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author | Karl Berry <karl@freefriends.org> | 2011-08-21 23:57:09 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2011-08-21 23:57:09 +0000 |
commit | 9ee7cfba1625748e157c7cda3091549eb0701cbf (patch) | |
tree | 54d32aa0aa0b6b3b21ae16cbbd63f38242590549 /Master/texmf-dist/doc/latex/mathspic/sourcecode.html | |
parent | cc6dec43bed861394613828f8ed1351b0952d702 (diff) |
mathspic (7jun11 and earlier)
git-svn-id: svn://tug.org/texlive/trunk@23640 c570f23f-e606-0410-a88d-b1316a301751
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diff --git a/Master/texmf-dist/doc/latex/mathspic/sourcecode.html b/Master/texmf-dist/doc/latex/mathspic/sourcecode.html deleted file mode 100644 index 5d963ef76dd..00000000000 --- a/Master/texmf-dist/doc/latex/mathspic/sourcecode.html +++ /dev/null @@ -1,5124 +0,0 @@ -<!-- 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> - |