-Ee8Ug-1" href="#NWD21HcNW-1Z"><dfn><process coordinates part of text command>=</dfn></a> <b>(<a href="#NWD21HcNW-1Y"><-U</a>)</b> + + if (/^[^\W\d_]\d{0,3}\s*[^,\w]/) { + my $Tcoord = get_point($lc); + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{$Tcoord}); + $Px = $x; + $Py = $y; + } + elsif (/[^\W\d_]\d{0,3}\s*,\s*shift|polar/i) { + s/^([^\W\d_]\d{0,3})//i; + my $PointA = $1; + if (exists($PointTable{lc($PointA)})) { + s/\s*//; + if (s/^,//) { + s/\s*//; + if (s/^shift(?=\W)//i) { + <a name="NW21HcNW-Ee8Ug-1-u1" href="#NWD21HcNW-1Q"><i><process <tt>shift</tt> case></i></a> + } + elsif (s/^polar(?=\W)//i) { + <a name="NW21HcNW-Ee8Ug-1-u2" href="#NWD21HcNW-1R"><i><process <tt>polar</tt> case></i></a> + } + } + } + else { + PrintErrorMessage("undefined point/var",$lc); + next LINE; + } + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + +</pre><p>In this section we process the optional part of the <code>text</code> command. +The general rule is that we are allowed to have up to two options one +from the characters <code>l</code> and <code>r</code> and one from the the characters +<code>B</code>, <code>b</code>, and <code>t</code>. We first check whether the next character is +letter, if it isn't we issue an error message and continue with the next +input line. If it is a letter we check whether it belongs to one of the +two groups and if it doesn't we issue an error message and continue with the +next input line. If the next character belongs to first group, i.e., it is +either <code>l</code> or <code>r</code>, we store this character into the variable <code>$pos</code>. Next, +<a name="NWD21HcNW-1a">we check whether there is another letter. If it is a letter, we store it</a> +in the variable <code>$np</code>. Now we make sure that this character belongs to the +other group, i.e., it is either <code>b</code>, <code>B</code>, or <code>t</code>. In case it belongs +to the other group, we append the value of <code>$np</code> to the string stored in +the variable <code>$pos</code>. Otherwise we issue an error message and continue with the +next input line. We work similarly for the other case. In order to check +whether a character belongs to some group of characters, we use the user +defined function <code>memberOf</code>. + +<pre><a name="NW21HcNW-RSg70-1" href="#NWD21HcNW-1a"><dfn><process optional part of text command>=</dfn></a> <b>(<a href="#NWD21HcNW-1Y"><-U</a>)</b> + + if (s/^(\w{1})\s*//) { + $pos .= $1; + if (memberOf($pos, "l", "r")) { + if (s/^(\w{1})\s*//) { + my $np = $1; + if (memberOf($np, "t", "b", "B")) { + $pos .= $np; + } + else { + if (memberOf($np, "l", "r")) { + PrintErrorMessage("$np can't follow 'l' or 'r'", $lc); + } + else { + PrintErrorMessage("$np is not a valid positioning option", $lc); + } + next LINE; + } + } + } + elsif (memberOf($pos, "t", "b", "B")) { + if (s/^(\w{1})\s*//) { + my $np = $1; + if (memberOf($np, "l", "r")) { + $pos .= $np; + } + else { + if (memberOf($np, "t", "b", "B")) { + PrintErrorMessage("$np can't follow 't', 'b', or 'B'", $lc); + } + else { + PrintErrorMessage("$np is not a valid positioning option", $lc); + } + next LINE; + } + } + } + else { + PrintErrorMessage("$pos is not a valid positioning option", $lc); + next LINE; + } + } + else { + PrintErrorMessage("illegal token in optional part of text command",$lc); + next LINE; + } + +</pre><p>The <code>const</code> command is used to store values into a comma separated +list of named constants. Constant names have the same format as point names, +i.e., they start with a letter and are followed by up to two digits. The +<a name="NWD21HcNW-1b">whole operation is performed by a </a><code>do-while</code> construct that checks that +there is a valid constant name, a <code>=</code> sign, and an expression. The +<code>do-while</code> construct terminates if the next token isn't a comma. Variable +<code>$Constname</code> is used to store the initial variable name, while we store +in variable <code>$varname</code> the lowercase version of the variable name. In addition, +we make sure a constant is not redefined (or else it wouldn't be a constant:-). +The last thing we do is to check whether there is a trailing comment. +In case there, we simply ignore itl; otherwise we print a warning message. + +<pre><a name="NW21HcNW-4F0xHm-1" href="#NWD21HcNW-1b"><dfn><process <tt>const</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + do{ + s/\s*//; + PrintErrorMessage("no identifier found after token const",$lc) + if $_ !~ s/^([^\W\d_]\d{0,3})//i; + my $Constname = $1; + my $constname = lc($Constname); + if (exists $ConstTable{$constname}) { + PrintErrorMessage("Redefinition of constant $constname",$lc); + } + s/\s*//; #remove leading white space + PrintErrorMessage("did not find expected = sign",$lc) + if $_ !~ s/^[=]//i; + my $val = expr($lc); + $VarTable{$constname} = $val; + $ConstTable{$constname} = 1; + print OUT "%% $Constname = $val\n" if $comments_on; + }while (s/^,//); + chk_comment($lc); + s/\s*//; + if (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } + +</pre><p>The <code>var</code> command is used to store values into a comma separated +list of named variables. Variable names have the same format as point names, +<a name="NWD21HcNW-1c">i.e., they start with a letter and are followed by up to two digits. The</a> +whole operation is performed by a <code>do-while</code> construct that checks that +there is a valid variable name, a <code>=</code> sign, and an expression. The +<code>do-while</code> construct terminates if the next token isn't a comma. The variable +<code>$Varname</code> is used to store the initial variable name, while we store +in the variable <code>$varname</code> the lowercase version of the variable name. +The last thing we do is to check whether there is a trailing comment. +In case there, we simply ignore itl; otherwise we print a warning message. + +<pre><a name="NW21HcNW-2NFa6I-1" href="#NWD21HcNW-1c"><dfn><process <tt>var</tt> command>=</dfn></a> <b>(<a href="#NWD21HcNW-q"><-U</a>)</b> + do{ + s/\s*//; + PrintErrorMessage("no identifier found after token var",$lc) + if $_ !~ s/^([^\W\d_]\d{0,3})//i; + my $Varname = $1; + my $varname = lc($Varname); + if (exists $ConstTable{$varname}) { + PrintErrorMessage("Redefinition of constant $varname",$lc); + } + s/\s*//; #remove leading white space + PrintErrorMessage("did not find expected = sign",$lc) + if $_ !~ s/^[=]//i; + my $val = expr($lc); + $VarTable{$varname} = $val; + print OUT "%% $Varname = $val\n" if $comments_on; + }while (s/^,//); + chk_comment($lc); + s/\s*//; + if (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } +</pre> + +<ul> +<li><a href="#NWD21HcNW-2"><i><*></i></a>: <a href="#NWD21HcNW-2">D1</a> +<li><a href="#NWD21HcNW-4"><i><Check for command line arguments></i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-4">D2</a> +<li><a href="#NWD21HcNW-6"><i><Check if .m file exists></i></a>: <a href="#NWD21HcNW-4">U1</a>, <a href="#NWD21HcNW-6">D2</a> +<li><a href="#NWD21HcNW-8"><i><Define global variables></i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-8">D2</a> +<li><a href="#NWD21HcNW-1D"><i><generate plot area related commands></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1D">D2</a> +<li><a href="#NWD21HcNW-1G"><i><generate the rest of the code for the <tt>paper</tt> command></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1G">D2</a> +<li><a href="#NWD21HcNW-3"><i><package <tt>DummyFH</tt> ></i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-3">D2</a> +<li><a href="#NWD21HcNW-t"><i><process <tt>angle</tt> part of command></i></a>: <a href="#NWD21HcNW-s">U1</a>, <a href="#NWD21HcNW-t">D2</a> +<li><a href="#NWD21HcNW-1V"><i><process <tt>ArrowShape</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1V">D2</a> +<li><a href="#NWD21HcNW-1E"><i><process <tt>axis</tt> part></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1E">D2</a> +<li><a href="#NWD21HcNW-1N"><i><process <tt>circumcircleCenter</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1N">D2</a> +<li><a href="#NWD21HcNW-1b"><i><process <tt>const</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1b">D2</a> +<li><a href="#NWD21HcNW-r"><i><process <tt>dasharray</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-r">D2</a> +<li><a href="#NWD21HcNW-s"><i><process <tt>drawAngleArcOrArrow</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-s">D2</a> +<li><a href="#NWD21HcNW-v"><i><process <tt>drawcircle</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-v">D2</a> +<li><a href="#NWD21HcNW-w"><i><process <tt>drawcircumcircle</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-w">D2</a> +<li><a href="#NWD21HcNW-x"><i><process <tt>drawexcircle</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-x">D2</a> +<li><a href="#NWD21HcNW-y"><i><process <tt>drawincircle</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-y">D2</a> +<li><a href="#NWD21HcNW-z"><i><process <tt>drawPerpendicular</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-z">D2</a> +<li><a href="#NWD21HcNW-10"><i><process <tt>drawpoint</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-10">D2</a> +<li><a href="#NWD21HcNW-11"><i><process <tt>drawRightAngle</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-11">D2</a> +<li><a href="#NWD21HcNW-12"><i><process <tt>drawsquare</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-12">D2</a> +<li><a href="#NWD21HcNW-1P"><i><process <tt>ExcircleCenter</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1P">D2</a> +<li><a href="#NWD21HcNW-1O"><i><process <tt>IncircleCenter</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1O">D2</a> +<li><a href="#NWD21HcNW-13"><i><process <tt>inputfile*</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-13">D2</a> +<li><a href="#NWD21HcNW-14"><i><process <tt>inputfile</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-14">D2</a> +<li><a href="#NWD21HcNW-1K"><i><process <tt>intersection</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1K">D2</a> +<li><a href="#NWD21HcNW-15"><i><process <tt>linethickness</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-15">D2</a> +<li><a href="#NWD21HcNW-1L"><i><process <tt>midpoint</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1L">D2</a> +<li><a href="#NWD21HcNW-16"><i><process <tt>paper</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-16">D2</a> +<li><a href="#NWD21HcNW-1J"><i><process <tt>perpendicular</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1J">D2</a> +<li><a href="#NWD21HcNW-1H"><i><process <tt>point/point*</tt> commands></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1H">D2</a> +<li><a href="#NWD21HcNW-1M"><i><process <tt>pointonline</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1M">D2</a> +<li><a href="#NWD21HcNW-1W"><i><process <tt>PointSymbol</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1W">D2</a> +<li><a href="#NWD21HcNW-1R"><i><process <tt>polar</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1R">D2</a>, <a href="#NWD21HcNW-1Z">U3</a> +<li><a href="#NWD21HcNW-u"><i><process <tt>radius</tt> part of command></i></a>: <a href="#NWD21HcNW-s">U1</a>, <a href="#NWD21HcNW-u">D2</a> +<li><a href="#NWD21HcNW-1S"><i><process <tt>rotate</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1S">D2</a> +<li><a href="#NWD21HcNW-1Q"><i><process <tt>shift</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1Q">D2</a>, <a href="#NWD21HcNW-1Z">U3</a> +<li><a href="#NWD21HcNW-1A"><i><process <tt>showAngle</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1A">D2</a> +<li><a href="#NWD21HcNW-1B"><i><process <tt>showArea</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1B">D2</a> +<li><a href="#NWD21HcNW-1C"><i><process <tt>showLength</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1C">D2</a> +<li><a href="#NWD21HcNW-1X"><i><process <tt>system</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1X">D2</a> +<li><a href="#NWD21HcNW-1Y"><i><process <tt>text</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1Y">D2</a> +<li><a href="#NWD21HcNW-1F"><i><process <tt>ticks</tt> part></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1F">D2</a> +<li><a href="#NWD21HcNW-17"><i><process <tt>unit</tt> part></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-17">D2</a> +<li><a href="#NWD21HcNW-1c"><i><process <tt>var</tt> command></i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1c">D2</a> +<li><a href="#NWD21HcNW-1T"><i><process <tt>vector</tt> case></i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1T">D2</a> +<li><a href="#NWD21HcNW-18"><i><process <tt>xrange</tt> part></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-18">D2</a> +<li><a href="#NWD21HcNW-19"><i><process <tt>yrange</tt> part></i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-19">D2</a> +<li><a href="#NWD21HcNW-5"><i><Process command line arguments></i></a>: <a href="#NWD21HcNW-4">U1</a>, <a href="#NWD21HcNW-5">D2</a> +<li><a href="#NWD21HcNW-1I"><i><process coordinates></i></a>: <a href="#NWD21HcNW-1H">U1</a>, <a href="#NWD21HcNW-1I">D2</a> +<li><a href="#NWD21HcNW-1Z"><i><process coordinates part of text command></i></a>: <a href="#NWD21HcNW-1Y">U1</a>, <a href="#NWD21HcNW-1Z">D2</a> +<li><a href="#NWD21HcNW-7"><i><process file></i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-7">D2</a> +<li><a href="#NWD21HcNW-q"><i><process input line></i></a>: <a href="#NWD21HcNW-p">U1</a>, <a href="#NWD21HcNW-q">D2</a> +<li><a href="#NWD21HcNW-1a"><i><process optional part of text command></i></a>: <a href="#NWD21HcNW-1Y">U1</a>, <a href="#NWD21HcNW-1a">D2</a> +<li><a href="#NWD21HcNW-1U"><i><process optional point shape part></i></a>: <a href="#NWD21HcNW-1H">U1</a>, <a href="#NWD21HcNW-1U">D2</a> +<li><a href="#NWD21HcNW-W"><i><subroutine <tt>Angle</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-W">D2</a> +<li><a href="#NWD21HcNW-K"><i><subroutine <tt>chk_comma</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-K">D2</a> +<li><a href="#NWD21HcNW-L"><i><subroutine <tt>chk_comment</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-L">D2</a> +<li><a href="#NWD21HcNW-G"><i><subroutine <tt>chk_lcb</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-G">D2</a> +<li><a href="#NWD21HcNW-E"><i><subroutine <tt>chk_lparen</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-E">D2</a> +<li><a href="#NWD21HcNW-I"><i><subroutine <tt>chk_lsb</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-I">D2</a> +<li><a href="#NWD21HcNW-H"><i><subroutine <tt>chk_rcb</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-H">D2</a> +<li><a href="#NWD21HcNW-F"><i><subroutine <tt>chk_rparen</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-F">D2</a> +<li><a href="#NWD21HcNW-J"><i><subroutine <tt>chk_rsb</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-J">D2</a> +<li><a href="#NWD21HcNW-S"><i><subroutine <tt>circumCircleCenter</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-S">D2</a> +<li><a href="#NWD21HcNW-T"><i><subroutine <tt>ComputeDist</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-T">D2</a> +<li><a href="#NWD21HcNW-d"><i><subroutine <tt>drawAngleArc</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-d">D2</a> +<li><a href="#NWD21HcNW-e"><i><subroutine <tt>drawAngleArrow</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-e">D2</a> +<li><a href="#NWD21HcNW-Z"><i><subroutine <tt>drawarrows</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-Z">D2</a> +<li><a href="#NWD21HcNW-b"><i><subroutine <tt>drawCurve</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-b">D2</a> +<li><a href="#NWD21HcNW-Y"><i><subroutine <tt>DrawLineOrArrow</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-Y">D2</a> +<li><a href="#NWD21HcNW-a"><i><subroutine <tt>drawlines</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-a">D2</a> +<li><a href="#NWD21HcNW-c"><i><subroutine <tt>drawpoints</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-c">D2</a> +<li><a href="#NWD21HcNW-l"><i><subroutine <tt>drawsquare</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-l">D2</a> +<li><a href="#NWD21HcNW-X"><i><subroutine <tt>excircle</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-X">D2</a> +<li><a href="#NWD21HcNW-f"><i><subroutine <tt>expr</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-f">D2</a> +<li><a href="#NWD21HcNW-N"><i><subroutine <tt>get_point</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-N">D2</a> +<li><a href="#NWD21HcNW-i"><i><subroutine <tt>get_string</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-i">D2</a> +<li><a href="#NWD21HcNW-V"><i><subroutine <tt>IncircleCenter</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-V">D2</a> +<li><a href="#NWD21HcNW-U"><i><subroutine <tt>intersection4points</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-U">D2</a> +<li><a href="#NWD21HcNW-j"><i><subroutine <tt>is_tainted</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-j">D2</a> +<li><a href="#NWD21HcNW-P"><i><subroutine <tt>Length</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-P">D2</a> +<li><a href="#NWD21HcNW-g"><i><subroutine <tt>memberOf</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-g">D2</a> +<li><a href="#NWD21HcNW-A"><i><subroutine <tt>mpp</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-A">D2</a> +<li><a href="#NWD21HcNW-k"><i><subroutine <tt>noOfDigits</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-k">D2</a> +<li><a href="#NWD21HcNW-O"><i><subroutine <tt>perpendicular</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-O">D2</a> +<li><a href="#NWD21HcNW-R"><i><subroutine <tt>pointOnLine</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-R">D2</a> +<li><a href="#NWD21HcNW-M"><i><subroutine <tt>print_headers</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-M">D2</a> +<li><a href="#NWD21HcNW-B"><i><subroutine <tt>PrintErrorMessage</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-B">D2</a> +<li><a href="#NWD21HcNW-D"><i><subroutine <tt>PrintFatalError</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-D">D2</a> +<li><a href="#NWD21HcNW-C"><i><subroutine <tt>PrintWarningMessage</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-C">D2</a> +<li><a href="#NWD21HcNW-p"><i><subroutine <tt>process_input</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-p">D2</a> +<li><a href="#NWD21HcNW-o"><i><subroutine <tt>setLineThickness</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-o">D2</a> +<li><a href="#NWD21HcNW-n"><i><subroutine <tt>sp2X</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-n">D2</a> +<li><a href="#NWD21HcNW-h"><i><subroutine <tt>tand</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-h">D2</a> +<li><a href="#NWD21HcNW-Q"><i><subroutine <tt>triangleArea</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-Q">D2</a> +<li><a href="#NWD21HcNW-m"><i><subroutine <tt>X2sp</tt> ></i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-m">D2</a> +<li><a href="#NWD21HcNW-9"><i><subroutine definitions></i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-9">D2</a> +</ul> +</body></html> + diff --git a/Master/texmf-dist/doc/latex/mathspic/sourcecode.nw b/Master/texmf-dist/doc/latex/mathspic/sourcecode.nw new file mode 100644 index 00000000000..d9c4753ca40 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/sourcecode.nw @@ -0,0 +1,5018 @@ +<center><h1> <tt>mathspic</tt> in Perl </h1></center> +<center><h2> +<table> +<tr><td><address> +<b>Apostolos Syropoulos</b><br> +366, 28th October Str.<br> +GR-671 00 Xanthi<br> +Greece<br> +email: <tt>asyropoulos@yahoo.com</tt> +</address></td> +<td><address> +<b>R.W.D. Nickalls</b><br> + Department of Anaesthesia<br> +Nottingham City Hospital NHS Trust<br> +Hucknall Road<br> +Nottingham, NG5-1PB<br> +United Kingdom<br> +email: <tt>dicknickalls@compuserve.com</tt> +</address></td> +</table></h2> +version 1.10 Feb 18, 2007 +</center> + +@ <h3><b>Introduction</b></h3><p> +<tt>mathspic</tt> is a graphics program which implements a simple +programming notation, <i>mathspic</i>, suitable for the +creation of diagrams or mathematical figures. +<tt>mathspic</tt>'s input is a LaTeX file containing +<tt>mathspic</tt> plotting commands. +<tt>mathspic</tt>'s output is the equivalent LaTeX file +containing PiCTeX plotting commands. +Technically, therefore, <tt>mathspic</tt> +is a preprocessor or `filter' for use with the PiCTeX drawing engine. +<tt>mathspic</tt> was originally written in PowerBASIC 3.5, a +DOS-based programming language. Since, many +potential users are working in rather different programming environments, +the authors thought of porting <tt>mathspic</tt> into another programming +cross-platform language which would be widely available. +The authors decided to rewrite <tt>mathspic</tt> in Perl +since not only is Perl pretty stable, but it has +extensive mathematical support.<p> + +<h3><b>Program Structure</b></h3><p> +Initially, we define a little package that is used to implement the [[loop]] +command. Then, we must do is to check the possible command line arguments. +Next, we process the input file. +If the user has used the [[-b]] (see below), the program will `beep' +if any errors are found during processing. +We need some auxiliary subroutines in order to properly parse the input +file and of course to handle the various commands. We also need a +few global variables. + +<<*>>= +#!/usr/bin/perl +# +#(c) Copyright 2005-2007 +# Apostolos Syropoulos & R.W.D. Nickalls +# asyropoulos@yahoo.com dicknickalls@compuserve.com +# +# This program can be redistributed and/or modified under the terms +# of the LaTeX Project Public License Distributed from CTAN +# archives in directory macros/latex/base/lppl.txt; either +# version 1 of the License, or any later version. +# +<<package <tt>DummyFH</tt> >> +package main; +use Math::Trig; +<<Define global variables>> +<<subroutine definitions>> +<<Check for command line arguments>> +<<process file>> +print $alarm if $no_errors > 0; +__END__ + +@ The package [[DummyFH]] is used in the implementation of the [[loop]] command. +It creates a dummy filehandle that is associated with an array of strings. Since +we only read data from this dummy filehandle, we implement the [[READLINE]] subroutine. +When we read a line from this dummy filehandle, we actually requesting the next entry +of the array (if any). That is why we use the package variable [[$index]]. When there +are no more entries in the array, subroutine [[READLINE]] returns the value [[undef]] +so to falsify loop that controls the consumption of input from this dummy filehandle. + +<<package <tt>DummyFH</tt> >>= +package DummyFH; +my $index = 0; +sub TIEHANDLE { + my $class = shift; + my $self= shift; + bless $self, $class; +} +sub READLINE { + my $self = shift; + #shift @$self; + if ($index > $#$self) { + $index = 0; + return undef; + } + else { + return $self->[$index++]; + } +} + +@ <tt>mathspic</tt> accepts at most four command-line switches, namely +<tt>-b</tt> for enabling the beep, <tt>-s</tt> for automatic +screen viewing of the output-file, +<tt>-c</tt> for cleaning out all comment-lines, +and <tt>-o</tt> with a following file-name +for specifying the output file-name. +<tt>mathspic</tt> requires the name of an existing input-file +(the so-called <tt>mathspic</tt>-file) containing +<tt>mathspic</tt>commands. +If no command-line arguments are supplied, we print a +suitable usage message indicating the syntax. +For each command-line argument we set a global +variable. The default behavior is that the `bell' does not beep +and comment-lines are not removed from the output-file. + +<<Check for command line arguments>>= +our $alarm=""; +our $comments_on=1; +our $out_file="default"; +our $argc=@ARGV; +if ($argc == 0 || $argc > 5 ){ # no command line arguments or more than 4 + # arguments + die "\nmathspic version $version_number\n" . + "Usage: mathspic [-h] [-b] [-c] [-o <out file>] <in file>\n\n"; +} +else { + <<Process command line arguments>> + print "This is mathspic version $version_number\n"; +} +<<Check if .m file exists>> + +@ In order to get the various command-line arguments we use a simple +[[while]] loop that checks each element of the array [[@ARGV]]. We check +for all the switches, and we get the name of the input-file. + +<<Process command line arguments>>= + our $file = ""; + SWITCHES: + while($_ = $ARGV[0]) { + shift; + if (/^-h$/) { + die "\nThis is mathspic version $version_number\n" . + "Type \"man mathspic\" for detailed help\n". + "Usage:\tmathspic [-h] [-b] [-c] [-o <out file>] <in file>\n" . + "\twhere,\n" . + "\t[-b]\tenables bell sound if error exists\n" . + "\t[-c]\tdisables comments in ouput file\n" . + "\t[-h]\tgives this help listing\n" . + "\t[-o]\tcreates specified output file\n\n"; + } + elsif (/^-b$/) { + $alarm = chr(7); + } + elsif (/^-c$/) { + $comments_on = 0; + } + elsif (/^-o$/) { + die "No output file specified!\n" if !@ARGV; + $out_file = $ARGV[0]; + shift; + } + elsif (/^-\w+/) { + die "$_: Illegal command line switch!\n"; + } + else { + $file = $_; + } + } + die "No input file specified!\n" if $file eq ""; + +@ In order to check whether the input-file exists, we simply use the +[[-e]] operator. First we check to see if [[$file]] exits. +If the input-file does exist then the variable [[$file]] contains +the file name. In case the user has not specified an output +file, the default output file name is the name of the input file with +extension [[.mt]]. Finally, the program outputs all error messages to +the screen and to a log file. The name of the log file consists of +the contents of the variable [[$file]] and the extension [[.mlg]]. + +<<Check if .m file exists>>= + our ($source_file, $log_file); + if (! -e $file) { + die "$file: no such file!\n" if (! (-e "$file.m")); + $source_file = "$file.m"; + } + else { + $source_file = $file; + $file = $1 if $file =~ /(\w[\w-\.]+)\.\w+/; + } + $out_file= "$file.mt" if $out_file eq "default"; + $log_file= "$file.mlg"; + +@ Now that we have all the command line arguments, we can start processing +the input file. This is done by calling the subroutine [[process_input]]. +Before that we must open all necessary files. Next, +we print some `header' information to the output file and to the log file. + +<<process file>>= + open(IN,"$source_file")||die "Can't open source file: $source_file\n"; + open(OUT,">$out_file")||die "Can't open output file: $out_file\n"; + open(LOG,">$log_file")||die "Can't open log file: $log_file\n"; + print_headers; + process_input(IN,""); + +@ In this section we define a few global variables. More specifically: +the variable [[$version_number]] contains the current version number of the +program, the variable [[$commandLineArgs]] contains the command line arguments. +These two variables are used in the [[print_headers]] subroutine. +The variable [[$command]] will contain the whole current input line. +Hash [[%PointTable]] is used to store point names and related +information. Hash [[%VarTable]] is used to store mathspic variable names +and related information, while the associative array [[%ConstTable]] contains the +names of constants. Note that the values of both constants and variables are +kept in [[%VarTable]]. +The variable [[$no_errors]] is incremented whenever the +program encounters an error in the input file. The variables [[$xunits]], +[[$yunits]] and [[$units]] are related to the [[paper]] command. +In particular, the variable [[$units]] is used to parse the unit part of the +[[unit]] part of the [[paper]] command. The variable [[$defaultsymbol]] is used to +set the point shape. The constant [[PI]] holds the value of the mathematical + constant pi. +The constant [[R2D]] holds the transformation factor to transform radians to +degrees. The constant [[D2R]] holds the transformation factor +to transform degrees to radians, i.e., the value [[1/R2D]]. The global variables +[[$arrowLength]], [[$arrowAngleB]] and [[$arrowAngleC]] are actually parameters that +are used by the subroutines that draw arrows. Since [[$arrowLength]] is actually +a length, variable [[$arrowLenghtUnits]] holds the units of measure in which +this length is expressed. The hash table [[%DimOfPoint]] contains the side or the +radius of a point whose plot-symbol is a square or a circle, respectively. In case the +default point symbol is a circle or a square, variable [[$GlobalDimOfPoints]] is used +to store the length of the radius or the length of the side of default point symbol, +respectively. Variable [[$LineThickness]] holds the current line thickness (the +default value is 0.4 pt). + +<<Define global variables>>= +our $version_number = "1.10 Feb 18, 2007"; +our $commandLineArgs = join(" ", @ARGV); +our $command = ""; +our $curr_in_file = ""; +our %PointTable = (); +our %VarTable = (); +our %ConstTable = (); +our $no_errors = 0; +our $xunits = "1pt"; +our $yunits = "1pt"; +our $units = "pt|pc|in|bp|cm|mm|dd|cc|sp"; +our $defaultsymbol = "\$\\bullet\$"; +our $defaultLFradius = 0; +use constant PI => atan2(1,1)*4; +use constant R2D => 180 / PI; +use constant D2R => PI / 180; +our $arrowLength = 2; +our $arrowLengthUnits = "mm"; +our $arrowAngleB = 30; +our $arrowAngleC = 40; +our %DimOfPoint = (); +our $GlobalDimOfPoints = 0; +our @Macros = (); +our $LineThickness = 0.4; + +@ In this section we define the various subroutines that are needed in order +to process the input file. + +<p> Subroutine <tt>mpp</tt> is a mathspic preprocessor that allows the definition +and use of macros with or without arguments. For the moment it is an experimental +feature and it should be used with care. + +<p> Subroutine <tt>PrintErrorMessage</tt> is used to print error messages +to the screen, to the output file and to the log file. + +<p> Subroutine <tt>PrintWarningMessage</tt> is used to print warning messages +to the screen, to the output file and to the log file. + +<p> Subroutine <tt>PrintFatalError</tt> is used to print an error message +to the screen and to abort execution, where the error is considered fatal +and not recoverable. + +<p>Subroutine <tt>chk_lparen</tt> checks whether the next input +character is a left parenthesis. Subroutine <tt>chk_rparen</tt> +checks whether the next input character is a right parenthesis. Subroutine +<tt>chk_comment</tt> checks whether a given command is followed by a trailing +comment. In the same spirit, we define the subroutines <tt>chk_lcb</tt>, +<tt>chk_rcb</tt>, <tt>chk_lsb</tt>, and <tt>chk_rsb</tt> which check for +opening and closing curly and square brackets respectively. +The subroutine [[chk_comma]] checks whether the next token is a comma. + +<p> Subroutine [[print_headers]] is used to print a header to the output file, +so a user knows that the file has been generated by <tt>mathspic</tt>. + +<p> Subroutine [[get_point]] is used to parse a point name and to +check whether the point exists (i.e whether the point has been defined). + +<p> Subroutine [[perpendicular]] is used to compute the coordinates of the +foot of perpendicular line from some point P to a line AB. + +<p> Subroutine [[Length]] is used to compute the distance between two +points A and B. + +<p> Subroutine [[triangleArea]] computes the area of a triangle defined +by three points. + +<p> Subroutine [[PointOnLine]] is used to compute the coordinates of +a point on a line segment AB and a distance d units from A towards B. + +<p> Subroutine [[circumCircleCenter]] takes six arguments that are the +coordinates of three points and computes the center of the circle that +passes through the three points which define the triangle. + +<p> Subroutine [[ComputeDist]] is used to compute a numeric value that is +specified by either a variable name, a pair of points, or just a number. + +<p> Subroutine [[intersection4points]] is used to compute the coordinates +of the point of intersection of two lines specified by the four arguments +(i.e. two arguments for each point). + +<p> Subroutine [[IncircleCenter]] is used to compute the center and +the radius of a circle that touches internally the sides of a triangle, +the coordinates of the three points which define the triangle +being the arguments of the subroutine. + +<p> Subroutine [[Angle]] determines the opening in degrees of an angle +defined by three points which are the arguments of this subroutine. + +<p> Subroutine [[excircle]] computes the center and the radius of +a circle that externally touches a given side (4th and 5th arguments) of +triangle (determined by the 1st, the 2nd and the 3rd argument). + +<p> Subroutine [[DrawLineOrArrow]] is used to parse the arguments of the commands + [[drawline]], [[drawthickline]], [[drawarrow]], [[drawthickarrow]] and + [[drawCurve]]. + +<p> Subroutine [[drawarrows]] is used to draw one or more arrows between points. + +<p> Subroutine [[drawlines]] is used to draw one or more lines between points. + +<p> Subroutine [[drawCurve]] is used to draw a curve between an odd number of points. + +<p> Subroutine [[drawpoints]] is used to draw the point symbol of one or more points. + +<p> Subroutine [[drawAngleArc]] is used to draw an arc line within an angle. + +<p> Subroutine [[drawAngleArrow]] is used to draw an arc line with an arrow on the end, +within an angle. + +<p> Subroutine [[expr]] and subroutines [[term]], [[factor]] and +[[primitive]] are used to parse an expression that follows a variable +declaration. + +<p> Subroutine [[memberOf]] is used to determine whether a string is a +member of a list of strings. + +<p> Subroutine [[tand]] computes the tangent of an angle, where the +angle is expressed in degrees. + +<p> Subroutine [[get_string]] scans a string in order to extract a +valid mathspic string. + +<p> Subroutine [[is_tainted]] checks whether a string contains data that +may be proved harmful if used as arguments to a shell escape. + +<p> Subroutine [[noOfDigits]] has one argument which is a number and +returns the number of decimal digits it has. + +<p> Subroutine [[drawsquare]] has one argument which is the radius of point +and yields LaTeX code that draws a square. + +<p> Subroutine [[X2sp]] can be used to transform a length to sp units. + +<p> Subroutine [[sp2X]] can be used to transform a length expressed in sp units + to any other acceptable unit. + +<p> Subroutine [[setLineThickness]] is used to determine the length of the + linethickness in the current paper units. + +<p> Subroutine [[process_input]] parses the input file and any other file + being included in the main file, and generates output. + +<<subroutine definitions>>= + <<subroutine <tt>mpp</tt> >> + <<subroutine <tt>PrintErrorMessage</tt> >> + <<subroutine <tt>PrintWarningMessage</tt> >> + <<subroutine <tt>PrintFatalError</tt> >> + <<subroutine <tt>chk_lparen</tt> >> + <<subroutine <tt>chk_rparen</tt> >> + <<subroutine <tt>chk_lcb</tt> >> + <<subroutine <tt>chk_rcb</tt> >> + <<subroutine <tt>chk_lsb</tt> >> + <<subroutine <tt>chk_rsb</tt> >> + <<subroutine <tt>chk_comma</tt> >> + <<subroutine <tt>chk_comment</tt> >> + <<subroutine <tt>print_headers</tt> >> + <<subroutine <tt>get_point</tt> >> + <<subroutine <tt>perpendicular</tt> >> + <<subroutine <tt>Length</tt> >> + <<subroutine <tt>triangleArea</tt> >> + <<subroutine <tt>pointOnLine</tt> >> + <<subroutine <tt>circumCircleCenter</tt> >> + <<subroutine <tt>ComputeDist</tt> >> + <<subroutine <tt>intersection4points</tt> >> + <<subroutine <tt>IncircleCenter</tt> >> + <<subroutine <tt>Angle</tt> >> + <<subroutine <tt>excircle</tt> >> + <<subroutine <tt>DrawLineOrArrow</tt> >> + <<subroutine <tt>drawarrows</tt> >> + <<subroutine <tt>drawlines</tt> >> + <<subroutine <tt>drawCurve</tt> >> + <<subroutine <tt>drawpoints</tt> >> + <<subroutine <tt>drawAngleArc</tt> >> + <<subroutine <tt>drawAngleArrow</tt> >> + <<subroutine <tt>expr</tt> >> + <<subroutine <tt>memberOf</tt> >> + <<subroutine <tt>tand</tt> >> + <<subroutine <tt>get_string</tt> >> + <<subroutine <tt>is_tainted</tt> >> + <<subroutine <tt>noOfDigits</tt> >> + <<subroutine <tt>drawsquare</tt> >> + <<subroutine <tt>X2sp</tt> >> + <<subroutine <tt>sp2X</tt> >> + <<subroutine <tt>setLineThickness</tt> >> + <<subroutine <tt>process_input</tt> >> + +@ Subroutine <tt>mpp</tt> is an implementation of a mathspic preprocessor that allows +the definition of one-line macros with or without arguments. Macro definition has the +following syntax: +<center> + <tt>"%def" macro_name "(" [ parameters ] ")" macro_code +</center> +where parameters is a list of comma separated strings (e.g., x,y,z). Once a macro is +defined it can be used or it can be undefined. To undefine a macro one has to use +the following command: +<center> + <tt>"%undef" [ macro_name ] +</center +This means that an undef command without an accompanying macro name has no effect +at all. In order to use a macro we simply type its name and its arguments in +parentheses. Note that macro arguments should not contain spaces. If a macro has no +argument, there is no need to type any parentheses. We will now describe briefly how +the macro processor operates. +<p> If the current input line starts with <tt>%def</tt>, then we assume that we have +a macro definition. We parse each component of the macro definition and finally we +store the macro name, the macro code and the macro parameters (if any) in an anonymous +hash that eventually becomes part of an array. If we encounter any error, we simply +skip to the next line after printing a suitable error message. Now, if the first tokens +of an input line are <tt>%undef</tt>, we assume the user wants to delete a macro. +In case these tokens are not followed by a macro name or the macro name has not been +defined we simply go on. Otherwise, we delete the corresponding macro data from the +global array [[@Macros]] that contains all the macro information. Macro expansion is +more difficult and it will be described in detail in a separate document. At this point +we would like to thank Joachim Schneider <joachim at hal dot rhein-necker dot de> +for a suggestion on improving macro expansion. + +<<subroutine <tt>mpp</tt> >>= +sub mpp { + my $in_line; + chomp($in_line = shift); + my $LC = shift; + my $out_line = $in_line; + my $macro_name = ""; + my @macro_param = (); + my $macro_code = ""; + if ($in_line =~ s/^%def\s*//) { + if ($in_line =~ s/^(\w+)\s*//){ + $macro_name = $1; + } + else { + PrintErrorMessage("No macro name has been found",$LC); + return "" + } + if ($in_line =~ s/^\(\s*//) { + # do nothing + } + else { + PrintErrorMessage("No left parenthesis after macro name has been found",$LC); + return ""; + } + if ($in_line =~ s/^\)//) { + # Macro has no parameters! + } + else { + MACROS: while (1) { + if ($in_line =~ s/^(\w+)\s*//) { + push (@macro_param, $1); + } + else { + PrintErrorMessage("No macro parameter name has been found",$LC); + return ""; + } + if ($in_line =~ s/^,\s*//) { + next MACROS; + } + else { + last MACROS; + } + } + if ($in_line =~ s/^\)//) { + # do nothing! + } + else { + PrintErrorMessage("No closing parenthesis after macro parameters",$LC); + return ""; + } + } + $in_line =~ s/([^%]+)(%.*)/$1/; + $macro_code = $in_line; + push ( @Macros , { 'macro_name' => $macro_name, + 'macro_code' => $macro_code, + 'macro_param' => \@macro_param }); + return $out_line; + } + elsif ($in_line =~ s/^%undef\s*//) { + if ($in_line =~ s/^(\w+)//) { + my $undef_macro = $1; + for(my $i = $#Macros; $i >= 0; $i--) { + if ($Macros[$i]->{'macro_name'} eq $undef_macro) { + splice(@Macros,$i,1); + } + } + } + return $out_line; + } + elsif ($in_line =~ s/^\s*%//) { + return $out_line; + } + else { + my $comment = $2 if $in_line =~ s/([^%]+)(%.+)/$1/; + EXPANSIONLOOP: while () { + my $org_in_line = $in_line; + for(my $i = $#Macros; $i >= 0; $i--) { + my $macro_name = $Macros[$i]->{'macro_name'}; + if ($in_line =~ /&$macro_name\b/) { ############################ + my $num_of_macro_args = @{$Macros[$i]->{'macro_param'}}; + if ( $num_of_macro_args > 0 ) { + # Macro with parameters + my $pattern = "&$macro_name\\("; + foreach my $p ( 1..$num_of_macro_args ) { + my $comma = ($p == $num_of_macro_args) ? "\\s*" : "\\s*,\\s*"; + $pattern .= "\\s*[^\\s\\)]+$comma"; + } + $pattern .= "\\)"; + while($in_line =~ /&$macro_name\b/) { + if ($in_line =~ /$pattern/) { + my $before = $`; + my $after = $'; + my $match = $&; + my $new_code = $Macros[$i]->{'macro_code'}; + $match =~ s/^&$macro_name\(\s*//; + $match =~ s/\)$//; + foreach my $arg ( 0..($num_of_macro_args - 1) ) { + my $old = $Macros[$i]->{'macro_param'}->[$arg]; + my $comma = ($arg == ($num_of_macro_args - 1)) ? "" : ","; + $match =~ s/^\s*([^\s,]+)\s*$comma//; + my $new = $1; + # 'g': Parameter may occur several times + # in $new_code. + # '\b': Substitute only whole words + # not x in xA + $new_code =~ s/\b$old\b/$new/g; + } + $in_line = "$before$new_code$after"; + } + else { + PrintErrorMessage("Usage of macro &$macro_name does not " . + "match its definition", $LC); + return ""; + } + } + } + else { + # Macro without parameters + my $replacement = $Macros[$i]->{'macro_code'}; + # '\b': Substitute only whole words + # not x in xA + $in_line =~ s/&$macro_name\b/$replacement/g; + } + } + } + last EXPANSIONLOOP if ( $org_in_line eq $in_line ); + } + return "$in_line$comment"; + } +} + +@ Subroutine <tt>PrintErrorMessage</tt> has two parameters: the +error message that will be printed on the screen, the log file and +the output file, and the line number of the line containing the +error was detected. +The general form of the error message is the following: +<pre> +line X: paper{units( + ,mm)xrange(0,20)yrange(0,30)axes(B)ticks(10,10)} + +***Error: Error_Message +</pre> +where [[X]] denotes the line number and [[Error_Message]] is the +actual error message. Note, that we print the tokens processed so far +and on the text line the unprocessed tokens, so that the user knows +exactly where the error is. In the variable [[$A]] we store the processed +tokens, while the variable [[$l]] holds the length of [[$A]] plus the +length of the [[$error_line]] (that is the number of the input line where +the error occurred) plus 7, i.e., 4 (the length of the word +[[line]]) plus 2 (the two blank spaces) plus 1 (the symbol [[:]]). +Finally, we increment the error counter (variable [[$no_errors]]). Note, that +in case the user has specified the [[-c]] command line switch, we will not +print any messages to the output file. + +<<subroutine <tt>PrintErrorMessage</tt> >>= + sub PrintErrorMessage { + my $errormessage = shift; + my $error_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($error_line); + + for my $fh (STDOUT, LOG) { + print $fh "$curr_in_file", "Line $error_line: $A\n"; + print $fh " " x $l ,$_,"***Error: $errormessage\n"; + } + if ($comments_on) { #print to output file file + print OUT "%% *** $curr_in_file", "Line $error_line: $A\n"; + print OUT "%% *** "," " x $l ,$_,"%% ... Error: $errormessage\n"; + } + $no_errors++; + } + +@ Subroutine <tt>PrintWarningMessage</tt> behaves exactly like the subroutine +<tt>PrintErrorMessage</tt>. The only difference is that the second +subroutine prints only a warning message. A warning is issued when +the system detects parameters that do nothing. + +<<subroutine <tt>PrintWarningMessage</tt> >>= + sub PrintWarningMessage { + my $warningMessage = shift; + my $warning_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($warning_line); + + for my $fh (STDOUT, LOG) { + print $fh "$curr_in_file", "Line $warning_line: $A\n"; + print $fh " " x $l ,$_,"***Warning: $warningMessage\n"; + } + if ($comments_on) { #print to output file file + print OUT "%% *** $curr_in_file", "Line $warning_line: $A\n"; + print OUT "%% *** "," " x $l ,$_,"%% ... Warning: $warningMessage\n"; + } + } + +@ The subroutine <tt>PrintFatalError</tt> behaves similarly to the subroutine +<tt>PrintErrorMessage</tt>. It prints an error message to the +screen and aborts execution. + +<<subroutine <tt>PrintFatalError</tt> >>= + sub PrintFatalError { + my $FatalMessage = shift; + my $fatal_line = shift; + my ($l,$A); + $l = 1+length($command)-length; + $A = substr($command,0,$l); + $l += 7 +length($fatal_line); + + die "$curr_in_file", "Line $fatal_line: $A\n" . + (" " x $l) . $_ . "***Fatal Error: $FatalMessage\n"; + } + +@ The subroutine <tt>chk_lparen</tt> accepts two arguments: the name +of the token that should be immediately before the left parenthesis (variable +[[$token]]), and the current line number (variable [[$lc]]). First we +skip any leading white space and then check whether the next +input character is a left parenthesis, then the subroutine skips any +trailing white space; otherwise it prints an error message. + +<<subroutine <tt>chk_lparen</tt> >>= +sub chk_lparen { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if (/^[^\(]/) { + PrintErrorMessage("Missing ( after $token",$lc); + } + else { + s/^\(\s*//; + } +} + +@ The subroutine <tt>chk_rparen</tt> accepts two parameters: the name +of the token that should be immediately after a right parenthesis (variable +[[$token]]), and the current line number (variable [[$lc]]). Initially, we +skip any leading white space and then we check whether the next input +token is a right parenthesis. If it is not we issue a error message and +return, otherwise we skip the parenthesis and any trailing white space. + +<<subroutine <tt>chk_rparen</tt> >>= +sub chk_rparen { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if (s/^\)//) { + s/\s*//; + } + else { + PrintErrorMessage("Missing ) after $token",$lc); + } +} + + +@ The subroutine <tt>chk_lcb</tt> behaves in a similar way to the subroutine +<tt>chk_lparen</tt>. + +<<subroutine <tt>chk_lcb</tt> >>= +sub chk_lcb { + my $token = $_[0]; + my $lc = $_[1]; + s/\s*//; + if ($_ !~ /^\{/) { + PrintErrorMessage("Missing { after $token",$lc); + } + else { + s/^{\s*//; + } +} + +@ Subroutine <tt>chk_rcb</tt> behaves in a similar way to the subroutine +<tt>chk_rparen</tt>. + +<<subroutine <tt>chk_rcb</tt> >>= +sub chk_rcb { + my $token = $_[0]; + my $lc = $_[1]; + if ($_ !~ /^\s*\}/) { + PrintErrorMessage("Missing } after $token",$lc); + } + else { + s/^\s*}\s*//; + } +} + +@ Subroutine <tt>chk_lsb</tt> behaves in a similar way to the subroutine +<tt>chk_lparen</tt>. + +<<subroutine <tt>chk_lsb</tt> >>= +sub chk_lsb { + my $token = $_[0]; + my $lc = $_[1]; + + s/\s*//; + if ($_ !~ /^\[/) { + PrintErrorMessage("Missing [ after $token",$lc); + } + else { + s/^\[\s*//; + } +} + +@ Subroutine <tt>chk_rsb</tt> behaves in a similar way to the subroutine +<tt>chk_rparen</tt>. + +<<subroutine <tt>chk_rsb</tt> >>= +sub chk_rsb { + my $token = $_[0]; + my $lc = $_[1]; + + s/\s*//; + if ($_ !~ /^\]/) { + PrintErrorMessage("Missing ] after $token",$lc); + } + else { + s/^\]\s*//; + } +} + +@ The subroutine [[chk_comma]] checks whether the next token is a comma. +If it is not then it prints an error message, otherwise it consumes the +comma and any white space that follows the comma. + +<<subroutine <tt>chk_comma</tt> >>= +sub chk_comma { + my $lc = $_[0]; + + s/\s*//; + if (/^[^,]/) { + PrintErrorMessage("Did not find expected comma",$lc); + } + else { + s/^,\s*//; + } +} + +@ The subroutine [[chk_comment]] has only one parameter which is the current +line number. It checks whether the next input character is a comment +character and in this case it does nothing!. Otherwise, if there is some trailing text +it simply prints a warning to the screen. + +<<subroutine <tt>chk_comment</tt> >>= +sub chk_comment { + my $lc = $_[0]; + + s/\s*//; + if (/^%/) { + # do nothing! + } + elsif (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } +} + +@ The subroutine [[print_headers]] prints a header to the output file, as +well as a header to the LOG file. +The header contains information regarding the version of the +program, a copyright notice, the command line, date and time information, +and the names of the various files processed/generated. + +<<subroutine <tt>print_headers</tt> >>= + sub print_headers + { + my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localtime; + $year+=1900; + $mon+=1; + $now_string = "$year/" . ($mon>9 ? "$mon/" : "0$mon/") . + ($mday>9 ? "$mday " : "0$mday ") . + ($hour>9 ? "$hour:" : "0$hour:") . + ($min>9 ? "$min:" : "0$min:") . + ($sec>9 ? "$sec" : "0$sec"); + print OUT "%* -----------------------------------------------\n"; + print OUT "%* mathspic (Perl version $version_number)\n"; + print OUT "%* A filter program for use with PiCTeX\n"; + print OUT "%* Copyright (c) 2005 A Syropoulos & RWD Nickalls \n"; + print OUT "%* Command line: $0 $commandLineArgs\n"; + print OUT "%* Input filename : $source_file\n"; + print OUT "%* Output filename: $out_file\n"; + print OUT "%* Date & time: $now_string\n"; + print OUT "%* -----------------------------------------------\n"; + # + print LOG "----\n"; + print LOG "$now_string\n"; + print LOG "mathspic (Perl version $version_number)\n"; + print LOG "Copyright (c) 2005 A Syropoulos & RWD Nickalls \n"; + print LOG "Input file = $source_file\n"; + print LOG "Output file = $out_file\n"; + print LOG "Log file = $log_file\n"; + print LOG "----\n"; + } + +@ The subroutine [[get_point]] parses an individual point name. +If the next token is also a point name then it returns the point name + (but only if the only if +the point name exists in the PointTable). In all other cases it returns +the string [[_undef_]] to indicate that something is wrong. + +<<subroutine <tt>get_point</tt> >>= + sub get_point { + + my ($lc) = $_[0]; + my ($PointName); + + if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name + $PointName = $1; + if (!exists($PointTable{lc($PointName)})) { + PrintErrorMessage("Undefined point $PointName",$lc); + return "_undef_"; + } + else { + return lc($PointName); + } + } + else { + PrintErrorMessage("Point name expected",$lc); + return "_undef_"; + } + } + +@ The subroutine [[perpendicular]] has 6 parameters that correspond to the +coordinates of some point P and to the coordinates of two points A and +B that define a line. The subroutine returns +a pair of numbers that correspond to the coordinates of a point that lies +at the foot of the perpendicular to the line AB that passes through point P. +The slope of line AB is m<sub>1</sub> and so its equation is +y=m<sub>1</sub>x+c<sub>1</sub>. Similarly, the slope of the line PF is +m<sub>2</sub>=-1/m<sub>1</sub> and its equation is +y=m<sub>2</sub>x+c<sub>2</sub>. Since the line AB passes through A, then +c<sub>1</sub>=y<sub>A</sub>-m<sub>1</sub>x<sub>A</sub>. Similarly, as P is +on line PF, then c<sub>2</sub>=y<sub>P</sub>-m<sub>2</sub>x<sub>P</sub>. +Now point F is on both lines, therefore +y<sub>F</sub>=m<sub>2</sub>x<sub>F</sub>+c<sub>2</sub> and +y<sub>F</sub>=m<sub>1</sub>x<sub>F</sub>+c<sub>1</sub>. Solving these +equations for x<sub>F</sub> and y<sub>F</sub> gives: +<center> +x<sub>F</sub>=(c<sub>2</sub>-c<sub>1</sub>)/(m<sub>1</sub>-m<sub>2</sub>)<br> +y<sub>F</sub>=(m<sub>1</sub>c<sub>2</sub>-m<sub>2</sub>c<sub>1</sub>)/ +(m<sub>1</sub>-m<sub>2</sub>) +</center> + +<<subroutine <tt>perpendicular</tt> >>= + sub perpendicular { + my ($xP, $yP, $xA, $yA, $xB, $yB) = @_; + my ($xF, $yF, $deltax, $deltay, $m1, $m2, $c1, $c2, $factor); + + $deltax = $xA - $xB; + return ($xA, $yP) if abs($deltax) < 0.0000001; + $deltay = $yA - $yB; + return ($xP, $yA) if abs($deltay) < 0.0000001; + $m1 = $deltay / $deltax; + eval { $m2 = (-1) / $m1;}; + PrintFatalError("Division by zero",$lc) if $@; + $c1 = $yA - $m1 * $xA; + $c2 = $yP - $m2 * $xP; + eval { $factor = 1 / ($m1 - $m2)}; + PrintFatalError("Division by zero",$lc) if $@; + return (($c2 - $c1) * $factor, ($m1 * $c2 - $m2 * $c1) * $factor); + } + +@ The subroutine [[Length]] computes the distance between two points A and B. +Notice, that the name of the subroutine starts with a capital L, just +to avoid conflict with the predefined Perl function. The subroutine +requires four parameters which are the coordinates of the two points. + +<<subroutine <tt>Length</tt> >>= + sub Length { + my ($xA, $yA, $xB, $yB)=@_; + return sqrt(($xB - $xA)**2 + ($yB - $yA)**2); + } + +@ The subroutine [[triangleArea]] computes the area of a triangle by using +Heron's formula, i.e., given a triangle ABC, we first compute +s=(AB+BC+CA)/2 and then the area of the triangle is equal to the +square root of s times (s-AB) times (s-BC) times (s-BA), where AB, BC, and CA +are the lengths of the three sides of the triangle. The subroutine accepts 6 +parameters, which correspond to the coordinates of three points that define +the triangle. + +<<subroutine <tt>triangleArea</tt> >>= + sub triangleArea { + my ($xA, $yA, $xB, $yB, $xC, $yC)=@_; + my ($lenAB, $lenBC, $lenCA, $s); + + $lenAB = Length($xA,$yA,$xB,$yB); + $lenBC = Length($xB,$yB,$xC,$yC); + $lenCA = Length($xC,$yC,$xA,$yA); + $s = ($lenAB + $lenBC + $lenCA) / 2; + return sqrt($s * ($s - $lenAB)*($s - $lenBC)*($s - $lenCA)); + } + +@ The subroutine [[poinOnLine]] accepts five arguments: the coordinates of two +points and the decimal number which corresponds to the distance from the +first point towards the second one. The way we compute the coordinates of +the point is fairly simple. + +<<subroutine <tt>pointOnLine</tt> >>= + sub pointOnLine { + my ($xA, $yA, $xB, $yB, $dist)=@_; + my ($deltax, $deltay, $xPol, $yPol); + + $deltax = $xB - $xA; + $deltay = $yB - $yA; + $xPol = $xA + ($dist * $deltax / &Length($xA,$yA,$xB,$yB)); + $yPol = $yA + ($dist * $deltay / &Length($xA,$yA,$xB,$yB)); + return ($xPol, $yPol); + } + + +@ As we have mentioned above the subroutine [[circumCircleCenter]] takes six +arguments that correspond to the coordinates of three points that +define a triangle. The subroutine computes the coordinates of +the center of a circle that passes through these three points, and the radius of +the circle. We now describe how the subroutine computes the center +of the circle and its radius. Let the triangle points be [[t1]], [[t2]] +and [[t3]]. We use the two pairs of points to define two sides, +i.e., [[t1t2]] and [[t2t3]]. For each +side we locate the midpoints and get the their coordinates. We check +whether either of these two lines is either vertical or horizontal. If this +is true, we know that one of the coordinates of the center of the circumcircle +is the same as that of the midpoints of the horizontal or vertical line. +Next, we determine the slopes of the lines [[t1t2]] and [[t2t3]]. +We now determine the slope of lines at right-angles to these lines. We solve the +resulting equations and obtain the center of the circumcircle. Now we get the +radius, and then we are done. + +<<subroutine <tt>circumCircleCenter</tt> >>= + + sub circumCircleCenter { + my ($xA, $yA, $xB, $yB, $xC, $yC, $lc)=@_; + my ($deltay12, $deltax12, $xs12, $ys12); + my ($deltay23, $deltax23, $xs23, $ys23); + my ($xcc, $ycc); + my ($m23, $mr23, $c23, $m12, $mr12, $c12); + my ($sideA, $sideB, $sideC, $a, $radius); + + if (abs(triangleArea($xA, $yA, $xB, $yB, $xC, $yC)) < 0.0000001) + { + PrintErrorMessage("Area of triangle is zero!",$lc); + return (0,0,0); + } + $deltay12 = $yB - $yA; + $deltax12 = $xB - $xA; + $xs12 = $xA + $deltax12 / 2; + $ys12 = $yA + $deltay12 / 2; + # + $deltay23 = $yC - $yB; + $deltax23 = $xC - $xB; + $xs23 = $xB + $deltax23 / 2; + $ys23 = $yB + $deltay23 / 2; + # + CCXYLINE:{ + if (abs($deltay12) < 0.0000001) + { + $xcc = $xs12; + if (abs($deltax23) < 0.0000001) + { + $ycc = $ys23; + last CCXYLINE; + } + else + { + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $ycc = $mr23 * $xs12 + $c23; + last CCXYLINE; + } + } + if (abs($deltax12) < 0.0000001) + { + $ycc = $ys12; + if (abs($deltay23) < 0.0000001) + { + $xcc = $xs23; + last CCXYLINE; + } + else + { + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $xcc = ($ys12 - $c23) / $mr23; + last CCXYLINE; + } + } + if (abs($deltay23) < 0.0000001) + { + $xcc = $xs23; + if (abs($deltax12) < 0.0000001) + { + $ycc = $ys12; + last CCXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + $ycc = $mr12 * $xcc + $c12; + last CCXYLINE; + } + } + if (abs($deltax23) < 0.0000001) + { + $ycc = $ys23; + if (abs($deltay12) < 0.0000001) + { + $xcc = $xs12; + last CCXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + $xcc = ($ycc - $c12) / $mr12; + last CCXYLINE; + } + } + $m12 = $deltay12 / $deltax12; + $mr12 = -1 / $m12; + $c12 = $ys12 - $mr12 * $xs12; + #----- + $m23 = $deltay23 / $deltax23; + $mr23 = -1 / $m23; + $c23 = $ys23 - $mr23 * $xs23; + $xcc = ($c23 - $c12) / ($mr12 - $mr23); + $ycc = ($c23 * $mr12 - $c12 * $mr23) / ($mr12 - $mr23); + } + # + $sideA = &Length($xA,$yA,$xB,$yB); + $sideB = &Length($xB,$yB,$xC,$yC); + $sideC = &Length($xC,$yC,$xA,$yA); + $a = triangleArea($xA, $yA, $xB, $yB, $xC, $yC); + $radius = ($sideA * $sideB * $sideC) / (4 * $a); + # + return ($xcc, $ycc, $radius); + } + +@ The subroutine [[ComputeDist]] is used to compute a distance that is +specified by either a float number, a pair of points, or a variable +name. In case we have a pair of identifiers, we check whether the first +one is a point. If it isn't a point we assume we have a variable followed +by a keyword. Otherwise, i.e., if it is a point name, we check whether +the second identifier is also a point name. If it is, we simply return +the distance between them, otherwise we issue an error message. +If we have only a single identifier, we check whether it is a +variable that has already been defined, and if so we return its value. + Since, this +subroutine is heavily used, it actually returns a pair of numbers: +the first one being the computed distance and the second one being an +error indicator. If the value of this indicator is 0, then there is no +error. If its value is 1, then there is an error. Moreover, in case there +is an error the distance is assumed to be equal to zero. + +<<subroutine <tt>ComputeDist</tt> >>= + sub ComputeDist { + my ($lc) = $_[0]; + my ($v1, $v2); + + if (s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//) #is it a number? + { + return ($1, 1); + } + elsif (/^[^\W\d_]\d{0,3}[^\W\d_]\d{0,3}/) #it is a pair of IDs? + { + s/^([^\W\d_]\d{0,3})//i; + $v1 = $1; + if (!exists($PointTable{lc($v1)})) { + if (exists($VarTable{lc($v1)})) { + return ($VarTable{lc($v1)}, 1); + } + PrintErrorMessage("Point $v1 has not been defined", $lc); + s/^\s*[^\W\d_]\d{0,3}//i; + return (0,0); + } + $v1 = lc($v1); + s/^\s*([^\W\d_]\d{0,3})//i; + $v2 = $1; + if (!exists($PointTable{lc($v2)})) + { + PrintErrorMessage("Point $v2 has not been defined", $lc); + return (0,0); + } + $v2 = lc($v2); + my ($x1,$y1,$pSV1,$pS1) = unpack("d3A*",$PointTable{$v1}); + my ($x2,$y2,$pSV2,$pS2) = unpack("d3A*",$PointTable{$v2}); + return (Length($x1,$y1,$x2,$y2), 1); + } + elsif (s/^([^\W\d_]\d{0,3})//i) # it is a single id + { + $v1 = $1; + if (!exists($VarTable{lc($v1)})) #it isn't a variable + { + PrintErrorMessage("Variable $v1 has not been defined", $lc); + return (0,0); + } + return ($VarTable{lc($v1)}, 1); + } + else + { + PrintErrorMessage("Unexpected token", $lc); + return (0,0); + } + } + +@ The subroutine [[intersection4points]] has 8 parameters that correspond to the +coordinates of four points that uniquely determine two lines, and computes the +the point of intersection of these two lines. + +<<subroutine <tt>intersection4points</tt> >>= + sub intersection4points { + my ($x1, $y1, $x2, $y2, $x3, $y3, $x4, $y4) = @_; + my ($deltay12, $deltax12, $deltay34, $deltax34); + my ($xcc, $ycc, $m34, $c34, $m12, $c12); + + $deltay12 = $y2 - $y1; + $deltax12 = $x2 - $x1; + # + $deltay34 = $y4 - $y3; + $deltax34 = $x4 - $x3; + I4PXYLINE:{ + if (abs($deltay12) < 0.0000001) + { + $ycc = $y1; + if (abs($deltax34) < 0.0000001) + { + $xcc = $x3; + last I4PXYLINE; + } + else + { + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $xcc = ($ycc - $c34) / $m34; + last I4PXYLINE; + } + } + if (abs($deltax12) < 0.0000001) + { + $xcc = $x1; + if (abs($deltay34) < 0.0000001) + { + $ycc = $y3; + last I4PXYLINE; + } + else + { + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $ycc = $m34 * $xcc + $c34; + last I4PXYLINE; + } + } + if (abs($deltay34) < 0.0000001) + { + $ycc = $y3; + if (abs($deltax12) < 0.0000001) + { + $xcc = $x1; + last I4PXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $xcc = ($ycc - $c12) / $m12; + last I4PXYLINE; + } + } + if (abs($deltax34) < 0.0000001) + { + $xcc = $x3; + if (abs($deltay12) < 0.0000001) + { + $ycc = $y1; + last I4PXYLINE; + } + else + { + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $ycc = $m12 * $xcc + $c12; + last I4PXYLINE; + } + } + $m12 = $deltay12 / $deltax12; + $c12 = $y1 - $m12 * $x1; + $m34 = $deltay34 / $deltax34; + $c34 = $y3 - $m34 * $x3; + $xcc = ($c34 - $c12) / ($m12 - $m34); + $ycc = ($c34 * $m12 - $c12 * $m34) / ($m12 - $m34); + } + return ($xcc, $ycc); + } + +@ The subroutine [[IncircleCenter]] computes the center and the +radius of the circle that is inside a triangle and touches the sides of +the triangle. The subroutine has six arguments that correspond to the +coordinates of three points that uniquely determine the triangle. Here are +the details: +<ul> +<li> Let the triangle points be A, B, C and sides a, b, c, where side B +is opposite angle B, etc. </li> +<li> Use angles A and B only.</li> +<li> Let the bisector of angle A meet side a in point A1, and let the +distance of A1 from B be designated BA1</li> +<li> Using the sine rule, one gets: BA1/c = a/(b+c), that is +BA1 = c * a/(b+c).</li> +<li> Now do the same for side b, and determine equivalent point B1. +CB1/a = b/(b+c), that is CB1 = a * b/(b+c).</li> +<li> We can now find the intersection of the line from point A to point A1, +and the line from point B to point B1. We have four points, so we use the +mathspic internal [[intersection4points]] subroutine to return the +coordinates of the intersection X<sub>i</sub>, Y<sub>i</sub>.</li> +<li> Now get the radius: R=(area of triangle)/(a+b+c)/2</li> +<li>Finally, return the radius and the coordinates of the center. +</ul> + +<<subroutine <tt>IncircleCenter</tt> >>= + sub IncircleCenter { + my ($Ax, $Ay, $Bx, $By, $Cx, $Cy) = @_; + my ($sideA, $sideB, $sideC); + my ($ba1, $xA1, $yA1, $cb1, $ac1, $xB1, $yB1, $xC1, $yC1, $a, $s, $r); + + #determine the lengths of the sides + $sideA = Length($Bx, $By, $Cx, $Cy); + $sideB = Length($Cx, $Cy, $Ax, $Ay); + $sideC = Length($Ax, $Ay, $Bx, $By); + # + $ba1 = ($sideC * $sideA) / ($sideB + $sideC); + ($xA1, $yA1) = pointOnLine($Bx, $By, $Cx, $Cy, $ba1); + $cb1 = ($sideA * $sideB) / ($sideC + $sideA); + ($xB1, $yB1) = pointOnLine($Cx, $Cy, $Ax, $Ay, $cb1); + $ac1 = ($sideB * $sideC) / ($sideA + $sideB); + ($xC1, $yC1) = pointOnLine($Ax, $Ay, $Bx, $By, $ac1); + ($xcenter, $ycenter) = &intersection4points($Ax, $Ay, $xA1, $yA1, + $Bx, $By, $xB1, $yB1); + # get radius + $a = &triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $s = ($sideA + $sideB +$sideC) / 2; + $r = $a / $s; + return ($xcenter, $ycenter, $r); + } + +@ The subroutine [[Angle]] takes six arguments which correspond to the +coordinates of three points that define an angle. The subroutine computes +the opening of the angle in degrees. In case there is an error it returns +the number -500. ****EXPLAIN THE ALGORITHM**** + +<<subroutine <tt>Angle</tt> >>= + sub Angle { + my ($Ax, $Ay, $Bx, $By, $Cx, $Cy) = @_; + my ($RAx, $RAy, $RBx, $RBy, $RCx, $RCy, $deltax, $deltay); + my ($lineBA, $lineBC, $lineAC, $k, $kk, $angle); + my ($T, $cosT, $sinT) = (0.3, cos(0.3), sin(0.3)); + + $RAx = $Ax * $cosT + $Ay * $sinT; + $RAy = -$Ax * $sinT + $Ay * $cosT; + $RBx = $Bx * $cosT + $By * $sinT; + $RBy = -$Bx * $sinT + $By * $cosT; + $RCx = $Cx * $cosT + $Cy * $sinT; + $RCy = -$Cx * $sinT + $Cy * $cosT; + $deltax = $RBx - $RAx; + $deltay = $RBy - $RAy; + $lineBA = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineBA < 0.0000001) + { + return -500; + } + $deltax = $RBx - $RCx; + $deltay = $RBy - $RCy; + $lineBC = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineBC < 0.0000001) + { + return -500; + } + $deltax = $RAx - $RCx; + $deltay = $RAy - $RCy; + $lineAC = sqrt($deltax*$deltax + $deltay*$deltay); + if ($lineAC < 0.0000001) + { + return -500; + } + $k = ($lineBA*$lineBA + $lineBC*$lineBC - $lineAC*$lineAC ) / + (2 * $lineBA * $lineBC); + $k = -1 if $k < -0.99999; + $k = 1 if $k > 0.99999; + $kk = $k * $k; + if (($kk * $kk) == 1) + { + $angle = PI if $k == -1; + $angle = 0 if $k == 1; + } + else + { + $angle = (PI / 2) - atan2($k / sqrt(1 - $kk),1); + } + return $angle * 180 / PI; + } + +@ The subroutine [[excircle]] computes the center and the radius of a circle that +externally touches a given side (4th and 5th arguments) of triangle (determined +by the 1rst, the 2nd and 3rd argument). Here are the details: +<ul> +<li> Let the triangle points be A, B, C, and the given side be BC.</li> +<li> Now calculate the radius of Excircle = (triangle area)/(s - side length), +where s = (a+b+c)/2</li> +<li>Calculate the distance from the angle (A) (opposite the given side BC) + to the excircle center = radius/sin(A/2)</li> +<li> Now determine the the Excircle center by locating it on the angle bisector +(i.e., same line that the IncircleCenter is on), but at distance d further +away from angle A. So, we now have the Incircle center (I), + determine deltaX and deltaY from I to A, calculate the distance AI, + and then extend the line from I by distance d to Excenter Xc, Yc.</li> +</ul> + +<<subroutine <tt>excircle</tt> >>= + sub excircle { + my ($A, $B, $C, $D, $E) = @_; + my ($Ax,$Ay,$Bx,$By,$Dx,$Dy,$Ex,$Ey,$ASVA,$ASA); + ($Ax,$Ay,$ASVA,$ASA)=unpack("d3A*",$PointTable{$A}); + ($Bx,$By,$ASVA,$ASA)=unpack("d3A*",$PointTable{$B}); + ($Cx,$Cy,$ASVA,$ASA)=unpack("d3A*",$PointTable{$C}); + ($Dx,$Dy,$ASVA,$ASA)=unpack("d3A*",$PointTable{$D}); + ($Ex,$Ey,$ASVA,$ASA)=unpack("d3A*",$PointTable{$E}); + my ($sideA, $sideB, $sideC, $s, $R, $theAdeg, $d); + my ($Xmypoint, $Ymypoint, $deltax, $deltay, $mylength, $xc, $yc); + + $sideA = &Length($Bx, $By, $Cx, $Cy); + $sideB = &Length($Cx, $Cy, $Ax, $Ay); + $sideC = &Length($Ax, $Ay, $Bx, $By); + $s = ($sideA + $sideB + $sideC) / 2; + $R = triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy) / + ($s - &Length($Dx, $Dy, $Ex, $Ey)); + if (($D eq $A && $E eq $B) || ($D eq $B && $E eq $A)) + { + $theAdeg = &Angle($Bx, $By, $Cx, $Cy, $Ax, $Ay); + $Xmypoint = $Cx; + $Ymypoint = $Cy; + } + elsif (($D eq $B && $E eq $C) || ($D eq $C && $E eq $B)) + { + $theAdeg = &Angle($Cx, $Cy, $Ax, $Ay, $Bx, $By); + $Xmypoint = $Ax; + $Ymypoint = $Ay; + } + elsif (($D eq $C && $E eq $A) || ($D eq $A && $E eq $C)) + { + $theAdeg = &Angle($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $Xmypoint = $Bx; + $Ymypoint = $By; + } + else + { + return (0,0,0); + } + $d = $R / sin($theAdeg * PI / 180 / 2); + my ($xIn, $yIn, $rin) = &IncircleCenter($Ax, $Ay, $Bx, $By, $Cx, $Cy); + $deltax = $xIn - $Xmypoint; + $deltay = $yIn - $Ymypoint; + $mylength = sqrt($deltax*$deltax + $deltay*$deltay); + $xc = $Xmypoint + $d * $deltax / $mylength; + $yc = $Ymypoint + $d * $deltay / $mylength; + return ($xc, $yc, $R); + } + +@ The [[DrawLineOrArrow]] subroutine is used to parse the arguments of the commands +[[drawline]], [[drawthickline]], [[drawarrow]], [[drawthickarrow]] and +[[drawCurve]]. In general, these commands have as arguments a list of points separated by +commas that are used to draw a set of lines. The list of points is +enclosed in parentheses. Here we give only the syntax of the [[drawline]] +comma, as the syntax of the other commands is identical: +<pre> + drawline ::= "drawline" "(" Points { "," Points } ")" + Points ::= Point { separator Point} + separator ::= blank | empty +</pre> +In the following code we +scan a list of points (possibly separated by blanks) and we stop when +we encounter either a comma or some other character. In case we have found +a comma, we check whether we have a [[drawline]] command and if this is +the case we plot the list of points. We continue with the next list of points, +until there are no more points. The inner while-loop is used to control the +consumption of point tokens and the external to reset the array [[PP]] which +holds the point names. + +<<subroutine <tt>DrawLineOrArrow</tt> >>= + sub DrawLineOrArrow { + my $draw_Line = shift; + my $lc = shift; + my $lineLength = -1; + my $stacklen = 0; + my @PP = (); +# if ($draw_Line != 2) { +# s/\s*//; +# if (s/^\[\s*//) { # optional length specifier +# $lineLength = expr($lc); +# if ($lineLength <= 0) { +# PrintErrorMessage("length must greater than zero",$lc); +# $lineLength = -1; +# } +# chk_rsb("optional part",$lc); +# } +# } + chk_lparen("$cmd",$lc); + DRAWLINES:while(1) { + @PP = () ; + while(1) { + if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name + $P = $1; + if (!exists($PointTable{lc($P)})) { + PrintErrorMessage("Undefined point $P",$lc); + } + else { + push (@PP,$P); + } + } + else { + $stacklen = @PP; + if ($draw_Line != 2) { + if ($stacklen <= 1) { + PrintErrorMessage("Wrong number of points",$lc); + } + else { + push(@PP,$lc); + if ($draw_Line == 0) { + drawarrows(@PP); + } + elsif ($draw_Line == 1) { + drawlines(@PP); + } + } + } + if (s/^,\s*// and $draw_Line != 2) { + next DRAWLINES; + } + else { + last DRAWLINES; + } + } + } + } + if ($draw_Line == 2) { + $stacklen = @PP; + if ($stacklen < 2) { + PrintErrorMessage("Wrong number of points",$lc); + } + elsif ($stacklen % 2 == 0) { + PrintErrorMessage("Number of points must be odd",$lc); + } + else { + drawCurve(@PP); + } + } + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + } + +@ The subroutine [[drawarrows]] is used to draw one or more lines. The subroutine +accepts as argument an array which contains the names of the points which +define the lines, plus the current program line number. Each arrow is printed +using the following code: +<center> +<tt>\arrow < </tt>ArrowLength <tt> mm> [</tt> beta <tt>,</tt> gamma <tt>] from +x1 y1 to x2 y2 </tt> +</center> +where beta is equal to tan([[$arrowAngleB]] * [[d2r]] /2) and gamma is equal to +2*tan([[$arrowAngleC]] * [[d2r]] / 2). + +<<subroutine <tt>drawarrows</tt> >>= + sub drawarrows { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p, $q, $r12, $d12); + my ($px,$py,$pSV,$pS, $qx,$qy,$qSV,$qS); + + $NumberOfPoints = $NoArgs - 1; + LOOP: for(my $i=0; $i < $NumberOfPoints - 1; $i++) + { + $p = $_[$i]; + $q = $_[$i+1]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + ($qx,$qy,$qSV,$qS) = unpack("d3A*",$PointTable{lc($q)}); + $pSV = $defaultLFradius if $pSV == 0; + $qSV = $defaultLFradius if $qSV == 0; + $r12 = $pSV + $qSV; + $d12 = Length($px,$py,$qx,$qy); + if ($d12 <= $r12) + { + if($d12 == 0) + { + PrintErrorMessage("points $p and $q are the same", $lc); + next LOOP; + } + PrintWarningMessage("arrow $p$q not drawn: points too close or ". + "radii too big", $lc); + next LOOP; + } + ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV > 0; + ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV > 0; + my ($beta, $gamma); + $beta = tan($arrowAngleB * D2R / 2); + $gamma = 2 * tan($arrowAngleC * D2R / 2); + printf OUT "\\arrow <%.5f%s> [%.5f,%.5f] from %.5f %.5f to %.5f %.5f\n", + $arrowLength, $arrowLengthUnits, $beta, $gamma, $px, $py, $qx, $qy; + } + } + +@ The subroutine [[drawlines]] is used to draw one or more lines. The subroutine +accepts as argument an array which contains the names of the points which +define the lines, plus the current program line number. If there are only +two points (i.e., only one line), then we output the following PiCTeX code: +<center> +<tt> \plot x1 y1 x2 y2 / %% pointname1 pointname2</tt> +</center> +If there are more than two points, then we need to write the PiCTeX code in +pairs with two points on each line (just to keep things simple) as follows: +<center> +<tt> \plot x1 y1 x2 y2 / %% pointname1 pointname2</tt> +<tt> \plot x2 y2 x3 y3 / %% pointname2 pointname3</tt> +<tt> \plot x3 y3 x4 y4 / %% pointname3 pointname4</tt> +</center> +An important part of the subroutine is devoted to checking whether either +or both of the pairs of points are associated with a line-free zone, and if +so, then we must take care not to draw the line inside the line-free zone. If +a point does have a line-free zone, then we use the [[pointOnLine]] +subroutine to determine the point on the line which is just on the line-free +boundary, and draw the line to the that point instead of to the exact +point-location. + +<<subroutine <tt>drawlines</tt> >>= + sub drawlines { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p, $q, $r12, $d12); + my ($px,$py,$pSV,$pS, $qx,$qy,$qSV,$qS); + + $NumberOfPoints = $NoArgs - 1; + LOOP: for(my $i=0; $i < $NumberOfPoints - 1; $i++) + { + $p = $_[$i]; + $q = $_[$i+1]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + ($qx,$qy,$qSV,$qS) = unpack("d3A*",$PointTable{lc($q)}); + $pSV = $defaultLFradius if $pSV == 0; + $qSV = $defaultLFradius if $qSV == 0; + $r12 = $pSV + $qSV; + $d12 = Length($px,$py,$qx,$qy); + if ($d12 <= $r12) + { + if($d12 == 0) + { + PrintErrorMessage("points $p and $q are the same", $lc); + next LOOP; + } + PrintWarningMessage("line $p$q not drawn: points too close or ". + "radii too big", $lc); + next LOOP; + } + ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV > 0; + ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV > 0; + if ($px == $qx || $py == $qy) + { + printf OUT "\\putrule from %.5f %.5f to %.5f %.5f %%%% %s%s\n", + $px,$py,$qx,$qy,$p,$q; + } + else + { + printf OUT "\\plot %.5f %.5f\t%.5f %.5f / %%%% %s%s\n", + $px, $py,$qx,$qy,$p,$q; + } + } + } + +@ The subroutine [[drawCurve]] is used to draw a curve that passes through an odd +number of points. The subroutine has as argument an array which contains the names of the +points which define the lines plus the current program line number. The subroutine +emits code that has the following general form: +<pre> + \setquadratic + \plot + X1 Y1 + X2 Y2 + X3 Y3 + \setlinear +</pre> + + +<<subroutine <tt>drawCurve</tt> >>= + sub drawCurve { + my ($NoArgs); + $NoArgs = @_; + my ($lc) = $_[$NoArgs-1]; #line number is the last argument + my ($NumberOfPoints, $p); + + $NumberOfPoints = $NoArgs - 1; + print OUT "\\setquadratic\n\\plot\n"; + for(my $i=0; $i <= $NumberOfPoints; $i++) + { + $p = $_[$i]; + my ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + printf OUT "\t%0.5f %0.5f", $px, $py; + print OUT (($i == $NumberOfPoints) ? " / %$p\n" : " %$p\n"); + } + print OUT "\\setlinear\n"; + } + +@ The subroutine [[drawpoints]] is used to draw one or more points. The subroutine +has as arguments a list of points. For each point we produce code that has +the following general form: +<center> +<tt> \put {SYMBOL} at Px PY</tt> +</center> +where [[SYMBOL]] is either the default plot symbol, i.e., [[$\bullet$]], +whatever the user has set with the [[PointSymbol]] command, or the plot +symbol specified in the definition of the point. + +<<subroutine <tt>drawpoints</tt> >>= + sub drawpoints { + my ($NumberOfPoints,$p); + $NumberOfPoints = @_; + my ($px,$py,$pSV,$pS); + + for($i=0; $i < $NumberOfPoints; $i++) + { + $p = $_[$i]; + ($px,$py,$pSV,$pS) = unpack("d3A*",$PointTable{lc($p)}); + if ($pS eq "" and $defaultsymbol =~ /circle|square/) { + $pS = $defaultsymbol; + } + POINTSWITCH: { + if ($pS eq "") # no plot symbol specified + { + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", + $defaultsymbol, $px, $py, $p; + last POINTSWITCH; + } + if ($pS eq "circle") # plot symbol is a circle + { + my $radius = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} : + $GlobalDimOfPoints; + if ($radius > 0) # draw a circle using the current units + { + if ($radius == 1.5) # use \bigcirc + { + printf OUT "\\put {\$\\bigcirc\$} at %.5f %.5f %%%% %s\n", + $px, $py, $p; + } + else + { + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f %%%% %s\n", + $px+$radius, $py, $px, $py, $p; + } + } + else #use \circ symbol + { + printf OUT "\\put {\$\\circ\$} at %.5f %.5f %%%% %s\n", + $px,$py,$p; + } + last POINTSWITCH; + } + if ($pS eq "square") + { + my $side = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} : + $GlobalDimOfPoints; + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", + drawsquare($side), $px, $py, $p; + last POINTSWITCH; + } + printf OUT "\\put {%s} at %.5f %.5f %%%% %s\n", $pS,$px,$py,$p; + } + } + } + +@ The subroutine [[drawAngleArc]] gets six arguments which correspond to +three points defining an angle (variables [[$P1]], [[$P2]] and [[$P3]]), +the radius, the internal/external specification and the direction +specification (clockwise or anticlockwise). +Depending on the values of these arguments, the subroutine +returns the corresponding PiCTeX code, the general format of +which is <pre> + \circulararc Angle degrees from x y center at x2 y2 +</pre> +where [[Angle]] is the angle that the three points P1 P2 P3 define +(computed by subroutine [[Angle]]), +and [[x]] and [[y]] are the coordinates of a point +residing on line P2P1 at distance equal to a [[$radius]] from +point [[$P2]]; and [[x2]], [[y2]] are the coordinates of the +center of the circle about which the arc is drawn, +i.e., point [[$P2]]. + +<<subroutine <tt>drawAngleArc</tt> >>= +sub drawAngleArc { + my ($P1, $P2, $P3, $radius, $inout, $direction) = @_; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + + my $internalAngle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + my $externalAngle = 360 - $internalAngle; + my ($x, $y) = pointOnLine($x2, $y2, $x1, $y1, $radius); + my $code = ""; + if ($inout eq "internal" and $direction eq "clockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + -1 * $internalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "internal" and $direction eq "anticlockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + $internalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "external" and $direction eq "clockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + -1 * $externalAngle, $x, $y, $x2, $y2; + } + elsif ($inout eq "external" and $direction eq "anticlockwise" ) { + $code = sprintf "\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n", + $externalAngle, $x, $y, $x2, $y2; + } + return $code; +} + +@ The subroutine [[drawAngleArrow]] gets six arguments which correspond to +three points defining an angle (variables [[$P1]], [[$P2]] and [[$P3]]), +the radius, the internal/external specification and the direction +specification. The subroutine mainly draws the arrowhead, and +calls the subroutine [[drawAngleArc]] to draw the +arc part of the arrow. + +<<subroutine <tt>drawAngleArrow</tt> >>= +sub drawAngleArrow { + my ($P1, $P2, $P3, $radius, $inout, $direction) = @_; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + + my $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction); + + my ($xqp, $yqp) = pointOnLine($x2, $y2, $x1, $y1, $radius); + my ($deltax, $deltay) = ($x1 - $x2, $y1 - $y2); + my $AL; + + if ($xunits =~ /mm/) { + $AL = 1; + } + elsif ($xunits =~ /cm/) { + $AL = 0.1; + } + elsif ($xunits =~ /pt/) { + $AL = 2.845; + } + elsif ($xunits =~ /bp/) { + $AL = 2.835; + } + elsif ($xunits =~ /pc/) { + $AL = 0.2371; + } + elsif ($xunits =~ /in/) { + $AL = 0.03937; + } + elsif ($xunits =~ /dd/) { + $AL = 2.659; + } + elsif ($xunits =~ /cc/) { + $AL = 0.2216; + } + elsif ($xunits =~ /sp/) { + $AL = 186467.98; + } + my $halfAL = $AL / 2; + my $d = sqrt($radius * $radius - $halfAL * $halfAL); + my $alpha = atan2($d / $halfAL, 1) * R2D; + my $beta = 2 * (90 - $alpha); + my $thetaqr; + if (abs($deltay) < 0.00001) { + if ($deltax > 0 ) {$thetaqr = 0 } + elsif ($deltax < 0) {$thetaqr = -180} + } + else { + if (abs($deltax) < 0.00001) { + $thetaqr = 90; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + } + my ($xqr, $yqr) = pointOnLine($x2, $y2, $x3, $y3, $radius); + $deltax = $x3 - $x2; + $deltay = $y3 - $y2; + $alpha = atan2(sqrt($radius * $radius - $halfAL * $halfAL) / $halfAL, 1) / + D2R; + $beta = 2 * (90 - $alpha); + LINE2 : { + if (abs($deltax) < 0.00001) { + if ($deltay > 0) { $thetaqr = 90 } + elsif ($deltay < 0) { $thetaqr = - 90 } + last LINE2; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + if (abs($deltay) < 0.00001) { + if ($deltax > 0) { $thetaqr = 0 } + elsif ($deltax < 0) { $thetaqr = -180 } + last LINE2; + } + else { + $thetaqr = atan2($deltay / $deltax, 1) * R2D; + } + if ($deltax < 0 and $deltay > 0) { $thetaqr += 180 } + elsif ($deltax < 0 and $deltay < 0) { $thetaqr += 180 } + elsif ($deltax > 0 and $deltay < 0) { $thetaqr += 360 } + } + my $xqrleft = $x2 + $radius * cos(($thetaqr + $beta) * D2R); + my $yqrleft = $y2 + $radius * sin(($thetaqr + $beta) * D2R); + my $xqrright = $x2 + $radius * cos(($thetaqr - $beta) * D2R); + my $yqrright = $y2 + $radius * sin(($thetaqr - $beta) * D2R); + if ($inout eq "internal" and $direction eq "clockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrleft, $yqrleft, $xqr, $yqr; + } + elsif ($inout eq "internal" and $direction eq "anticlockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrright, $yqrright, $xqr, $yqr; + } + elsif ($inout eq "external" and $direction eq "clockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrleft, $yqrleft, $xqr, $yqr; + } + elsif ($inout eq "external" and $direction eq "anticlockwise") { + $code .= sprintf "\\arrow <1.5mm> [0.5, 1] from %.5f %.5f to %.5f %.5f\n", + $xqrright, $yqrright, $xqr, $yqr; + } + return $code; +} + +@ The subroutine [[expr]] is used to parse an expression. We are using a +recursive descent parser to parse and evaluate an expression. The +general syntax of an expression is as follows: +<pre> +expr ::= term { addop term } +addop ::= "+" | "-" +term ::= factor { mulop factor } +mulop ::= "*" | "/" | "rem" +factor ::= primitive [ ** factor ] +primitive ::= [ "+" | "-"] primitive | number | variable | + pair-of-points | "(" expr ")" | + "sin (" expr ")" | "cos (" expr ")" | "area (" ThreePoints ")" | + "tan (" expr ")" | "exp (" expr ")" | "int" "(" expr ")" | + "log (" expr ")" | "atan (" expr ")" | "sgn" "(" expr ")" | + "sqrt (" expr ")" | "acos (" expr ")" | "asin (" expr ")" | + "atan (" expr ")" | "_pi_" | "_e_" | + "xcoord (" point ")" | "ycoord (" point ")" | "angle "(" ThreePoints ")"| + "angledeg" "(" ThreePoints ")" | "direction" "(" TwoPoints ")" | + "directiondeg" "(" TwoPoints ")" | "_linethickness_" +</pre> +Note that [[_pi_]] and [[_e_]] can be used to access the value of the constants +Pi and e. + +<<subroutine <tt>expr</tt> >>= +sub expr { + my $lc = $_[0]; + my($left,$op,$right); + + $left = term($lc); + while ($op = addop()) { + $right = term($lc); + if ($op eq '+') + { $left += $right } + else + { $left -= $right } + } + return $left; +} + +sub addop { + s/^([+-])// && $1; +} + +sub term { + my $lc = $_[0]; + my ($left, $op, $right); + $left = factor($lc); + while ($op = mulop()) { + $right = factor($lc); + if ($op eq '*') + { $left *= $right } + elsif ($op =~ /rem/i) { + eval {$left %= $right}; + PrintFatalError("Division by zero", $lc) if $@; + } + else { + eval {$left /= $right}; + PrintFatalError("Division by zero", $lc) if $@; + } + } + return $left; +} + +sub mulop { + (s#^([*/])## || s/^(rem)//i) && lc($1); +} + +sub factor { + my $lc = $_[0]; + my ($left); + + $left = primitive($lc); + if (s/^\*\*//) { + $left **= factor($lc); + } + return $left; +} + +sub primitive { + my $lc = $_[0]; + my $val; + s/\s*//; + if (s/^\(//) { #is it an expr in parentheses + $val = expr($lc); + s/^\)// || PrintErrorMessage("Missing right parenthesis", $lc); + } + elsif (s/^-//) { # is it a negated primitive + $val = - primitive(); + } + elsif (s/^\+//) { # is it a positive primitive + $val = primitive(); + } + elsif (s/^angledeg//i) { + chk_lparen("angledeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $d12 = Length($x1, $y1, $x2, $y2); + my $d23 = Length($x2, $y2, $x3, $y3); + my $d31 = Length($x3, $y3, $x1, $y1); + if ( $d12 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_2' are the same", $lc); + $val = 0; + } + elsif ( $d23 == 0 ) { + PrintErrorMessage("points `$point_2' and `$point_3' are the same", $lc); + $val = 0; + } + elsif ( $d31 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_3' are the same", $lc); + $val = 0; + } + else { + $val = Angle($x1, $y1, $x2, $y2, $x3, $y3); + $val = 0 if $val == -500; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^angle//i) { + chk_lparen("angle".$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $d12 = Length($x1, $y1, $x2, $y2); + my $d23 = Length($x2, $y2, $x3, $y3); + my $d31 = Length($x3, $y3, $x1, $y1); + if ( $d12 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_2' are the same", $lc); + $val = 0; + } + elsif ( $d23 == 0 ) { + PrintErrorMessage("points `$point_2' and `$point_3' are the same", $lc); + $val = 0; + } + elsif ( $d31 == 0 ) { + PrintErrorMessage("points `$point_1' and `$point_3' are the same", $lc); + $val = 0; + } + else { + $val = Angle($x1, $y1, $x2, $y2, $x3, $y3); + if ($val == -500) { + $val = 0; + } + else { + $val = D2R * $val; + } + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^area//i) { + chk_lparen("angledeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + $val = triangleArea($x1, $y1, $x2, $y2, $x3, $y3); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^asin//i) { + chk_lparen("asin"); + $val = expr(); + PrintFatalError("Can't take asin of $val", $lc) if $val < -1 || $val > 1; + $val = asin($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^acos//i) { + chk_lparen("acos"); + $val = expr(); + PrintFatalError("Can't take acos of $val", $lc) if $val < -1 || $val > 1 ; + $val = acos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^atan//i) { + chk_lparen("atan"); + $val = expr(); + $val = atan($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^cos//i) { + chk_lparen("cos"); + $val = expr(); + $val = cos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^directiondeg//i) { + chk_lparen("directiondeg",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $x3 = $x1+1; + if ( ($y2 - $y1) >= 0) { + $val = Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + } + else { + $val = 360 - Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^direction//i) { + chk_lparen("direction",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $x3 = $x1+1; + if ( ($y2 - $y1) >= 0) { + $val = Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + $val = D2R * $val; + } + else { + $val = 360 - Angle($x3, $y1, $x1, $y1, $x2, $y2); + $val = 0 if $val == -500; + $val = D2R * $val; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^exp//i) { + chk_lparen("exp"); + $val = expr(); + $val = exp($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^int//i) { + chk_lparen("int"); + $val = expr(); + $val = int($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^log//i) { + chk_lparen("log"); + $val = expr(); + PrintFatalError("Can't take log of $val", $lc) if $val <= 0; + $val = log($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sin//i) { + chk_lparen("sin"); + $val = expr(); + $val = sin($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sgn//i) { + chk_lparen("sgn"); + $val = expr(); + if ($val > 0) { + $val = 1; + } + elsif ($val == 0) { + $val = 0; + } + else { + $val = -1; + } + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^sqrt//i) { + chk_lparen("sqrt"); + $val = expr(); + $val = sqrt($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^tan//i) { + chk_lparen("tan"); + $val = expr(); + $val = sin($val)/cos($val); + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^xcoord//i) { + chk_lparen("xcoord"); + my $point_name = get_point; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_name}); + $val = $x1; + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^ycoord//i) { + chk_lparen("ycoord"); + my $point_name = get_point; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_name}); + $val = $y1; + chk_rparen("Missing right parenthesis", $lc); + } + elsif (s/^_pi_//i) { + $val = PI; + } + elsif (s/^_e_//i) { + $val = 2.71828182845905; + } + elsif (s/^_linethickness_//i) { + $val = $LineThickness / $xunits; + } + else { + my $err_code; + ($val,$err_code) = ComputeDist($lc); + } + s/\s*//; + return $val; +} + +@ The subroutine [[memberOf]] is used to check whether a string is part of +a list of strings. We assume that the first argument is the string in +question. We compare each list element against the string in question and +if we find it we stop and return the value [[1]] (denoting truth). Otherwise, +we simply return the value [[0]] (denoting false). + +<<subroutine <tt>memberOf</tt> >>= +sub memberOf { + my $elem = shift(@_); + + my $found = 0; + foreach $item (@_){ + if ($item eq $elem){ + $found = 1; + last; + } + } + return $found; +} + +@ The subroutine [[tand]] computes the tangent of an angle. The angle is +supposed to be in degrees. We simply transform it into radians and then +compute the actual result. + +<<subroutine <tt>tand</tt> >>= +sub tand { + my $d = $_[0]; + $d = $d * PI / 180; + return sin($d)/cos($d); +} + +@ The subroutine [[get_string]] is used to extract a leading valid mathspic string +from the input line. A string must start with a quotation mark, i.e., [["]], +and must end with the same symbol. A string may contain quotation marks which +must be escaped with a backslash, i.e., [[\]]. Initially, we remove all +leading white space. If the next character of the string is not a quotation +mark we print an error message and stop. Otherwise, we split the string into +an array of characters and store the characters up to the next quotation +mark to the array [[@cmd]]. In case the next character is a backslash and +we aren't at the end of the input string and the next character is a +quotation mark, we have an escape sequence. This means that we store these +two characters in the [[@cmd]] array and skip to characters after the quotation +mark. Otherwise, we simply store the character in the [[@cmd]] array and +skip to the next character. This process is repeated until either we consume +all the characters of the string or until we find a sole quotation mark. +Since we are not sure what has forced the loop to exit, we check whether +there are still characters in the input string and we check whether this +is a quotation mark. If these tests fail we have a string without a +closing quotation mark. In all cases we return a triplet consisting of +a number denoting success (1) or failure (0) and what we have consumed +from the input string, and what is left from the input string. + +<<subroutine <tt>get_string</tt> >>= +sub get_string { + my $string = shift; + my $lc = shift; + + $string =~ s/^\s+//; + if ($string !~ s/^\"//) { + PrintErrorMessage("No starting \" found",$lc); + return (1,$string,$string); + } + my @ch = split //,$string; + my @cmd; + while (@ch and $ch[0] ne "\"") { + if ($ch[0] eq "\\" and (defined $ch[1]) and $ch[1] eq "\"") { + shift @ch; + push @cmd, $ch[0]; + shift @ch; + } + else { + push @cmd, $ch[0]; + shift @ch; + } + } + if (! defined $ch[0]) { + PrintErrorMessage("No closing \" found",$lc); + return (1,join("",@cmd), join("",@ch)) + } + else { + shift @ch; + return (0, join("",@cmd), join("",@ch)) + } +} + +@ The definition as well as an explanation of the functionality of the +following subroutine can be found in "Programming Perl", 3rd edition. + +<<subroutine <tt>is_tainted</tt> >>= +sub is_tainted { + my $arg = shift; + my $nada = substr($arg,0,0); + local $@; + eval { eval "# $nada"}; + return length($@) != 0; +} + +@ The subroutine [[noOfDigits]] has one argument which is a number and returns +the number of decimal digits it has. If the number matches the regular +expression [[^\d+(?!\.)]] (a series of digits <i>not</i> followed by a +period), then the number of decimal digits is zero. If the +number matches the +regular expression [[^\d+\.(\d+)?]], then number of decimal digits equals +[[length($1)]]. Naturally, it maybe zero! + +<<subroutine <tt>noOfDigits</tt> >>= +sub noOfDigits { + my $num = $_[0]; + + if ($num =~ /^[\+-]?\d+(?!\.)/) { + return 0; + } + elsif ($num =~ /^[\+-]\d+\.(\d+)?/) { + return length($1); + } +} + +@ Subroutine [[drawsquare]] is use by the [[drawpoints]] routine to plot a +point whose point symbol is a square. The subroutine has one argument, which is +equal to the radius of the point. From this argument it computes the side of +the square. + +<<subroutine <tt>drawsquare</tt> >>= +sub drawsquare { + my $s = $_[0]; + #$s *= sqrt(2); + $s = sprintf "%.5f", $s; + my $code = "\\setlength{\\unitlength}{$xunits}%\n"; + $code .= "\\begin{picture}($s,$s)\\put(0,0)" . + "{\\framebox($s,$s){}}\\end{picture}"; + return $code; +} + +@ Subroutine [[X2sp]] has two arguments: a number and a length unit. It returns +the length expresssed in sp units. + +<<subroutine <tt>X2sp</tt> >>= +sub X2sp { + my $LT = shift; + my $units = shift; + + if ($units eq "pc") { + return $LT * 786432; + } + elsif ($units eq "pt") { + return $LT * 65536; + } + elsif ($units eq "in") { + return $LT * 4736286.72; + } + elsif ($units eq "bp") { + return $LT * 65781.76; + } + elsif ($units eq "cm") { + return $LT * 1864679.811023622; + } + elsif ($units eq "mm") { + return $LT * 186467.981102362; + } + elsif ($units eq "dd") { + return $LT * 70124.086430424; + } + elsif ($units eq "cc") { + return $LT * 841489.037165082; + } + elsif ($units eq "sp") { + return $LT; + } +} + + +@ Subroutine [[sp2X]] has two arguments: a number that denotes a length in sp units + and a length unit. It returns the length expresssed in units that are specified by + the second argument. + +<<subroutine <tt>sp2X</tt> >>= +sub sp2X { + my $LT = shift; + my $units = shift; + + if ($units eq "pc") { + return $LT / 786432; + } + elsif ($units eq "pt") { + return $LT / 65536; + } + elsif ($units eq "in") { + return $LT / 4736286.72; + } + elsif ($units eq "bp") { + return $LT / 65781.76; + } + elsif ($units eq "cm") { + return $LT / 1864679.811023622; + } + elsif ($units eq "mm") { + return $LT / 186467.981102362; + } + elsif ($units eq "dd") { + return $LT / 70124.086430424; + } + elsif ($units eq "cc") { + return $LT / 841489.037165082; + } + elsif ($units eq "sp") { + return $LT; + } +} + +@ Subroutine [[setLineThickness]] takes two arguments: the value of the variable + [[$xunits]] and a string denoting the linethickness. It returns the linthickness + expressed in the units of the [[$xunits]]. + +<<subroutine <tt>setLineThickness</tt> >>= +sub setLineThickness { + my $Xunits = shift; + my $LT = shift; + $Xunits =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//; + my $xlength = "$1"; + $Xunits =~ s/^\s*($units)//; + my $x_in_units = $1; + $LT =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//; + my $LTlength = "$1"; + $LT =~ s/^\s*($units)//; + my $LT_in_units = $1; + $LTlength = X2sp($LTlength,$LT_in_units); + $LTlength = sp2X($LTlength,$x_in_units); + return $LTlength; +} + +@ The subroutine [[process_input]] accepts one argument which is a file handle +that corresponds to the file that the subroutine is supposed to process. +The processing cycle is fairly simple: we input one line at the time, remove +any leading space characters and the trailing new line character, and then +start the actual processing. The variable [[$INFILE]] contains the name of +the input file and the variable [[$lc]] is the local line counter. The +commands [[beginSkip]] and [[endSkip]] can be used to ignore blocks +of code and so we need to process them here. The variable [[$no_output]] +is used as a switch to toggle from process mode to no-precess mode. +If the first token is [[beginSkip]], we set the variable [[$no_output]] to 1, +print a comment to the output file and continue with the next input line. +If the first token is [[endSkip]], we check whether we are in a no-process +mode. If this is the case, we revert to process mode; otherwise we print +an error message. Finally, depending on whether we are in process or no-process +mode we process the input text or simply printed commented out to the output +file. Note, that we don't allow nested comment blocks, as this makes really +no sense! + +<<subroutine <tt>process_input</tt> >>= + sub process_input { + my ($INFILE,$currInFile) = @_; + my $lc = 0; + my $no_output = 0; + $curr_in_file = $currInFile; + LINE: while(<$INFILE>) { + $lc++; + chomp($command = $_); + s/^\s+//; + if (/^beginSkip\s*/i) { + $no_output = 1; + print OUT "%%$_" if $comments_on; + next LINE; + } + elsif (/^endSkip\s*/i) { + if ($no_output == 0) { + PrintErrorMessage("endSkip without beginSkip",$lc); + } + else { + $no_output = 0; + } + print OUT "%%$_" if $comments_on and !$no_output; + next LINE; + } + elsif ($no_output == 1) { + next LINE; + } + else { + if (/^[^\\]/) { + my $out_line = mpp($command,$lc) unless /^\\/; #call macro pre-processor + $_ = "$out_line\n"; + } + <<process input line>> + } + } + } + +@ Each command line starts with a particular <i>token</i> and depending on +which one we have we perform different actions. If the first character +is [[%]] we have a comment line, and depending on the value of the variable +[[$comments_on]] we either output the comment on the output file (default +action) or just ignore it and continue with the next input line. In case the +first token is the name of a valid command we process the command and +output the corresponding code. Otherwise, we print an error message to +the screen and to the log file and continue with the next input line. +Note that the input language is case-insensitive and so one is free to write a +command name using any combination of upper and lower case +letters, e.g., the tokens [[lAtEx]], +[[LaTeX]], and [[latex]] are considered exactly the same. +The valid <i>MathsPIC</i> commands are the following (don't pay attention +to the case!): +<ul> +<li> +Commands [[drawAngleArc]] and [[drawAngleArrow]] are used to draw an arc and an +arrow, respectively. Since, their user interface is identical, we process +them as if they were identical commands. +</li> +<li> +Command [[drawcircle]] is used to draw a circle with a specified radius. +</li> +<li> +Command [[drawCircumCircle]] is used to draw the circumcircle of triangle +specified by three points. +</li> +<li> +Command [[drawexcircle]] is used to draw the excircle of triangle +relative to a given side of the triangle. +</li> +<li> +Command [[drawincircle]] is used to draw the incircle of triangle. +</li> +<li> +Command [[drawincurve]] is used to draw a curve that passes through a number of points. +</li> +<li> Command [[drawline]] is used to draw either +a line (not necessarily a straight one) or a number of lines from a list +or lists of points. The lines are specified as pairs of points that can +be separated by blank spaces. +<li> Command [[drawthickline]] is used to draw either +a thick line (not necessarily a straight one) or a number of lines from a list +or lists of points. The lines are specified as pairs of points that can +be separated by blank spaces. +</li> +<li> +Command [[drawPerpendicular]] draws a perpendicular line from point A to +line BC. +</li> +<li> Command [[drawpoint]] is used to draw one, two or more points. +The point names can be separated by blanks. +</li> +<li> +Command [[drawRightAngle]] draws an angle, specified by three points, +of a size specified by a side length. +</li> +<li> +Command [[drawsquare]] draws a square, centered at the coordinates of the +first arguments, which is assumed to be a point, with side equal to the +second argument. +</li> +<li> +Command [[inputfile*]] is used to verbatim include a file into the output +file. +</li> +<li> +Command [[inputfile]] is used to include a <i>MathsPIC</i> program file +into the main file. +</li> +<li> +Command [[linethickness]] should be used to set the thickness of lines. +</li> +<li> +The [[paper]] command sets the paper scale, size, axes, etc. The most +general format of the command follows: +<center> +<tt>paper{units(mm), xrange(0,120), yrange(0,100),axes(LRTB)}</tt> +</center> +Note, that one may opt not to write the commas between the different +parts of command. +</li> +<li> +Command [[point*]] allocates <i>new</i> co-ordinates and optionally +a T<sub>E</sub>X point-name, to an existing point-name. +Command [[point]] allocates co-ordinates and, optionally a T<sub>E</sub>X +point character, to a <i>new</i> point-name. Since, both commands have +identical syntax, we handle them together. +</li> +<li> Command [[PointSymbol]] is used to set or reset the default +point symbol, i.e., when one plots a point this is the symbol that will +appear on the final DVI/PostScript file. +</li> +<li> +In the original DOS version of <tt>mathspic</tt> the command +[[setPointNumber]] was used to set the length of the arrays that keep the +various point related information. Since, in Perl arrays are dynamic objects +and one can push as many objects as he/she wants, the command is implemented +as an no-op. For reasons of compatibility, we only check the syntax of the +command. +</li> +<li> +Commands [[showAngle]] and [[showArea]] can be used to get +the angle or the area determined by three points. In addition, the command +[[showLenght]] can be used to get the length between two points. These three +commands produce a comment to the output file. +</li> +<li> The [[system]] command provides a shell escape. +</li> +<li> +The [[text]] command is used to put a symbol/text at a +particular point location. +</li> +<li> +Command [[var]] is used to store a numeric value into a comma separated +list of variables. +</li> +<li> +Command [[const]] is used to store a numeric value into a comma separated +list of variables, whose value cannot be altered. +</li> +<li> +If a line starts with a backslash, [[\]], then we copy verbatim this +line to the output file. In case the second character is a space character, +then we simply output a copy of the line without the leading backslash. +</li> +</ul> +Empty lines are always ignored. + +<<process input line>>= + + if (/^\s*%/) + { + print OUT "$_" if $comments_on; + } + elsif (s/^\s*(beginloop(?=\W))//i) { + s/\s+//; + my $times = expr($lc); + print OUT "%% BEGINLOOP $times\n" if $comments_on; + my @C = (); + REPEATCOMMS: while (<$INFILE>) { + if (/^\s*endloop/i) { + last REPEATCOMMS; + } + else { + push @C, $_; + } + } + if (! /^\s*endloop/i) { + PrintFatalError("unexpected end of file",$lc); + } + else { + s/^\s*endloop//i; + for(my $i=1; $i<=$times; $i++) { + tie *DUMMY, 'DummyFH', \@C; + process_input(DUMMY, $currInFile); + untie *DUMMY; + } + print OUT "%% ENDLOOP\n" if $comments_on; + } + } + elsif (s/^\s*(ArrowShape(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>ArrowShape</tt> command>> + } + elsif (s/^\s*(const(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <<process <tt>const</tt> command>> + } + elsif (s/^\s*(dasharray(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>dasharray</tt> command>> + } + elsif (s/^\s*(drawAngleArc(?=\W))//i or s/^\s*(drawAngleArrow(?=\W))//i ) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawAngleArcOrArrow</tt> command>> + } + elsif (s/^\s*(drawArrow(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(0,$lc); + } + elsif (s/^\s*(drawcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawcircle</tt> command>> + } + elsif (s/^\s*(drawcurve(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(2,$lc); + } + elsif (s/^\s*(drawcircumcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawcircumcircle</tt> command>> + } + elsif (s/^\s*(drawexcircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawexcircle</tt> command>> + } + elsif (s/^\s*(drawincircle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawincircle</tt> command>> + } + elsif (s/^\s*(drawline(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + DrawLineOrArrow(1,$lc); + } + elsif (s/^\s*(drawthickarrow(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n"; + print OUT "{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n"; + print OUT " \\global\\linethickness=0.31\\wd1}%\n"; + DrawLineOrArrow(0,$lc); + print OUT "\\setlength{\\linethickness}{0.4pt}%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + } + elsif (s/^\s*(drawthickline(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n"; + print OUT "{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n"; + print OUT " \\global\\linethickness=0.31\\wd1}%\n"; + DrawLineOrArrow(1,$lc); + print OUT "\\setlength{\\linethickness}{0.4pt}%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + } + elsif (s/^\s*(drawperpendicular(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawPerpendicular</tt> command>> + } + elsif (s/^\s*(drawpoint(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawpoint</tt> command>> + } + elsif (s/^\s*(drawRightAngle(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawRightAngle</tt> command>> + } + elsif (s/^\s*(drawsquare(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>drawsquare</tt> command>> + } + elsif (s/^\s*inputfile\*//i) + { + <<process <tt>inputfile*</tt> command>> + } + elsif (s/^\s*(inputfile(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>inputfile</tt> command>> + } + elsif (s/^\s*(linethickness(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>linethickness</tt> command>> + } + elsif (s/^\s*(paper(?=\W))//i) + { + my ($cmd) = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>paper</tt> command>> + } + elsif (s/^\s*(PointSymbol(?=\W))//i) + { + my $cmd = $1; + print OUT "%% $cmd$_" if $comments_on; + <<process <tt>PointSymbol</tt> command>> + } + elsif (s/^\s*point(?=\W)//i) + { + my ($Point_Line); + chomp($Point_Line=$_); + <<process <tt>point/point*</tt> commands>> + } + elsif (/^\s*setPointNumber(?=\W)/i) + { + PrintWarningMessage("Command setPointNumber is ignored",$lc); + next LINE; + } + elsif (s/^\s*(showAngle(?=\W))//i) + { + <<process <tt>showAngle</tt> command>> + } + elsif (s/^\s*(showArea(?=\W))//i) + { + <<process <tt>showArea</tt> command>> + } + elsif (s/^\s*(showLength(?=\W))//i) + { + <<process <tt>showLength</tt> command>> + } + elsif (/^\s*showPoints(?=\W)/i) + { + print OUT "%%-------------------------------------------------\n"; + print OUT "%% L I S T O F P O I N T S \n"; + print OUT "%%-------------------------------------------------\n"; + foreach my $p (keys(%PointTable)) { + my ($x, $y, $pSV, $pS) = unpack("d3A*",$PointTable{$p}); + printf OUT "%%%%\t%s\t= ( %.5f, %.5f ), LF-radius = %.5f, symbol = %s\n", + $p, $x, $y, $pSV, $pS; + } + print OUT "%%-------------------------------------------------\n"; + print OUT "%% E N D O F L I S T O F P O I N T S \n"; + print OUT "%%-------------------------------------------------\n"; + next LINE; + } + elsif (/^\s*showVariables(?=\W)/i) + { + print OUT "%%-------------------------------------------------\n"; + print OUT "%% L I S T O F V A R I A B L E S \n"; + print OUT "%%-------------------------------------------------\n"; + foreach my $var (keys(%VarTable)) { + print OUT "%%\t", $var, "\t=\t", $VarTable{$var}, "\n"; + } + print OUT "%%-------------------------------------------------\n"; + print OUT "%% E N D O F L I S T O F V A R I A B L E S \n"; + print OUT "%%-------------------------------------------------\n"; + next LINE; + } + elsif (s/^\s*(system(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <<process <tt>system</tt> command>> + } + elsif (s/^\s*(text(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <<process <tt>text</tt> command>> + } + elsif (s/^\s*(var(?=\W))//i) + { + print OUT "%% $1$_" if $comments_on; + <<process <tt>var</tt> command>> + } + elsif (/^\s*\\(.+)/) + { + my $line = $1; + if ($line =~ /^\s+(.+)/) + { + print OUT " $line\n"; + } + else + { + print OUT "\\$line\n"; + } + next LINE; + } + elsif (0==length) #empty line + { + next LINE; + } + else { + PrintErrorMessage("command not recognized",$lc); + next LINE; + } + +@ Command [[dasharray]] takes an arbitrary number of arguments that are used to +specify a dash pattern. Its general syntax follows: +<center> + <tt> "dasharray" "(" d<sub>1</sub> "," g<sub>1</sub> "," d<sub>2</sub> "," + g<sub>2</sub> "," ... ")"</tt> +</center> +where <tt>d<sub>i</sub></tt> denotes the length of a dash and <tt>g<sub>i</sub></tt> +denotes the length of gap between two consecutive dashes. Each <tt>d<sub>i</sub></tt> +and <tt>g<sub>i</sub></tt> is a length (i.e., a number accompanied by a length of unit). +Since we do not a priori know the number of arguments, we push them onto a stack and +then we produce a command of the form +<center> + <tt> \setdashpattern < d<sub>1</sub>, g<sub>1</sub>, d<sub>2</sub>, + g<sub>2</sub>, ...></tt> +</center> + +<<process <tt>dasharray</tt> command>>= + chk_lparen($cmd,$lc); + my @DashArray = (); + my $dash = ""; + my $dashpattern = ""; + PATTERN: while (1) { + $dash = sprintf("%.5f", expr($lc)); + if (s/^\s*($units)//i) { + push (@DashArray, "$dash$1"); + } + else { + PrintErrorMessage("Did not found unit after expression", $lc); + } + s/\s*//; + if (/^[^,]/) { + last PATTERN; + } + else { + s/^,\s*//; + } + } + print OUT "\\setdashpattern <"; + while (@DashArray) { + $dashpattern .= shift @DashArray; + $dashpattern .= ","; + } + $dashpattern =~ s/,$//; + print OUT $dashpattern, ">\n"; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +@ The command [[drawAngleArc]] draws an arc in the specified angle, a +distance <i>radius</i> from the angle. The angle is either <i>internal</i> +(<= 180 degrees) or <i>external</i> (>180 degrees). The direction of the +arc is either <i>clockwise</i> or <i>anticlockwise</i>. The command +[[drawAngleArrow]] draws an arrow just like the command [[drawAngleArc]] +draws an arc. The syntax of these commands is as follows: +<pre> + cmds ::= ( "drawAngleArc" | "drawAngleArrow" ) args + args ::= "{" angle comma radius comma internal comma clockwise "}" + angle ::= "angle" "(" three-points ")" + radius ::= "radius" "(" distance ")" + distance ::= expression + internal ::= "internal" | "external" + clockwise ::= "clockwise" | "anticlockwise" + comma ::= "," | empty +</pre> +We first collect all relevant information by parsing the [[args]] and then +call the either the subroutine [[drawAngleArc]] or the subroutine +[[drawAngleArrow]] to produce the actual code +which is then printed into the output file. In order to be able to distinguish +which command we are dealing with we simply use the variable [[$cmd]]. +We now start parsing the input line. We first check whether there is a +left curly bracket. Next, we parse the [[angle]], the [[distance]], the +[[internal]] and the [[clockwise]] parts of the command. Finally, we check +for right curly bracket and a trailing comment. Depending on +the value of +the variable [[$cmd]] we call either the subroutine [[drawAngleArc]] or the +subroutine [[drawAngleArrow]]. These subroutines return the code that will be +finally output to the output file. + +<<process <tt>drawAngleArcOrArrow</tt> command>>= + + chk_lcb($cmd,$lc); + <<process <tt>angle</tt> part of command>> + s/^,\s*// or s/\s*//; #parse optional comma + <<process <tt>radius</tt> part of command>> + s/^,\s*// or s/\s*//; #parse optional comma + my $inout = ""; + if (s/^(internal(?=\W))//i or s/^(external(?=\W))//i) { + $inout = $1; + } + else { + PrintErrorMessage("Did not find expected 'internal' specifier", $lc); + next LINE; + } + s/^,\s*// or s/\s*//; #parse optional comma + my $direction = ""; + if (s/^(clockwise(?=\W))//i or s/^(anticlockwise(?=\W))//i) { + $direction = $1; + } + else { + PrintErrorMessage("Did not find expected 'direction' specifier", $lc); + next LINE; + } + chk_rcb("arguments of $cmd",$lc); + chk_comment($lc); + my $code; + if (lc($cmd) eq "drawanglearc") { + $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction); + } + else { + $code = drawAngleArrow($P1, $P2, $P3, $radius, $inout, $direction); + } + print OUT $code if $code ne ""; + +@ We first check whether the first token is the word [[angle]]. In case it +isn't, this yields an unrecoverable error. In case the expected word is +there, we check for a left parenthesis. Next, we parse the three points that +must follow. For this purpose we use the user-defined subroutine +[[get_point]]. Now we check that the angle has a reasonable value, i.e., if +it is less than -400 or equal to zero, the value yields an unrecoverable error. +We finish by checking whether there is a right parenthesis. + +<<process <tt>angle</tt> part of command>>= + my ($P1, $P2, $P3); + if (s/^angle(?=\W)//i) { + chk_lparen("token angle of command $cmd",$lc); + $P1 = get_point($lc); + next LINE if $P1 eq "_undef_"; + $P2 = get_point($lc); + next LINE if $P2 eq "_undef_"; + $P3 = get_point($lc); + next LINE if $P3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$P2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$P3}); + my $Angle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + if ($Angle <= 0) { + if ($Angle == 0) { + PrintErrorMessage("Angle is equal to zero",$lc); + next LINE; + } + elsif ($Angle < -400) { + PrintErrorMessage("Something is wrong with the points",$lc); + next LINE; + } + } + chk_rparen("angle part of command $cmd",$lc); + } + else { + PrintErrorMessage("Did not find expected angle part",$lc); + next LINE; + } + +@ In this section we parse the [[radius]] part of the [[drawAngleArc]] or the +[[drawAngleArrow]] command. We first check whether the next token is the word +[[radius]]. If it is not, then we continue with the next line. + +<<process <tt>radius</tt> part of command>>= + + my $radius; + if (s/^radius(?=\W)//i) { + chk_lparen("token radius of command $cmd",$lc); + $radius = expr($lc); + chk_rparen("radius part of command $cmd",$lc); + } + else { + PrintErrorMessage("Did not found expected angle part",$lc); + next LINE; + } + +@ Command [[drawcircle]] accepts two arguments--a point name that is +used to specify the center of the circle and the radius of the circle. +The radius is simply an expression, whose value must be greater than zero. +Otherwise, we print an error message and continue with the next input line. +The general syntax of the command is as follows: +<pre> + "drawcircle" "(" point-name "," rad ")" +</pre> +The code we emit for a point with coordinates [[x]] and [[y]] and for radius +equal to [[R]] is: +<pre> + \circulararc 360 degrees from X y center at x y +</pre> +where [[X = x+R]].<p> +Initially, we check whether there is an opening left parenthesis. Next, +we get the point name by using the subroutine [[get_point]] which +issues an error message if the point hasn't been defined. In this +case we stop processing the command, as there is absolutely no reason to +do otherwise. Next, we parse the comma and then the radius by using +the subroutine [[ComputeDist]]. If there is no problem, we emit the code +and finally we check for a closing right parenthesis and for +possible garbage that may follow the command. + +<<process <tt>drawcircle</tt> command>>= + chk_lparen("drawcircle",$lc); + my $Point = get_point($lc); + next LINE if $Point eq "_undef_"; + chk_comma($lc); + my $R = expr($lc); + if ($R <= 0) { + PrintErrorMessage("Radius must be greater than zero",$lc); + next LINE; + } + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{lc($Point)}); + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $x+$R, $y, $x, $y; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +@ Command [[drawcircumcircle]] is used to draw the circumcircle of triangle +specified by three points which are the arguments of the command. We start +by parsing the opening left parenthesis. Next, we get the three points +that define the triangle. We are now able to compute the center and +the radius of the circumcircle by calling the subroutine [[circumCircleCenter]]. +If the triangle area is equal to zero, then this subroutine will return +the array [[(0,0,0)]] to indicate this fact. +We now have all necessary information to draw the circumcircle. We use the +following code to do the job: +<pre> + \circulararc 360 degrees from X y center x y +</pre> +where [[x]] and [[y]] are the coordinates of the center, [[R]] its +radius and [[X=x+R]]. What is left is to check whether there is a +closing right parenthesis and any trailing garbage. + + +<<process <tt>drawcircumcircle</tt> command>>= + chk_lparen("drawcircumcircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + my ($xc, $yc,$r) = circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc); + next LINE if $xc == 0 and $yc == 0 and $r == 0; + print OUT "%% circumcircle center = ($xc,$yc), radius = $r\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$r, $yc, $xc, $yc; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +@ The syntax of the [[drawexcircle]] command is as follows: +<pre> + drawexcircle ::= "drawexcircle" "(" ThreePoints "," TwoPoints ")" + [ modifier ] + modifier ::= "[" expr "]" + +</pre> +The [[modifier]] is an expression that is used to modify the radius of the +excicle. We start by checking whether there is a left parenthesis. Then we +get names of the three points. In case any of the points is not defined +we issue an error message and continue with the next input line. Next, we +check whether there is a comma that separates the three points defining the +triangle from the two points defining a side of the triangle (variables +[[$point1]], [[$point2]], and [[$point3]]). Moreover, we must ensure that +the area of the area defined by these points is not equal to +zero. If it is we issue an error message and we continue with the next +input line. Now, we are ready to get the two +point names that define the side of the triangle (variables [[$point3]] and +[[$point5]]). At this point we must make sure that these points are different +points and that they are members of the list of points that define the triangle. +We make this check by calling the subroutine [[memberOf]]. Next, we check +whether there is a closing right parenthesis. We now compute the center +and the radius of the excircle by calling the subroutine [[excircle]]. The +coordinates of the center are stored in the variables [[$xc]] and [[$yc]], +while the radius is stored in the variable [[$r]]. If the next +non-blank input character is a left square bracket, then we know the user has +specified the optional part. We use the subroutine [[expr]] to get the value of +the optional part. The value of the optional part is stored in the variable [[$R]]. +At this point we check whether the sum of the radius +plus the optional part is equal to zero and if it is we continue with the +next input line. Next, we check for a closing right square bracket. We are +now ready to emit the source code. The first thing we must check is that +the radius is not too big for PiCTeX, i.e., not greater than 500/2.845. +Then we print some informative text to the output file and of course the +actual code. We use the following code to do the job: +<pre> + \circulararc 360 degrees from (xc+R) yc center xc yc +</pre> +The last thing we check is whether there is some trailing garbage. + +<<process <tt>drawexcircle</tt> command>>= + chk_lparen("drawexcircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) < 0.0001) { + PrintErrorMessage("Area of triangle is zero!",$lc); + next LINE; + } + chk_comma($lc); + my $point4 = get_point($lc); + if (!memberOf($point4, $point1, $point2, $point3)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + next LINE if $point4 eq "_undef_"; + my $point5 = get_point($lc); + next LINE if $point5 eq "_undef_"; + if (!memberOf($point5, $point1, $point2, $point3)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + if ($point4 eq $point5) { + PrintErrorMessage("Side points are identical",$lc); + next LINE; + } + chk_rparen("arguments of $cmd",$lc); + my ($xc, $yc, $r) = excircle($point1, $point2, $point3, + $point4, $point5); + my $R=$r; + if (s/^\s*\[\s*//) { + $R += expr($lc); + if ($R < 0.0001) { + PrintErrorMessage("Radius has become equal to zero!",$lc); + next LINE; + } + chk_rsb($lc); + } + if ($R > (500 / 2.845)) { + PrintErrorMessage("Radius is greater than 175mm!",$lc); + next LINE; + } + print OUT "%% excircle center = ($xc,$yc) radius = $R\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$R, $yc, $xc, $yc; + chk_comment($lc); + +@ The syntax of the [[drawincircle]] command is as follows: +<pre> + drawincircle ::= "drawincircle" "(" ThreePoints ")" [ modifier] + modifier ::= "[" expr "]" +</pre> +where [[ThreePoints]] correspond to the points defining the triangle and +[[modifier]] is an optional modification factor. +The first thing we do is to check whether +there is an opening left parenthesis. Then we get the names of the three +points that define the triangle (variables [[$point1]], [[$point2]], +and [[$point3]]). Next, we make sure that the area of the +triangle defined by these three points is not equal to zero. If it is, then +we issue an error message and continue with the next input line. Now, we +compute the center and the radius of the incircle (variables [[$xc]], [[$yc]], +and [[$r]]). If the next non-blank input character is a left square bracket, +then we now the user has specified the optional part. We use subroutine +[[expr]] to get the value of the optional part. The value of +the optional part +is stored in the variable [[$R]]. At this point we check whether the sum of the +radius plus the optional part is equal to zero and if it is we continue with +the next input line. Next, we check for a closing right square bracket. +We are now ready to emit the source code. The first thing we must check is +that the radius is not too big for PiCTeX, i.e., not greater than 500/2.845. +Then we print some informative text to the output file and of course the +actual code. We use the following code to do the job: +<pre> + \circulararc 360 degrees from (xc+R) yc center xc yc +</pre> +The last thing we check is whether there is some trailing garbage. + +<<process <tt>drawincircle</tt> command>>= + chk_lparen("drawincircle",$lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) < 0.0001) { + PrintErrorMessage("Area of triangle is zero!",$lc); + next LINE; + } + my ($xc, $yc, $r) = IncircleCenter($x1,$y1,$x2,$y2,$x3,$y3); + my $R=$r; + if (s/^\s*\[\s*//) { + $R += expr($lc); + if ($R < 0.0001) { + PrintErrorMessage("Radius has become equal to zero!",$lc); + next LINE; + } + chk_rsb($lc); + } + if ($R > (500 / 2.845)) { + PrintErrorMessage("Radius is greater than 175mm!",$lc); + next LINE; + } + print OUT "%% incircle center = ($xc,$yc) radius = $R\n" if $comments_on; + printf OUT "\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n", + $xc+$R, $yc, $xc, $yc; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +@ The command [[drawPerpendicular]] command draws a line from point A to line +BC, such that it is perpendicular to line BC. The general syntax of the +command is as follows: +<pre> + drawPenpedicular ::= "drawPenpedicular" "(" Point "," TwoPoints ")" +</pre> +The first thing we do is to parse the left parenthesis. Then we parse +the name of the first point, namely [[$A$]]. If this point is undefined +we print an error message and continue with the next line. Next, we parse +the expected leading comma and the names of the other two points. Certainly, +in case either of these two points has not been defined, we simply print an +error message and continue with the next input line. Finally, we check for +a closing right parenthesis and a possible trailing comment. Now we are +ready to compute the coordinates of the foot of the +perpendicular line. We do so my calling subroutine +[[perpendicular]]. Certainly, before we do this we have to get the +coordinates of the points that we have parsed. Finally, we output the +PiCTeX code: +<pre> + \plot x1 y1 xF xY / +</pre> +where [[x1]] and [[y1]] are coordinates of the point A and [[xF]] and [[yF]] +the coordinates of the foot. + +<<process <tt>drawPerpendicular</tt> command>>= + + chk_lparen($cmd,$lc); + my $A = get_point($lc); + next LINE if $A eq "_undef_"; + chk_comma($lc); + my $B = get_point($lc); + next LINE if $A eq "_undef_"; + s/\s*//; #ignore white space + my $C = get_point($lc); + next LINE if $A eq "_undef_"; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + # + #start actual computation + # + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$A}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$B}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$C}); + my ($xF, $yF) = perpendicular($x1, $y1, $x2, $y2, $x3, $y3); + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $x1, $y1, $xF, $yF; + +@ The [[drawpoint]] command has a number of points as arguments and produces +PiCTeX code that draws a plot symbol at the coordinates of each point. The +syntax of the command is as follows: +<pre> + drawpoint ::= "drawpoint" "(" Point { separator Point } ")" +</pre> +The [[while]] loop is used to consume all points that are +between an opening left parenthesis and a closing right parenthesis. All +points are pushed on the local array [[PP]]. When we have parsed the lists +of points, we call the subroutine [[drawpoints]] to emit the actual PiCTeX code. +Finally, we check whether there is a closing parenthesis +parenthesis, and whether +there is some trailing text that makes no sense. In case there are no points +between the parentheses, then we issue an appropriate error message and +we continue with the next input line. + +<<process <tt>drawpoint</tt> command>>= + my ($stacklen); + chk_lparen("$cmd",$lc); + if (/^\)/) { + PrintErrorMessage("There are no point to draw",$lc); + next LINE; + } + my(@PP); + DRAWPOINTS:while(1) { + if (s/^([^\W\d_]\d{0,3})//i) { #point name + $P = $1; + if (!exists($PointTable{lc($P)})) { + PrintErrorMessage("Undefined point $P",$lc); + next DRAWPOINTS; + } + else { + push (@PP,$P); + s/\s*//; + } + } + else { + last DRAWPOINTS; + } + } + drawpoints(@PP); + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +@ The syntax of the [[drawRightAngle]] command is as follows: +<pre> + drawRightAngle "(" ThreePoints "," dist ")" + dist ::= expr | TwoPoints +</pre> +Before we proceed with the actual computation we parse the left parenthesis, +the three points, the comma, the [[dist]], and the right parenthesis. In case +we have neither three points nor a [[dist]] we print an error message and +continue with the next input line, i.e., these errors are irrecoverable. +The names of the three points are stored in variables [[$point1]], +[[$point2]], and [[$point3]]. The value of the distance is stored +in the variable [[$dist]]. +Let's now explain the semantics of this command.<p> + +Our aim is to draw lines S<sub>1</sub>-S, S<sub>2</sub>-S (S<sub>1</sub> +and S<sub>2</sub> are at distance d from B). All the relevant points are +depicted in the following figure: +<center> +<img src="fig1.jpg"> +</center> +Some notes are in order: +<ol> +<li> BS bisects angle ABC, and meets AC in Q, so start by determining point +Q, then determine S, and then S<sub>1</sub> and S<sub>2</sub>, and then +draw S<sub>1</sub>-S and S<sub>2</sub>-S.</li> +<li> Distance AQ is given by AC/(1+tan(BCA))</li> +<li> The coordinates of Q are computed using the subroutine [[pointOnLine]].</li> +<li> Now we compute the coordinates of S on line BQ.</li> +<li> We compute the coordinates of S<sub>1</sub> and S<sub>2</sub> by using +The subroutine [[pointOnLine]].</li> +</ol> +In order to implement the above steps we first compute the length of the line +AB. Note that A is [[$point1]], etc. Next we compute the angle BAC. Now +we compute the distance AQ (variable [[$line1]]). The coordinates of point +Q are stored in variables [[$xQ]] and [[$yQ]]. The coordinates of point +S are stored in variables [[$xS]] and [[$yS]]. Now we have to determine the +coordinates of points S<sub>1</sub> and S<sub>2</sub>. These coordinates +are stored in variables [[$xS1]], [[$yS1]] and [[$xS2]], [[$yS2]], +respectively. Finally, we emit the PiCTeX target code. + +<<process <tt>drawRightAngle</tt> command>>= + + chk_lparen("drawRightAngle",lc); + my $point1 = get_point($lc); + next LINE if $point1 eq "_undef_"; + my $point2 = get_point($lc); + next LINE if $point2 eq "_undef_"; + my $point3 = get_point($lc); + next LINE if $point3 eq "_undef_"; + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point1}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point2}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point3}); + chk_comma($lc); + my $dist = expr($lc); + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + # + #actual computation + # + my $lengthAC = Length($x1, $y1, $x3, $y3); + my $angleBAC = Angle($x2, $y2, $x1, $y1, $x3, $y3); + my $line1 = $lengthAC / (1 + tand($angleBAC)); + # + # determine coordinates of point Q + # + my ($xQ, $yQ) = pointOnLine($x1, $y1, $x3, $y3, $line1); + # + # determine coordinates of point S + # + my $deltax = $xQ - $x2; + my $deltay = $yQ - $y2; + my $lengthBQ = sqrt($deltax * $deltax + $deltay * $deltay); + my $xS = $x2 + ($dist * sqrt(2) * $deltax / $lengthBQ); + my $yS = $y2 + ($dist * sqrt(2) * $deltay / $lengthBQ); + # + # determine coordinates of points S1 and S2 + # + my ($xS1, $yS1) = pointOnLine($x2, $y2, $x3, $y3, $dist); + ($xS2, $yS2) = ($xS, $yS); + # + # emit PiCTeX code + # + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $xS1, $yS1, $xS2, $yS2; + ($xS1, $yS1) = pointOnLine($x2, $y2, $x1, $y1, $dist); + printf OUT "\\plot %.5f %.5f %.5f %.5f /\n", + $xS1, $yS1, $xS2, $yS2; + +@ The command [[drawsquare]] has two arguments: a point, which specifies the +coordinates of the point where the square will be placed, and a number, which +specifies the length of the side of the square. The syntax of the command is as follows: +<center> + <tt> "drawSquare" "(" Point "," expression ")" </tt> +</center> +Note that RWDN has suggested to alter the value of the [[$side]] variable (see the +line with [[RWDN]] comment). + +<<process <tt>drawsquare</tt> command>>= + chk_lparen("drawSquare",$lc); + my $p = get_point($lc); + chk_comma($lc); + my $side = expr($lc); + $side = $side - (1.1 * $LineThickness/$xunits); #Suggested by RWDN + my ($x,$y,$pSV,$pS) = unpack("d3A*",$PointTable{$p}); + printf OUT "\\put {%s} at %.5f %.5f %%drawsquare\n", drawsquare($side), $x, $y; + chk_rparen("arguments of $cmd",$lc); + chk_comment($lc); + +@ The argument of the [[inputfile*]] command is a file name that is always +enclosed in parentheses: +<pre> + starred-input-file ::= "inputfile*" "(" file-name ")" + file-name ::= (alpha | period) { alpha | period } + alpha ::= letter | digit | "_" | "-" +</pre> +Note, that the input file is assumed to contain TeX code. +We first check to see if there is a left parenthesis. Then we consume +the file name. We check if the file exists and then we copy verbatim the +input file to the output file. Next, we check for the closing parenthesis. +Now, if there is a trailing comment we copy it to the output file depending +on the value of the variable [[$comments_on]], else if there is some other +text we simply ignore it and issue a warning message. + +<<process <tt>inputfile*</tt> command>>= + chk_lparen("inputfile*",$lc); + my $row_in = ""; + if (s/^((\w|-|\.)+)//) { + $row_in = $1; + } + else { + PrintErrorMessage("No input file name found",$lc); + next LINE; + } + if (!(-e $row_in)) { + PrintErrorMessage("File $row_in does not exist",$lc); + next LINE; + } + open(ROW, "$row_in")|| die "Can't open file $row_in\n"; + while (defined($in_line=<ROW>)) { print OUT $in_line; } + print OUT "%% ... end of input file <$row_in>\n"; + close ROW; + chk_rparen("input file name",$lc); + chk_comment($lc); + + +@ The [[inputfile]] command has at most two arguments, second being +optional: a file name enclosed in curly brackets and the number of +times this file should be included in square brackets: +<pre> + inputfile ::= "inputfile" "(" file-name ")" [ Times ] + Times ::= "[" expr "]" +</pre> +Note that the input file is assumed to contain mathspic commands. In addition, if +the expression is equal to a decimal number, it is truncated. +As in the case of the [[inputfile*]] command we parse the left parenthesis, +the file name, the right parenthesis and the optional argument if it exists. +In order to process the commands contained in the input file, we call +The subroutine [[process_input]]. + +<<process <tt>inputfile</tt> command>>= + + chk_lparen("inputfile",$lc); + my $comm_in = ""; + if (s/^((\w|-|\.)+)//) { + $comm_in = $1; + } + else { + PrintErrorMessage("No input file name found",$lc); + next LINE; + } + if (!(-e $comm_in)) { + PrintErrorMessage("File $comm_in does not exist",$lc); + next LINE; + } + chk_rparen("input file name",$lc); + my $input_times = 1; #default value + if (s/^\[//) { + $input_times = expr($lc); + chk_rsb("optional argument",$lc); + } + print OUT "%% ... start of file <$comm_in> loop [$input_times]\n"; + for (my $i=0; $i<int($input_times); $i++) { + open(COMM,"$comm_in") or die "Can't open file $comm_in\n"; + print OUT "%%% Iteration number: ",$i+1,"\n"; + my $old_file_name = $curr_in_file; + process_input(COMM,"File $comm_in, "); + $curr_in_file = $old_file_name; + close COMM; + } + print OUT "%% ... end of file <$comm_in> loop [$input_times]\n"; + chk_comment($lc); + +@ The [[linethickness]] command should be used to set the thickness of lines. +The command has one argument, which is a length or the word [[default]]. +The default line thickness is 0.4 pt. + +<<process <tt>linethickness</tt> command>>= + chk_lparen("linethickness", $lc); + if (s/^default//i) { + print OUT "\\linethickness=0.4pt\\Linethickness{0.4pt}%%\n"; + print OUT "\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n"; + $LineThickness = setLineThickness($xunits,"0.4pt"); + } + else { + my $length = expr($lc); + if (s/^\s*($units)//i) { + my $units = $1; + printf OUT "\\linethickness=%.5f%s\\Linethickness{%.5f%s}%%\n", + $length, $units, $length, $units; + $LineThickness = setLineThickness($xunits,"$length$units"); + my $mag; + if ($units eq "pc") { + $mag = $length * 12; + } + elsif ($units eq "in") { + $mag = $length * 72.27; + } + elsif ($units eq "bp") { + $mag = $length * 1.00375; + } + elsif ($units eq "cm") { + $mag = $length * 28.45275; + } + elsif ($units eq "mm") { + $mag = $length * 2.845275; + } + elsif ($units eq "dd") { + $mag = $length * 1.07001; + } + elsif ($units eq "cc") { + $mag = $length * 0.08917; + } + elsif ($units eq "sp") { + $mag = $length * 0.000015259; + } + elsif ($units eq "pt") { + $mag = $length; + } + $mag = 10 * $mag / 1.00278219; + printf OUT "\\font\\CM=cmr10 at %.5fpt%%\n", $mag; + print OUT "\\setplotsymbol ({\\CM .})%\n"; + } + else { + PrintErrorMessage("Did not found expect units part",$lc); + } + } + chk_rparen("linethickness", $lc); + chk_comment($lc); + + +@ We first output the input line as a comment into the output file. Now, +after the [[paper]] token we look for an opening brace. Then we process +the [[units]] part of the command, if the token [[units]] is present. Note +that the [[units]] part is optional. Next we process the [[xrange]] and the +[[yrange]] part of the command, which are also optional parts of the command. +We are now ready to process the [[axis]] part. Note, that the user is allowed +to alternatively specify this part with the word [[axes]]. +The variable [[$axis]] +is supposed to hold the various data relate to the [[axis]] part. The last +thing we check is the [[ticks]] part. In case the user has not specified +this part we assume that both ticks are equal to zero. If everything is +according to the language syntax, we expect a closing right curly bracket. +Now, that we have all relevant information we can output the rest of the code, +as some parts of it have already been output during parsing. The last thing we +do is to check whether there is any trailing comment. + +<<process <tt>paper</tt> command>>= + chk_lcb("paper", $lc); + if (s/^units(?=\W)//i) + { + <<process <tt>unit</tt> part>> + $nounits = 0; + } + else + { + $nounits = 1; + } + s/^,\s*// or s/\s*//; + if (s/^xrange//i) + { + <<process <tt>xrange</tt> part>> + $noxrange = 0; + } + else + { + $noxrange = 1; + } + s/^,\s*// or s/\s*//; + if (s/^yrange//i) + { + <<process <tt>yrange</tt> part>> + $noyrange = 0; + } + else + { + $noyrange = 1; + } + <<generate plot area related commands>> + s/^,\s*// or s/\s*//; + $axis = ""; + if (s/^ax[ei]s(?=\W)//i) + { + <<process <tt>axis</tt> part>> + } + $axis = uc($axis); + s/^,\s*// or s/\s*//; + if (s/^ticks(?=\W)//i) + { + <<process <tt>ticks</tt> part>> + } + else + { + $xticks = $yticks = 0; + } + chk_rcb("paper", $lc); + <<generate the rest of the code for the <tt>paper</tt> command>> + chk_comment($lc); + +@ We first check whether there is a left parenthesis. Next, we check +whether there is decimal number or a variable name. In case there isn't one we assume it +is the number 1. Now, we get the units. If there is no valid unit, we issue +an error and the x-unit is set to its default value. In case, there is +a trailing comma, we assume the user wants also to specify the y-unit and +we process this part just like we did with the x-unit part. Finally, we +output the corresponding PiCTeX command. In case there is no y-unit +we assume it is equal to the x-unit. + +<<process <tt>unit</tt> part>>= + + chk_lparen("units",$lc); + if(s/^\)//) + { + PrintWarningMessage("Missing value in \"units\"--default is 1pt", + $lc); + $xunits = "1pt"; + } + else { + $xunits = expr($lc); + s/\s*//; + if (s/^($units)//i) { + $xunits .= "$1"; + $LineThickness = setLineThickness($xunits,"0.4pt"); + } + elsif(s/^(\w)+//i) { + PrintErrorMessage("$1 is not a valid mathspic unit",$lc); + $xunits = "1pt"; + } + else { + PrintErrorMessage("No x-units found",$lc); + $xunits = "1pt"; + } + s/\s*//; #ignore white space + if (s/^,//) { # there is a comma so expect an y-units + s/\s*//; #ignore white space + $yunits = expr($lc); + s/\s*//; #ignore white space + if (s/^($units)//i) { + $yunits .= "$1"; + } + elsif(s/^(\w)+//i) { + PrintErrorMessage("$1 is not a valid mathspic unit",$lc); + $yunits = "1pt"; + } + else { + PrintErrorMessage("No y-units found",$lc); + $yunits = $xunits; + } + } + else { + $yunits = $xunits; + } + chk_rparen("units",$lc); + } + +@ The [[xrange]] token must be followed by a left parenthesis, so we +check whether the next token is a left parenthesis. We store in the variables +[[$xlow]] and [[$xhigh]] the values of the range. The range is specified +as pair of decimal numbers/variable/pair of points, separated by a +comma. We use the subroutine [[ComputeDist]] to get the value of the lower +end and the upper end of the range. The last thing we check is whether +the lower end is less than the upper end. If this isn't the case we +issue an error message and we skip into the next input line. + +<<process <tt>xrange</tt> part>>= + + chk_lparen("xrange",$lc); + my $ec; + ($xlow,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($xhigh,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + if ($xlow >= $xhigh) + { + PrintErrorMessage("xlow >= xhigh in xrange",$lc); + next LINE; + } + chk_rparen("$xhigh",$lc); + +@ The [[yrange]] token must be followed by a left parenthesis, so we +check whether the next token is a left parenthesis. We store in the variables +[[$ylow]] and [[$yhigh]] the values of the range. The range is specified +as pair of decimal numbers/variable/pair of points, separated by a +comma. We use the subroutine [[ComputeDist]] to get the value of the lower +end and the upper end of the range. The last thing we check is whether +the lower end is less than the upper end. If this isn't the case we +issue an error message and we skip into the next input line. + +<<process <tt>yrange</tt> part>>= + + chk_lparen("yrange",$lc); + my $ec; + ($ylow,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($yhigh,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + if ($ylow >= $yhigh) + { + PrintErrorMessage("ylow >= yhigh in yrange",$lc); + next LINE; + } + chk_rparen("$yhigh",$lc); + +@ The [[showAngle]] command has three arguments that correspond to three distinct +points and emits a comment of the form: +<center> +<tt>%% angle(ABC) = 45</tt> +</center> +Note that the computed angle is expressed in degrees. + +<<process <tt>showAngle</tt> command>>= + chk_lparen("showangle",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + my $angle = Angle($x1, $y1, $x2, $y2, $x3, $y3); + $angle = 0 if $angle == -500; + printf OUT "%%%% angle(%s%s%s) = %.5f deg ( %.5f rad)\n", $point_1, + $point_2, $point_3, $angle, $angle*D2R; + chk_rparen("Missing right parenthesis", $lc); + +@ The [[showArea]] command has three arguments that correspond to three distinct +points and emits a comment of the form: +<center> +<tt>%% area(ABC) = 45</tt> +</center> +Note that the computed angle is expressed in degrees. + +<<process <tt>showArea</tt> command>>= + chk_lparen("showarea",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + my $point_3 = get_point($lc); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$point_3}); + print OUT "%% area($point_1$point_2$point_3) = ", + triangleArea($x1, $y1, $x2, $y2, $x3, $y3), "\n"; + chk_rparen("Missing right parenthesis", $lc); + +@ The [[showLength]] command has two arguments that correspond to two distinct +points and emits a comment of the form: +<center> +<tt>%% length(AB) = 45</tt> +</center> +Note that the computed angle is expressed in degrees. + +<<process <tt>showLength</tt> command>>= + chk_lparen("showlength",$lc); + my $point_1 = get_point($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$point_1}); + my $point_2 = get_point($lc); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$point_2}); + print OUT "%% length($point_1$point_2) = ", + Length($x1, $y1, $x2, $y2), "\n"; + chk_rparen("Missing right parenthesis", $lc); + + +@ If the user hasn't specified units then we use the previous values to +set the coordinate system. If the user hasn't specified either the +[[xunits]] part or the [[yunits]], then we don't emit code. In case he/she +has specified both parts we generate the command that sets the plot area. + +<<generate plot area related commands>>= + + if (!$nounits) + { + printf OUT "\\setcoordinatesystem units <%s,%s>\n", + $xunits,$yunits; + } + if(!$noxrange && !$noyrange) + { + printf OUT "\\setplotarea x from %.5f to %.5f, y from %.5f to %.5f\n", + $xlow, $xhigh, $ylow, $yhigh; + + } + +@ We first check to see whether there is an opening left parenthesis. Next +we get the various options the user may have entered. The valid options +are the letters L, R, T, B, X, and Y. These letters may be followed by +an optional star [[*]] with space characters between the letter and the star. +We use a loop, that stops when a right parenthesis is found, to +go through all +possible arguments and append each argument in the string [[$axis]]. Note +one can have blank space between different arguments. The last thing we do is +to check for the closing right parenthesis. + +<<process <tt>axis</tt> part>>= + + chk_lparen("axis",$lc); + while(/^[^\)]/) + { + if (s/^([lrtbxy]{1}\*?)//i) + { + $axis .= $1; + } + elsif (s/^([^lrtbxy])//i) + { + PrintErrorMessage("Non-valid character \"$1\" in axis()",$lc); + } + s/\s*//; + } + chk_rparen("axis(arguments",$lc); + +@ As usual we start by skipping white space. Next we check whether there is +an opening left parenthesis. Now, we expect two numbers/variables/pair of +point representing the [[ticks]] increment value. These [[ticks]] increment +values must be separated by a comma (and possibly some white space around +them). We use the subroutine [[ComputeDist]] to get the value of the [[ticks]] +increment value and we assign to the variables [[$xticks]] and [[$yticks]] +the value of x-ticks and y-ticks increment value. In case there is a +problem we issue an error message and continue with the next line. The last +thing we check is whether there is a closing right parenthesis. + +<<process <tt>ticks</tt> part>>= + chk_lparen("ticks",$lc); + my $ec; + ($xticks,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_comma($lc); + ($yticks,$ec) = ComputeDist($lc); + next LINE if $ec == 0; + chk_rparen("ticks(arguments",$lc); + +@ We actually emit code if the user has specified either the [[X]] or +[[Y]] option in the [[axis]] part. If the user has specified the +[[Y*]] or the [[X*]] option in the axis part, we just emit the commands +[[\axis left shiftedto x=0]] or [[\axis bottom shiftedto y=0]] respectively +and exit. If the use has specified ticks, then, depending on the options +he had supplied with the [[axis]] part, we emit code that +implements the user's wishes. +**** HERE WE MUST EXPLAIN THE MEANING OF THE CODE EMITTED!!! ***** + +<<generate the rest of the code for the <tt>paper</tt> command>>= +YBRANCH: { + if (index($axis, "Y")>-1) + { + if (index($axis, "Y*")>-1) + { + print OUT "\\axis left shiftedto x=0 / \n"; + last YBRANCH; + } + if ($yticks > 0) + { + if (index($axis, "T")>-1 && index($axis, "B")==-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT "$ylow to -$yticks by $yticks\n from $yticks to "; + print OUT $yhigh-$yticks," by $yticks /\n"; + } + elsif (index($axis, "T")==-1 && index($axis, "B")>-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT $ylow+$yticks," to -$yticks by $yticks\n from "; + print OUT "$yticks to $yhigh by $yticks /\n"; + } + elsif (index($axis, "T")>-1 && index($axis, "B")>-1) + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT $ylow+$yticks," to -$yticks by $yticks\n from "; + print OUT "$yticks to ",$yhigh-$yticks," by $yticks /\n"; + } + else + { + print OUT "\\axis left shiftedto x=0 ticks numbered from "; + print OUT "$ylow to -$yticks by $yticks\n from "; + print OUT "$yticks to $yhigh by $yticks /\n"; + } + } + else + { + print OUT "\\axis left shiftedto x=0 /\n"; + } + } + } + XBRANCH: { if (index($axis, "X")>-1) + { + if (index($axis, "X*")>-1) + { + print OUT "\\axis bottom shiftedto y=0 /\n"; + last XBRANCH; + } + if ($xticks > 0) + { + if (index($axis, "L")>-1 && index($axis, "R")==1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT $xlow + $xticks," to -$xticks by $xticks\n from"; + print OUT " $xticks to $xhigh by $xticks /\n"; + } + elsif (index($axis, "L")==-1 && index($axis, "R")>-1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT "$xlow to -$xticks by $xticks\n from "; + print OUT "$xticks to ",$xhigh-$xticks," by $xticks /\n"; + } + elsif (index($axis, "L")>-1 && index($axis, "R")>-1) + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT $xlow + $xticks," to -$xticks by $xticks\n from "; + print OUT "$xticks to ",$xhigh - $xticks," by $xticks /\n"; + } + else + { + print OUT "\\axis bottom shiftedto y=0 ticks numbered from "; + print OUT "$xlow to -$xticks by $xticks\n from "; + print OUT "$xticks to $xhigh by $xticks /\n"; + } + } + else + { + print OUT "\\axis bottom shiftedto y=0 /\n"; + } + } } + LBRANCH: {if (index($axis, "L")>-1) + { + if (index($axis, "L")>-1) + { + if (index($axis, "L*")>-1) + { + print OUT "\\axis left /\n"; + last LBRANCH; + } + if ($yticks > 0) + { + print OUT "\\axis left ticks numbered from "; + print OUT "$ylow to $yhigh by $yticks /\n"; + } + else + { + print OUT "\\axis left /\n"; + } + } + } } + RBRANCH: { if (index($axis, "R")>-1) + { + if (index($axis, "R*")>-1) + { + print OUT "\\axis right /\n"; + last RBRANCH; + } + if ($yticks > 0) + { + print OUT "\\axis right ticks numbered from $ylow to $yhigh by "; + print OUT "$yticks /\n"; + } + else + { + print OUT "\\axis right /\n"; + } + } } + TBRANCH: { if (index($axis, "T")>-1) + { + if (index($axis, "T*")>-1) + { + print OUT "\\axis top /\n"; + last TBRANCH; + } + if ($xticks > 0) + { + print OUT "\\axis top ticks numbered from $xlow to $xhigh by "; + print OUT "$xticks /\n"; + } + else + { + print OUT "\\axis top /\n"; + } + } } + BBRANCH: { if (index($axis, "B")>-1) + { + if (index($axis, "B*")>-1) + { + print OUT "\\axis bottom /\n"; + last BBRANCH; + } + if ($xticks > 0) + { + print OUT "\\axis bottom ticks numbered from $xlow to $xhigh by "; + print OUT "$xticks /\n"; + } + else + { + print OUT "\\axis bottom /\n"; + } + } } + + +@ The syntax of the [[point]] commands follows: +<pre> +point[*](PointName){Coordinates}[PointSymbol] +</pre> +where [[PointName]] is valid point name, [[Coordinates]] is either a +pair of numbers denoting the coordinates of the point or an expression +by means of which the system computes the coordinates of the point, and +the [[PointSymbol]] is a valid T<sub><font size=+1>E</font></sub>X +command denoting a point symbol. A valid point name consists of a +letter and at most two trailing digits. That is, the names [[a11]], +[[b2]] and [[c]] are valid names while [[qw]] and [[s123]] are not. +The first thing we do is to set the point shape to the default symbol +(this has been initialized in the main program). Next, we check whether +we have a [[point]]command or a [[point*]] simply by inspecting the very +next token. Note that there must be no blank spaces between the token +[[point]] and the star symbol. Next, we get the point name: remember that +the point name is surrounded by parentheses. In case we don't find a valid +point name we issue an error message and continue with the next line of +input. Suppose the point name was a valid one. If we have a [[point*]] +command we must ensure that the this particular point name has been defined. +If we have a [[point]] command we must ensure that this particular point +name has not been defined. Point names are stored in the hash [[%PointTable]]. +We are now ready to process the coordinates part and the optional +plot symbol part. + +<<process <tt>point/point*</tt> commands>>= + my ($pointStar, $PointName, $origPN); + $pointStar = 0; # default value: he have a point command + $pointStar = 1 if s/^\*//; + chk_lparen("point" . (($pointStar)?"*":""),$lc); + if (s/^([^\W\d_](?![^\W\d_])\d{0,3})//i) { + # + # Note: the regular expression (foo)(?!bar) means that we are + # looking a foo not followed by a bar. Moreover, the regular + # expression [^\W\d_] means that we are looking for letter. + # + $origPN = $1; + $PointName = lc($1); + } + else { + PrintErrorMessage("Invalid point name",$lc); + next LINE; + } + #if ($pointStar and !exists($PointTable{$PointName})) { + # PrintWarningMessage("Point $origPN has not been defined",$lc); + #} + if (!$pointStar and exists($PointTable{$PointName})) { + PrintWarningMessage("Point $origPN has been used already",$lc); + } + chk_rparen("point" . (($pointStar)?"*":""). "($origPN",$lc); + chk_lcb("point" . (($pointStar)?"*":""). "($origPN)",$lc); + my ($Px, $Py); + <<process coordinates>> + chk_rcb("coordinates part",$lc); + my $sv = $defaultsymbol; + my $sh = $defaultLFradius; + my $side_or_radius = undef; + if (s/^\[\s*//) { # the user has opted to specify the optional part + <<process optional point shape part>> + chk_rsb("optional part",$lc); + } + # to avoid truncation problems introduced by the pack function, we + # round each number up to five decimal digits + $Px = sprintf("%.5f", $Px); + $Py = sprintf("%.5f", $Py); + print OUT "%% point$Point_Line \t$origPN = ($Px, $Py)\n" if $comments_on; + chk_comment($lc); + $PointTable{$PointName} = pack("d3A*",$Px,$Py,$sh,$sv); + if (defined($side_or_radius)) { + $DimOfPoint{$PointName} = $side_or_radius; + } + +@ In this section we parse the [[Coordinates]] part of the [[point]] command. +The complete syntax of the [[Coordinates]] part follows: +<pre> +Coordinates ::= Variable | + Distance "," Distance | + "midpoint" "(" Point-Name Point-Name ")" | + "pointOnLine" "(" Two-Points "," Distance ")" | + "intersection" "(" Two-Points "," Two-Points ")" | + "perpendicular" "(" Point-Name "," Two-Points ")" | + "circumCircleCenter" "(" Three-Points ") | + "incircleCenter" "(" Three-Points ")" | + "excircleCenter" "(" Three-Points "," Two-Points ")" | + Point-Name [ "," Modifier ] + +Modifier ::= "shift" "(" Distance "," Distance ")" | + "polar" "(" Distance, Distance [ "deg" | "rad" ] ")" | + "rotate" "(" Point-Name, Distance [ "deg" | "rad" ] ")" | + "vector" "(" Two-Points ")" + +Distance ::= expression + +Two-Points ::= Point-Name Point-Name + +Three-Points ::= Point-Name Two-Points +</pre> +We now briefly explain the functionality of each option: +<ul> +<li>midpoint(AB): the midpoint between points A and B</li> +<li>pointOnLine(AB,d): point at distance d from A towards B</li> +<li>intersection(AB,CD): intersection of lines defined by AB and CD</li> +<li>perpendicular(A,BC): point of the foot of the perpendicular from A to line BC</li> +<li>circumCircleCenter(ABC): center of circumcircle of triangle ABC</li> +<li>incircleCenter(ABC):center of incircle of triangle ABC</li> +<li>excircleCenter(ABC,BC): center of excircle of triangle ABC, touching +side BC</li> +<li>A, shift(x,y): Point displaced from A by x and y along the X and Y +axes</li> +<li>A, polar(r,d): Point displaced from A by distance r in direction d</li> +<li>A, rotate(B,d): Rotate A about B by d</li> +</ul> +We now explain how the following piece of code operates. In case the first +token is a number, we assume that the coordinates are specified by a +number and another number, a variable or a pair of points. So, we check +whether there is a comma and use the subroutine [[ComputeDist]] to get the +second coordinate. In case the next token is one of the words +[[perpendicular]], [[intersection]], [[midpoint]], [[pointonline]], +[[circumcircleCenter]], [[IncircleCenter]], or [[ExcircleCenter]] +we consume the corresponding token and process the corresponding case. +In case the first two tokens are two identifiers, then we assume that we +have a pair of numbers. We compute their distance, check whether there is +a leading comma and compute the y-coordinate by calling subroutine +[[ComputeDist]]. In case the next token is a single identifier, we store +its name in the variable [[$PointA]]. If this identifier is a defined point name, +we check whether the next token is a comma. In case it is, we check whether +he token after the comma is either the token [[shift]], [[polar]], or +[[rotate]] and process each case accordingly. If it is +none of these tokens we issue an error message and continue with the next +input line. Now, if the token after the identifier isn't a comma, we assume +that the coordinates of the point will be identical to those of the point +whose name has been stored in the variable [[$PointA]]. If the identifier is a +variable name, we assume that the x-coordinate is the value of this variable. +We check whether the next token is a comma, and compute the y-coordinate by +calling the subroutine [[ComputeDist]]. The x-coordinate is stored in the variable +[[$Px]] and the y-coordinate in the variable [[$Py]]. + +<<process coordinates>>= + if (s/^perpendicular(?=\W)//i) { + <<process <tt>perpendicular</tt> case>> + } + elsif (s/^intersection(?=\W)//i) { + <<process <tt>intersection</tt> case>> + } + elsif (s/^midpoint(?=\W)//i) { + <<process <tt>midpoint</tt> case>> + } + elsif (s/^pointonline(?=\W)//i) { + <<process <tt>pointonline</tt> case>> + } + elsif (s/^circumcircleCenter(?=\W)//i) { + <<process <tt>circumcircleCenter</tt> case>> + } + elsif (s/^IncircleCenter(?=\W)//i) { + <<process <tt>IncircleCenter</tt> case>> + } + elsif (s/^ExcircleCenter(?=\W)//i) { + <<process <tt>ExcircleCenter</tt> case>> + } + elsif (/^[^\W\d_]\d{0,3}\s*[^,\w]/) { + m/^([^\W\d_]\d{0,3})\s*/i; + if (exists($PointTable{lc($1)})) { + my $Tcoord = get_point($lc); + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{$Tcoord}); + $Px = $x; + $Py = $y; + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + } + elsif (/[^\W\d_]\d{0,3}\s*,\s*shift|polar|rotate|vector/i) { #a point? + s/^([^\W\d_]\d{0,3})//i; + my $PointA = $1; + if (exists($PointTable{lc($PointA)})) { + s/\s*//; + if (s/^,//) { + s/\s*//; + if (s/^shift(?=\W)//i) { + <<process <tt>shift</tt> case>> + } + elsif (s/^polar(?=\W)//i) { + <<process <tt>polar</tt> case>> + } + elsif (s/^rotate(?=\W)//i) { + <<process <tt>rotate</tt> case>> + } + elsif (s/^vector(?=\W)//i) { + <<process <tt>vector</tt> case>> + } + else { + PrintErrorMessage("unexpected token",$lc); + next LINE; + } + } + else { + my ($xA,$yA,$pSVA,$pSA)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $xA; + $Py = $yA; + } + } + else { + PrintErrorMessage("Undefined point $PointA",$lc); + next LINE; + } + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + +@ In the following piece of code we process the [[perpendicular]] +case of the [[point]] specification. We first check whether there is an +opening left parenthesis. Next, we get the first point name. In case +there is no point name, we simply abandon the processing of this +line and continue with the next one. Then we see whether there is +a trailing comma. Omitting this token yields a non-fatal error. +Then we get two more points. As before, if we can't find any of these +points this yields a fatal-error. Note, that each time we check that the +point names correspond to existing point names. Then, we call subroutine +[[perpendicular]] to calculate the coordinates of the point. + +<<process <tt>perpendicular</tt> case>>= + chk_lparen("perpendicular",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + chk_comma($lc); + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py) = perpendicular($x1,$y1,$x2,$y2,$x3,$y3); + +@ In the following piece of code we process the [[intersection]] case of the +[[point]] specification. We get the four point names and if there is +no error we compute the intersection point by calling subroutine +[[intersection]]. + +<<process <tt>intersection</tt> case>>= + chk_lparen("intersection",$lc); + my $FirstPoint = get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_comma($lc); + my $ThirdPoint = get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + my $ForthPoint = get_point($lc); + next LINE if $ForthPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + my ($x4,$y4,$pSV4,$pS4)=unpack("d3A*",$PointTable{$ForthPoint}); + ($Px, $Py) = intersection4points($x1,$y1,$x2,$y2,$x3,$y3,$x4,$y4); + + +@ Given two points A and B, the midpoint option computes the coordinates +of a third point that lies on the middle of the line segment defined by +these two points. We get the the two points, and then we compute the +coordinates of the midpoint by means of the simple formula: +<center> +m<sub>x</sub>=x<sub>1</sub>+(y<sub>2</sub> - y<sub>1</sub>)/2 <br> +m<sub>y</sub>=y<sub>1</sub>+(x<sub>2</sub> - x<sub>1</sub>)/2 +</center> + +<<process <tt>midpoint</tt> case>>= + chk_lparen("midpoint",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + $Px = $x1 + ($x2 - $x1)/2; + $Py = $y1 + ($y2 - $y1)/2; + +@ Given two points A and B and length d, the [[PointOnLine]] option +computes the coordinates of a point that lies d units in the direction from +A towards B. We first get the coordinates of the two points that define +the line and then we get the distance, which can be a number, a variable, +or a pair of points. + +<<process <tt>pointonline</tt> case>>= + chk_lparen("pointonline",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + chk_comma($lc); + # now get the distance + my $distance = expr($lc); + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + ($Px, $Py) = pointOnLine($x1,$y1,$x2,$y2,$distance); + +@ The [[circumcircleCenter]] is used when one wants to compute the coordinates +of the center of circle that passes through the three points +of a triangle defined +by the three arguments of the option. All we do is get the coordinates +of the three points and then we call the subroutine [[circumCircleCenter]] +to compute the center. + +<<process <tt>circumcircleCenter</tt> case>>= + chk_lparen("circumCircleCenter",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py,$r) = &circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc); + next LINE if $Px == 0 and $Py == 0 and $r == 0; + +@ The [[IncircleCenter]] option is to determine the coordinates of a point +that is the center of circle that internally touches the sides +of a triangle defined by three given points. +The coordinates are computed by the subroutine [[IncircleCenter]]. + +<<process <tt>IncircleCenter</tt> case>>= + chk_lparen("IncircleCenter",$lc); + my $FirstPoint = &get_point($lc); + next LINE if $FirstPoint eq "_undef_"; + my $SecondPoint = &get_point($lc); + next LINE if $SecondPoint eq "_undef_"; + my $ThirdPoint = &get_point($lc); + next LINE if $ThirdPoint eq "_undef_"; + chk_rparen("No closing parenthesis found",$lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{$FirstPoint}); + my ($x2,$y2,$pSV2,$pS2)=unpack("d3A*",$PointTable{$SecondPoint}); + my ($x3,$y3,$pSV3,$pS3)=unpack("d3A*",$PointTable{$ThirdPoint}); + ($Px, $Py, $r) = IncircleCenter($x1,$y1,$x2,$y2,$x3,$y3); + +@ The [[ExcircleCenter]] option is used to define the coordinates of point +that is the center of an excircle of a triangle. We first check +whether there is an opening left parenthesis. Next, we get the names of the +three points that define the triangle. Then, we +check whether there is a comma. Now we get the names of the two points that +define one side of the triangle. We check whether the two points we +get are of the set of the triangle points. If not we issue +an error message and continue with the next input line. Then we make sure +that these two points are not identical. We compute the actual +coordinates by calling the subroutine [[excircle]]. Finally, we +make sure there is a closing right parenthesis. + +<<process <tt>ExcircleCenter</tt> case>>= + chk_lparen("ExcircleCenter",$lc); + my $PointA = get_point($lc); + next LINE if $PointA eq "_undef_"; + my $PointB = get_point($lc); + next LINE if $PointB eq "_undef_"; + my $PointC = get_point($lc); + next LINE if $PointC eq "_undef_"; + chk_comma($lc); + my $PointD = &get_point($lc); + next LINE if $PointD eq "_undef_"; + if (!memberOf($PointD, $PointA, $PointB, $PointC)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + my $PointE = get_point($lc); + next LINE if $PointE eq "_undef_"; + if (!memberOf($PointE, $PointA, $PointB, $PointC)) { + PrintErrorMessage("Current point isn't a side point",$lc); + next LINE; + } + if ($PointD eq $PointE) { + PrintErrorMessage("Side points are identical",$lc); + next LINE; + } + ($Px, $Py, $r) = excircle($PointA, $PointB, $PointC, + $PointD, $PointE); + chk_rparen("after coordinates part",$lc); + +@ The [[shift]] option allows us to define a point's coordinates relative +to the coordinates of an existing point by using two shift parameters. Each +parameter can be either a float, a variable name, or a pair of points. + +<<process <tt>shift</tt> case>>= + + chk_lparen("shift",$lc); + my $dist1 = expr($lc); + chk_comma($lc); + my $dist2 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + $Px = $x1 + $dist1; + $Py = $y1 + $dist2; + chk_rparen("shift part",$lc); + +@ The [[polar]] option allows us to define a point's coordinates relative +to the coordinates of an existing point using the polar coordinates of some +other point. We first check whether there is a left parenthesis, +Then we parse the various parts of the [[polar]] option. +In case the user has specified the angle in degrees, we have +to transform it into radians, as all trigonometric function expect their +arguments to be radians. Next, we compute the coordinates of the point. +We conclude by checking whether there is a closing parenthesis. + +<<process <tt>polar</tt> case>>= + chk_lparen("polar",$lc); + my ($R1, $Theta1); + $R1 = expr($lc); + chk_comma($lc); + $Theta1 = expr($lc); + my ($x1,$y1,$pSV1,$pS1)=unpack("d3A*",$PointTable{lc($PointA)}); + s/\s*//; + if (s/^rad(?=\W)//i) { + # do nothing! + } + elsif (s/^deg(?=\W)//i) { + $Theta1 = $Theta1 * PI / 180; + } + else { + #$Theta1 = $Theta1 * PI / 180; + } + $Px = $x1 + $R1 * cos($Theta1); + $Py = $y1 + $R1 * sin($Theta1); + chk_rparen("after polar part",$lc); + +@ The [[rotate]] option allows us to define a point's coordinates by +rotating an existing point, Q, about a third point, P, by a +specified angle. +The method to achieve this is to first get the coordinates of points +P and Q and then +<ol> +<li> translate origin to P</li> +<li> rotate about P</li> +<li> translate from P back to origin, etc</li> +</ol> +As in the case of the [[polar]] option, we check for an opening parenthesis. +Next, we parse the point name and the angle. At this point we are able to +compute the coordinates of the rotated point. We conclude by checking +whether there is a closing parenthesis. + +<<process <tt>rotate</tt> case>>= + chk_lparen("rotate",$lc); + my $Q = lc($PointA); + my $P = get_point($lc); + next LINE if $P eq "_undef_"; + chk_comma($lc); + my $Theta1 = expr($lc); + my ($xP,$yP,$pSV1,$pS1)=unpack("d3A*",$PointTable{$P}); + my ($xQ,$yQ,$pSV2,$pS2)=unpack("d3A*",$PointTable{$Q}); + s/\s*//; + if (s/^rad(?=\W)//i) + { + # do nothing! + } + elsif (s/^deg(?=\W)//i) + { + $Theta1 = $Theta1 * PI / 180; + } + else + { + $Theta1 = $Theta1 * PI / 180; + } + # shift origin to P + $xQ -= $xP; + $yQ -= $yP; + # do the rotation + $Px = $xQ * cos($Theta1) - $yQ * sin($Theta1); + $Py = $xQ * sin($Theta1) + $yQ * cos($Theta1); + # return origin back to original origin + $Px += $xP; + $Py += $yP; + chk_rparen("after rotate part",$lc); + +@ [[vector(PQ)]] is actually is a shorthand of [[shift(xQ-xP,yQ-yP)]]. Thus, it +is implemented by borrowing code from the [[shift]] modifier. + +<<process <tt>vector</tt> case>>= + chk_lparen("vector",$lc); + my ($x0,$y0,$pSV0,$pS0) = unpack("d3A*",$PointTable{lc($PointA)}); + my $P = get_point($lc); + my $Q = get_point($lc); + my ($x1,$y1,$pSV1,$pS1) = unpack("d3A*",$PointTable{$P}); + my ($x2,$y2,$pSV2,$pS2) = unpack("d3A*",$PointTable{$Q}); + $Px = $x0 + $x2 - $x1; + $Py = $y0 + $y2 - $y1; + chk_rparen("vector part",$lc); + + +@ When lines are drawn to a point, the line will (unless otherwise +specified) extend to the point location. However, this can be prevented by +allocating an optional circular line-free zone to a point by specifying the +radius (in square brackets) of the optional point shape part. Currently, in this part +we are allowed to describe the point shape and the radius value. If only the +radius is specified, e.g., <tt>[radius=5]</tt>, then the line-free zone will be +applied to the default point character, i.e., <tt>$\bullet$</tt> or whatever it +has been set to. Here is the syntax we employ: +<pre> +Optional_point_shape_part ::= "[" [ symbol_part ] [","] [ radius_part ]" +symbol_part ::= "symbol" "=" symbol +symbol ::= "circle" "(" expression ")" | + "square" "(" expression ")" | + LaTeX_Code +radius_part ::= "radius" "=" expression +</pre> +Note that it is possible to have right square bracket in the <tt>LaTeX_Code</tt> but it +has to be escaped (i.e., <tt>\]</tt>). + +<<process optional point shape part>>= + if (/^(symbol|radius|side)\s*/i) { + my @previous_options = (); + my $number_of_options = 1; + my $symbol_set = 0; + while (s/^(symbol|radius)\s*//i and $number_of_options <= 2) { + my $option = lc($1); + if (s/^=\s*//) { + if (memberOf($option,@previous_options)) { + PrintErrorMessage("Option \"$option\" has been already defined", $lc); + my $dummy = expr($lc); + } + elsif ($option eq "radius") { + $sh = expr($lc); + $sv = $defaultsymbol if ! $symbol_set; + } + elsif ($option eq "symbol") { + if (s/^circle\s*//i) { + $sv = "circle"; + chk_lparen("after token circle",$lc); + $side_or_radius = expr($lc); + chk_rparen("expression",$lc); + } + elsif (s/^square\s*//i) { + $sv = "square"; + chk_lparen("after token square",$lc); + $side_or_radius = expr($lc); + chk_rparen("expression",$lc); + } + elsif (s/^(((\\\]){1}|(\\,){1}|(\\\s){1}|[^\],\s])+)//) { + $sv = $1; + $sv =~ s/\\\]/\]/g; + $sv =~ s/\\,/,/g; + $sv =~ s/\\ / /g; + s/\s*//; + } + $symbol_set = 1; + } + } + else { + PrintErrorMessage("unexpected token", $lc); + next LINE; + } + $number_of_options++; + push (@previous_options, $option); + s/^,\s*//; + } + } + else { + PrintErrorMessage("unexpected token", $lc); + next LINE; + } + +@ The [[ArrowShape]] command has either one or three arguments. If the only argument of +the command is the token [[default]], then the parameters associated with the +arrow shape resume their default values. Now, if there are three arguments, these are +used to specify the shape of an arrow. The command actually sets the three global variables +[[$arrowLength]], [[$arrowAngleB]] and [[$arrowAngleC]]. Arguments whose value is equal +to zero, do not affect the value of the corresponding global variables. To reset the +values of the global variables one should use the commane with [[default]] as it +only argument. The syntax of the command is as follows: +<center> +<tt>"ArrowShape" "(" expr [ units ] "," expr "," expr ")"</tt> or<br> +<tt>"ArrowShape" "(" "default" ")" </tt> +</center>> +Here [[units]] is any valid TeX unit (e.g., "mm", "cm", etc.). Note that if +any of the three expressions is equal to zero, the default value is taken +instead. As direct consequence, if the value of the first expression is zero, +the units part is actually ignored. + +<<process <tt>ArrowShape</tt> command>>= + + chk_lparen("$cmd",$lc); + if (s/^default//i) { + $arrowLength = 2; + $arrowLengthUnits = "mm"; + $arrowAngleB = 30; + $arrowAngleC = 40; + } + else { + my ($LocalArrowLength, $LocalArrowAngleB ,$LocalArrowAngleC) = (0,0,0); + $LocalArrowLength = expr($lc); + if (s/^\s*($units)//i) { + $arrowLengthUnits = "$1"; + } + else { + $xunits =~ /(\d+(\.\d+)?)\s*($units)/; + $LocalArrowLength *= $1; + $arrowLengthUnits = "$3"; + } + chk_comma($lc); + $LocalArrowAngleB = expr($lc); + chk_comma($lc); + $LocalArrowAngleC = expr($lc); + $arrowLength = ($LocalArrowLength == 0 ? 2 : $LocalArrowLength); + $arrowLengthUnits = ($LocalArrowLength == 0 ? "mm" : $arrowLengthUnits); + $arrowAngleB = ($LocalArrowAngleB == 0 ? 30 : $LocalArrowAngleB); + $arrowAngleC = ($LocalArrowAngleC == 0 ? 40 : $LocalArrowAngleC); + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + print OUT "%% arrowLength = $arrowLength$arrowLengthUnits, ", + "arrowAngleB = $arrowAngleB ", + "and arrowAngleC = $arrowAngleC\n" if $comments_on; + +@ The [[PointSymbol]] command is used to set the point symbol and possibly its +line-free radius. The point symbol can be either a LaTeX symbol or the word [[default]] +which corresponds to the default point symbol, i.e., <tt>$\bullet$</tt>. The line-free +radius can be an expression. Here is the complete syntax: +<pre> + pointsymbol ::= "pointsymbol" ( symbol [ "," radius]) + symbol ::= "default" | circle | square | LaTeX_Code + circle ::= "circle" "(" expression ")" + square ::= "square" "(" expression ")" + radius ::= expression +</pre> +Note that the <tt>LaTeX_Code</tt> can contain the symbols <tt>\,</tt> and +<tt>\)</tt> which are escape sequences for a comma and right parenthesis, respectively. + +<<process <tt>PointSymbol</tt> command>>= + + chk_lparen("$cmd",$lc); + if (s/^default//i) #default point symbol + { + $defaultsymbol = "\$\\bullet\$"; + } + elsif (s/^(circle|square)//i) { + $defaultsymbol = $1; + chk_lparen($defaultsymbol, $lc); + $GlobalDimOfPoints = expr($lc); + chk_rparen("expression", $lc); + } + elsif (s/^(((\\,){1}|(\\\)){1}|(\\\s){1}|[^\),\s])+)//) #arbitrary LaTeX point + { + $defaultsymbol = $1; + $defaultsymbol=~ s/\\\)/\)/g; + $defaultsymbol=~ s/\\,/,/g; + $defaultsymbol=~ s/\\ / /g; + } + else + { + PrintErrorMessage("unrecognized point symbol",$lc); + } + if (s/\s*,\s*//) { + $defaultLFradius = expr($lc); + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + +@ The [[system]] command provides a shell escape. However, we use a subroutine +to check whether the argument of the command contains tainted data. If this +is the case, then we simply ignore this command. The syntax of the command +is as follows: +<pre> + system-cmd ::= "system" "(" string ")" +</pre> +where string is just a sequence of characters enclosed in quotation marks. +We start by parsing a left parenthesis and then we get the command by +calling the subroutine [[get_string]]. If there is an error we skip this +command. Otherwise, we assign to the variable [[$_]] what is left. Now we check +if the variable [[$command]] contains any tainted data. If it doesn't, we +execute the command, otherwise we print an error message and skip to the +next input line. Next, we check for closing right parenthesis and a possible +trailing comment. + +<<process <tt>system</tt> command>>= + + chk_lparen("$cmd",$lc); + my ($error, $command, $rest) = get_string($_); + next LINE if $error == 1; + $_ = $rest; + if (! is_tainted($command)) { + system($command); + } + else { + PrintErrorMessage("String \"$command\" has tainted data", $lc); + next LINE; + } + chk_rparen("after $cmd arguments",$lc); + chk_comment("after $cmd command",$lc); + +@ The [[text]] command is used to put a piece of text or a symbol on +a particular point of the resulting graph. The syntax of the command is +as follows: +<pre> + text-comm ::= "text" "(" text ")" "{"coords"} "[" pos-code "]" + text ::= ascii string + coords ::= Coord "," Coord | + Point-Name "," "shift" "(" Coord "," Coord ")" | + Point-Name "," "polar" "(" Coord "," Coord [angle-unit] ")" + Coord ::= decimal number | variable | pair-of-Point-Names + pair-of-Point-Names ::= Point-Name Point-Name + angle-unit ::= "deg" | "rad" + pos-code ::= lr-code [tb-code] | tb-code [lr-code] + lr-code ::= "l" | "r" + tb-code ::= "t" | "b" | "B" +</pre> +Initially, we parse the [[text]]. Since the text may contain parentheses +we assume that the user enters pairs of matching parentheses. Note, that +this is a flaw in the original design of the language, which may be remedied +in future releases of the software. Then, we check the [[coords]] part. Next, +if there is a left square bracket, we assume the user has specified the +[[pos-code]]. We conclude by checking a possible trailing comment. +The next thing we do is to generate the PiCTeX code. The two possible +forms follow: +<center> +<tt>\put {TEXT} [POS] at Px Py</tt><br> +<tt>\put {TEXT} at Px Py</tt><br> +</center> + +<<process <tt>text</tt> command>>= + + chk_lparen("text",$lc); + my ($level,$text)=(1,""); + TEXTLOOP: while (1) + { + $level++ if /^\(/; + $level-- if /^\)/; + s/^(.)//; + last TEXTLOOP if $level==0; + $text .= $1; + } + chk_lcb("text part",$lc); + my ($Px, $Py,$dummy,$pos); + $pos=""; + s/\s*//; + <<process coordinates part of text command>> + chk_rcb("coordinates part of text command",$lc); + if (s/^\[//) + { + s/\s*//; + <<process optional part of text command>> + s/\s*//; + chk_rsb("optional part of text command",$lc); + } + chk_comment($lc); + if ($pos eq "") + { + printf OUT "\\put {%s} at %f %f\n", $text, $Px, $Py; + } + else + { + printf OUT "\\put {%s} [%s] at %f %f\n", $text, $pos, $Px, $Py; + } + +@ In this section we define the code that handles the coordinates part +of the [[text]] command. The code just implements the grammar given above. +If the first token is a number, we assume this is the x-coordinate. If +it is a variable, we assume its value is the x-coordinate. However, if +it is a point name, we check whether the next token is another point name. +In this case we compute the distance between the two points. In case we +have a single point followed by a comma, we expect to have either a polar +or a shift part, which we process the same we processed them in the point +command. + +<<process coordinates part of text command>>= + + if (/^[^\W\d_]\d{0,3}\s*[^,\w]/) { + my $Tcoord = get_point($lc); + my ($x,$y,$pSV,$pS)=unpack("d3A*",$PointTable{$Tcoord}); + $Px = $x; + $Py = $y; + } + elsif (/[^\W\d_]\d{0,3}\s*,\s*shift|polar/i) { + s/^([^\W\d_]\d{0,3})//i; + my $PointA = $1; + if (exists($PointTable{lc($PointA)})) { + s/\s*//; + if (s/^,//) { + s/\s*//; + if (s/^shift(?=\W)//i) { + <<process <tt>shift</tt> case>> + } + elsif (s/^polar(?=\W)//i) { + <<process <tt>polar</tt> case>> + } + } + } + else { + PrintErrorMessage("undefined point/var",$lc); + next LINE; + } + } + else { + $Px = expr(); + chk_comma($lc); + $Py = expr(); + } + +@ In this section we process the optional part of the [[text]] command. +The general rule is that we are allowed to have up to two options one +from the characters [[l]] and [[r]] and one from the the characters +[[B]], [[b]], and [[t]]. We first check whether the next character is +letter, if it isn't we issue an error message and continue with the next +input line. If it is a letter we check whether it belongs to one of the +two groups and if it doesn't we issue an error message and continue with the +next input line. If the next character belongs to first group, i.e., it is +either [[l]] or [[r]], we store this character into the variable [[$pos]]. Next, +we check whether there is another letter. If it is a letter, we store it +in the variable [[$np]]. Now we make sure that this character belongs to the +other group, i.e., it is either [[b]], [[B]], or [[t]]. In case it belongs +to the other group, we append the value of [[$np]] to the string stored in +the variable [[$pos]]. Otherwise we issue an error message and continue with the +next input line. We work similarly for the other case. In order to check +whether a character belongs to some group of characters, we use the user +defined function [[memberOf]]. + +<<process optional part of text command>>= + + if (s/^(\w{1})\s*//) { + $pos .= $1; + if (memberOf($pos, "l", "r")) { + if (s/^(\w{1})\s*//) { + my $np = $1; + if (memberOf($np, "t", "b", "B")) { + $pos .= $np; + } + else { + if (memberOf($np, "l", "r")) { + PrintErrorMessage("$np can't follow 'l' or 'r'", $lc); + } + else { + PrintErrorMessage("$np is not a valid positioning option", $lc); + } + next LINE; + } + } + } + elsif (memberOf($pos, "t", "b", "B")) { + if (s/^(\w{1})\s*//) { + my $np = $1; + if (memberOf($np, "l", "r")) { + $pos .= $np; + } + else { + if (memberOf($np, "t", "b", "B")) { + PrintErrorMessage("$np can't follow 't', 'b', or 'B'", $lc); + } + else { + PrintErrorMessage("$np is not a valid positioning option", $lc); + } + next LINE; + } + } + } + else { + PrintErrorMessage("$pos is not a valid positioning option", $lc); + next LINE; + } + } + else { + PrintErrorMessage("illegal token in optional part of text command",$lc); + next LINE; + } + +@ The [[const]] command is used to store values into a comma separated +list of named constants. Constant names have the same format as point names, +i.e., they start with a letter and are followed by up to two digits. The +whole operation is performed by a [[do-while]] construct that checks that +there is a valid constant name, a [[=]] sign, and an expression. The +[[do-while]] construct terminates if the next token isn't a comma. Variable +[[$Constname]] is used to store the initial variable name, while we store +in variable [[$varname]] the lowercase version of the variable name. In addition, +we make sure a constant is not redefined (or else it wouldn't be a constant:-). +The last thing we do is to check whether there is a trailing comment. +In case there, we simply ignore itl; otherwise we print a warning message. + +<<process <tt>const</tt> command>>= + do{ + s/\s*//; + PrintErrorMessage("no identifier found after token const",$lc) + if $_ !~ s/^([^\W\d_]\d{0,3})//i; + my $Constname = $1; + my $constname = lc($Constname); + if (exists $ConstTable{$constname}) { + PrintErrorMessage("Redefinition of constant $constname",$lc); + } + s/\s*//; #remove leading white space + PrintErrorMessage("did not find expected = sign",$lc) + if $_ !~ s/^[=]//i; + my $val = expr($lc); + $VarTable{$constname} = $val; + $ConstTable{$constname} = 1; + print OUT "%% $Constname = $val\n" if $comments_on; + }while (s/^,//); + chk_comment($lc); + s/\s*//; + if (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } + +@ The [[var]] command is used to store values into a comma separated +list of named variables. Variable names have the same format as point names, +i.e., they start with a letter and are followed by up to two digits. The +whole operation is performed by a [[do-while]] construct that checks that +there is a valid variable name, a [[=]] sign, and an expression. The +[[do-while]] construct terminates if the next token isn't a comma. The variable +[[$Varname]] is used to store the initial variable name, while we store +in the variable [[$varname]] the lowercase version of the variable name. +The last thing we do is to check whether there is a trailing comment. +In case there, we simply ignore itl; otherwise we print a warning message. + +<<process <tt>var</tt> command>>= + do{ + s/\s*//; + PrintErrorMessage("no identifier found after token var",$lc) + if $_ !~ s/^([^\W\d_]\d{0,3})//i; + my $Varname = $1; + my $varname = lc($Varname); + if (exists $ConstTable{$varname}) { + PrintErrorMessage("Redefinition of constant $varname",$lc); + } + s/\s*//; #remove leading white space + PrintErrorMessage("did not find expected = sign",$lc) + if $_ !~ s/^[=]//i; + my $val = expr($lc); + $VarTable{$varname} = $val; + print OUT "%% $Varname = $val\n" if $comments_on; + }while (s/^,//); + chk_comment($lc); + s/\s*//; + if (/^[^%]/) { + PrintWarningMessage("Trailing text is ignored",$lc); + } diff --git a/Master/texmf-dist/doc/latex/mathspic/sourcecode.pdf b/Master/texmf-dist/doc/latex/mathspic/sourcecode.pdf Binary files differnew file mode 100644 index 00000000000..d56402e5dd2 --- /dev/null +++ b/Master/texmf-dist/doc/latex/mathspic/sourcecode.pdf |