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+<!-- 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>&lt;*&gt;=</dfn></a>
+#!/usr/bin/perl
+#
+#(c) Copyright 2005-2007
+# Apostolos Syropoulos &amp; 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>&lt;package <tt>DummyFH</tt> &gt;</i></a>
+package main;
+use Math::Trig;
+<a name="NW21HcNW-1p0Y9w-1-u2" href="#NWD21HcNW-8"><i>&lt;Define global variables&gt;</i></a>
+<a name="NW21HcNW-1p0Y9w-1-u3" href="#NWD21HcNW-9"><i>&lt;subroutine definitions&gt;</i></a>
+<a name="NW21HcNW-1p0Y9w-1-u4" href="#NWD21HcNW-4"><i>&lt;Check for command line arguments&gt;</i></a>
+<a name="NW21HcNW-1p0Y9w-1-u5" href="#NWD21HcNW-7"><i>&lt;process file&gt;</i></a>
+print $alarm if $no_errors &gt; 0;
+__END__
+
+</pre><p><a name="NWD21HcNW-3">The package </a><code>DummyFH</code> is used in the implementation of the <code>loop</code> command.
+It creates a dummy filehandle that is associated with an array of strings. Since
+we only read data from this dummy filehandle, we implement the <code>READLINE</code> subroutine.
+When we read a line from this dummy filehandle, we actually requesting the next entry
+of the array (if any). That is why we use the package variable <code>$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>&lt;package <tt>DummyFH</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-2">&lt;-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 &gt; $#$self) {
+ $index = 0;
+ return undef;
+ }
+ else {
+ return $self-&gt;[$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>&lt;Check for command line arguments&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-2">&lt;-U</a>)</b>
+our $alarm=&quot;&quot;;
+our $comments_on=1;
+our $out_file=&quot;default&quot;;
+our $argc=@ARGV;
+if ($argc == 0 || $argc &gt; 5 ){ # no command line arguments or more than 4
+ # arguments
+ die &quot;\nmathspic version $version_number\n&quot; .
+ &quot;Usage: mathspic [-h] [-b] [-c] [-o &lt;out file&gt;] &lt;in file&gt;\n\n&quot;;
+}
+else {
+ <a name="NW21HcNW-122Dzz-1-u1" href="#NWD21HcNW-5"><i>&lt;Process command line arguments&gt;</i></a>
+ print &quot;This is mathspic version $version_number\n&quot;;
+}
+<a name="NW21HcNW-122Dzz-1-u2" href="#NWD21HcNW-6"><i>&lt;Check if .m file exists&gt;</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>&lt;Process command line arguments&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-4">&lt;-U</a>)</b>
+ our $file = &quot;&quot;;
+ SWITCHES:
+ while($_ = $ARGV[0]) {
+ shift;
+ if (/^-h$/) {
+ die &quot;\nThis is mathspic version $version_number\n&quot; .
+ &quot;Type \&quot;man mathspic\&quot; for detailed help\n&quot;.
+ &quot;Usage:\tmathspic [-h] [-b] [-c] [-o &lt;out file&gt;] &lt;in file&gt;\n&quot; .
+ &quot;\twhere,\n&quot; .
+ &quot;\t[-b]\tenables bell sound if error exists\n&quot; .
+ &quot;\t[-c]\tdisables comments in ouput file\n&quot; .
+ &quot;\t[-h]\tgives this help listing\n&quot; .
+ &quot;\t[-o]\tcreates specified output file\n\n&quot;;
+ }
+ elsif (/^-b$/) {
+ $alarm = chr(7);
+ }
+ elsif (/^-c$/) {
+ $comments_on = 0;
+ }
+ elsif (/^-o$/) {
+ die &quot;No output file specified!\n&quot; if !@ARGV;
+ $out_file = $ARGV[0];
+ shift;
+ }
+ elsif (/^-\w+/) {
+ die &quot;$_: Illegal command line switch!\n&quot;;
+ }
+ else {
+ $file = $_;
+ }
+ }
+ die &quot;No input file specified!\n&quot; if $file eq &quot;&quot;;
+
+</pre><p><a name="NWD21HcNW-6">In order to check whether the input-file exists, we simply use the</a>
+<code>-e</code> operator. First we check to see if <code>$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>&lt;Check if .m file exists&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-4">&lt;-U</a>)</b>
+ our ($source_file, $log_file);
+ if (! -e $file) {
+ die &quot;$file: no such file!\n&quot; if (! (-e &quot;$file.m&quot;));
+ $source_file = &quot;$file.m&quot;;
+ }
+ else {
+ $source_file = $file;
+ $file = $1 if $file =~ /(\w[\w-\.]+)\.\w+/;
+ }
+ $out_file= &quot;$file.mt&quot; if $out_file eq &quot;default&quot;;
+ $log_file= &quot;$file.mlg&quot;;
+
+</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>&lt;process file&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-2">&lt;-U</a>)</b>
+ open(IN,&quot;$source_file&quot;)||die &quot;Can't open source file: $source_file\n&quot;;
+ open(OUT,&quot;&gt;$out_file&quot;)||die &quot;Can't open output file: $out_file\n&quot;;
+ open(LOG,&quot;&gt;$log_file&quot;)||die &quot;Can't open log file: $log_file\n&quot;;
+ print_headers;
+ process_input(IN,&quot;&quot;);
+
+</pre><p>In this section we define a few global variables. More specifically:
+the variable <code>$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&nbsp;pt).
+
+<pre><a name="NW21HcNW-xIn58-1" href="#NWD21HcNW-8"><dfn>&lt;Define global variables&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-2">&lt;-U</a>)</b>
+our $version_number = &quot;1.10 Feb 18, 2007&quot;;
+our $commandLineArgs = join(&quot; &quot;, @ARGV);
+our $command = &quot;&quot;;
+our $curr_in_file = &quot;&quot;;
+our %PointTable = ();
+our %VarTable = ();
+our %ConstTable = ();
+our $no_errors = 0;
+our $xunits = &quot;1pt&quot;;
+our $yunits = &quot;1pt&quot;;
+our $units = &quot;pt|pc|in|bp|cm|mm|dd|cc|sp&quot;;
+our $defaultsymbol = &quot;\$\\bullet\$&quot;;
+our $defaultLFradius = 0;
+use constant PI =&gt; atan2(1,1)*4;
+use constant R2D =&gt; 180 / PI;
+use constant D2R =&gt; PI / 180;
+our $arrowLength = 2;
+our $arrowLengthUnits = &quot;mm&quot;;
+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>&lt;subroutine definitions&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-2">&lt;-U</a>)</b>
+ <a name="NW21HcNW-2AA3uL-1-u1" href="#NWD21HcNW-A"><i>&lt;subroutine <tt>mpp</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u2" href="#NWD21HcNW-B"><i>&lt;subroutine <tt>PrintErrorMessage</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u3" href="#NWD21HcNW-C"><i>&lt;subroutine <tt>PrintWarningMessage</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u4" href="#NWD21HcNW-D"><i>&lt;subroutine <tt>PrintFatalError</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u5" href="#NWD21HcNW-E"><i>&lt;subroutine <tt>chk_lparen</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u6" href="#NWD21HcNW-F"><i>&lt;subroutine <tt>chk_rparen</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u7" href="#NWD21HcNW-G"><i>&lt;subroutine <tt>chk_lcb</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u8" href="#NWD21HcNW-H"><i>&lt;subroutine <tt>chk_rcb</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u9" href="#NWD21HcNW-I"><i>&lt;subroutine <tt>chk_lsb</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u10" href="#NWD21HcNW-J"><i>&lt;subroutine <tt>chk_rsb</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u11" href="#NWD21HcNW-K"><i>&lt;subroutine <tt>chk_comma</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u12" href="#NWD21HcNW-L"><i>&lt;subroutine <tt>chk_comment</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u13" href="#NWD21HcNW-M"><i>&lt;subroutine <tt>print_headers</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u14" href="#NWD21HcNW-N"><i>&lt;subroutine <tt>get_point</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u15" href="#NWD21HcNW-O"><i>&lt;subroutine <tt>perpendicular</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u16" href="#NWD21HcNW-P"><i>&lt;subroutine <tt>Length</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u17" href="#NWD21HcNW-Q"><i>&lt;subroutine <tt>triangleArea</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u18" href="#NWD21HcNW-R"><i>&lt;subroutine <tt>pointOnLine</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u19" href="#NWD21HcNW-S"><i>&lt;subroutine <tt>circumCircleCenter</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u20" href="#NWD21HcNW-T"><i>&lt;subroutine <tt>ComputeDist</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u21" href="#NWD21HcNW-U"><i>&lt;subroutine <tt>intersection4points</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u22" href="#NWD21HcNW-V"><i>&lt;subroutine <tt>IncircleCenter</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u23" href="#NWD21HcNW-W"><i>&lt;subroutine <tt>Angle</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u24" href="#NWD21HcNW-X"><i>&lt;subroutine <tt>excircle</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u25" href="#NWD21HcNW-Y"><i>&lt;subroutine <tt>DrawLineOrArrow</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u26" href="#NWD21HcNW-Z"><i>&lt;subroutine <tt>drawarrows</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u27" href="#NWD21HcNW-a"><i>&lt;subroutine <tt>drawlines</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u28" href="#NWD21HcNW-b"><i>&lt;subroutine <tt>drawCurve</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u29" href="#NWD21HcNW-c"><i>&lt;subroutine <tt>drawpoints</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u30" href="#NWD21HcNW-d"><i>&lt;subroutine <tt>drawAngleArc</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u31" href="#NWD21HcNW-e"><i>&lt;subroutine <tt>drawAngleArrow</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u32" href="#NWD21HcNW-f"><i>&lt;subroutine <tt>expr</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u33" href="#NWD21HcNW-g"><i>&lt;subroutine <tt>memberOf</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u34" href="#NWD21HcNW-h"><i>&lt;subroutine <tt>tand</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u35" href="#NWD21HcNW-i"><i>&lt;subroutine <tt>get_string</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u36" href="#NWD21HcNW-j"><i>&lt;subroutine <tt>is_tainted</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u37" href="#NWD21HcNW-k"><i>&lt;subroutine <tt>noOfDigits</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u38" href="#NWD21HcNW-l"><i>&lt;subroutine <tt>drawsquare</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u39" href="#NWD21HcNW-m"><i>&lt;subroutine <tt>X2sp</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u40" href="#NWD21HcNW-n"><i>&lt;subroutine <tt>sp2X</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u41" href="#NWD21HcNW-o"><i>&lt;subroutine <tt>setLineThickness</tt> &gt;</i></a>
+ <a name="NW21HcNW-2AA3uL-1-u42" href="#NWD21HcNW-p"><i>&lt;subroutine <tt>process_input</tt> &gt;</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>&lt;subroutine <tt>mpp</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub mpp {
+ my $in_line;
+ chomp($in_line = shift);
+ my $LC = shift;
+ my $out_line = $in_line;
+ my $macro_name = &quot;&quot;;
+ my @macro_param = ();
+ my $macro_code = &quot;&quot;;
+ if ($in_line =~ s/^%def\s*//) {
+ if ($in_line =~ s/^(\w+)\s*//){
+ $macro_name = $1;
+ }
+ else {
+ PrintErrorMessage(&quot;No macro name has been found&quot;,$LC);
+ return &quot;&quot;
+ }
+ if ($in_line =~ s/^\(\s*//) {
+ # do nothing
+ }
+ else {
+ PrintErrorMessage(&quot;No left parenthesis after macro name has been found&quot;,$LC);
+ return &quot;&quot;;
+ }
+ if ($in_line =~ s/^\)//) {
+ # Macro has no parameters!
+ }
+ else {
+ MACROS: while (1) {
+ if ($in_line =~ s/^(\w+)\s*//) {
+ push (@macro_param, $1);
+ }
+ else {
+ PrintErrorMessage(&quot;No macro parameter name has been found&quot;,$LC);
+ return &quot;&quot;;
+ }
+ if ($in_line =~ s/^,\s*//) {
+ next MACROS;
+ }
+ else {
+ last MACROS;
+ }
+ }
+ if ($in_line =~ s/^\)//) {
+ # do nothing!
+ }
+ else {
+ PrintErrorMessage(&quot;No closing parenthesis after macro parameters&quot;,$LC);
+ return &quot;&quot;;
+ }
+ }
+ $in_line =~ s/([^%]+)(%.*)/$1/;
+ $macro_code = $in_line;
+ push ( @Macros , { 'macro_name' =&gt; $macro_name,
+ 'macro_code' =&gt; $macro_code,
+ 'macro_param' =&gt; \@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 &gt;= 0; $i--) {
+ if ($Macros[$i]-&gt;{'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 &gt;= 0; $i--) {
+ my $macro_name = $Macros[$i]-&gt;{'macro_name'};
+ if ($in_line =~ /&amp;$macro_name\b/) { ############################
+ my $num_of_macro_args = @{$Macros[$i]-&gt;{'macro_param'}};
+ if ( $num_of_macro_args &gt; 0 ) {
+ # Macro with parameters
+ my $pattern = &quot;&amp;$macro_name\\(&quot;;
+ foreach my $p ( 1..$num_of_macro_args ) {
+ my $comma = ($p == $num_of_macro_args) ? &quot;\\s*&quot; : &quot;\\s*,\\s*&quot;;
+ $pattern .= &quot;\\s*[^\\s\\)]+$comma&quot;;
+ }
+ $pattern .= &quot;\\)&quot;;
+ while($in_line =~ /&amp;$macro_name\b/) {
+ if ($in_line =~ /$pattern/) {
+ my $before = $`;
+ my $after = $';
+ my $match = $&amp;;
+ my $new_code = $Macros[$i]-&gt;{'macro_code'};
+ $match =~ s/^&amp;$macro_name\(\s*//;
+ $match =~ s/\)$//;
+ foreach my $arg ( 0..($num_of_macro_args - 1) ) {
+ my $old = $Macros[$i]-&gt;{'macro_param'}-&gt;[$arg];
+ my $comma = ($arg == ($num_of_macro_args - 1)) ? &quot;&quot; : &quot;,&quot;;
+ $match =~ s/^\s*([^\s,]+)\s*$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;
+ }
+ $in_line = &quot;$before$new_code$after&quot;;
+ }
+ else {
+ PrintErrorMessage(&quot;Usage of macro &amp;$macro_name does not &quot; .
+ &quot;match its definition&quot;, $LC);
+ return &quot;&quot;;
+ }
+ }
+ }
+ else {
+ # Macro without parameters
+ my $replacement = $Macros[$i]-&gt;{'macro_code'};
+ # '\b': Substitute only whole words
+ # not x in xA
+ $in_line =~ s/&amp;$macro_name\b/$replacement/g;
+ }
+ }
+ }
+ last EXPANSIONLOOP if ( $org_in_line eq $in_line );
+ }
+ return &quot;$in_line$comment&quot;;
+ }
+}
+
+</pre><p>Subroutine <tt>PrintErrorMessage</tt> has two parameters: the
+error message that will be printed on the screen, the log file and
+the output file, and the line number of the line containing the
+error was detected.
+The general form of the error message is the following:
+<pre>
+line X: paper{units(
+ ,mm)xrange(0,20)yrange(0,30)axes(B)ticks(10,10)}
+
+***Error: Error_Message
+</pre>
+where <code>X</code> denotes the line number and <code>Error_Message</code> is the
+actual error message. Note, that we print the tokens processed so far
+and on the text line the unprocessed tokens, so that the user knows
+<a name="NWD21HcNW-B">exactly where the error is. In the variable </a><code>$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>&lt;subroutine <tt>PrintErrorMessage</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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 $fh &quot;$curr_in_file&quot;, &quot;Line $error_line: $A\n&quot;;
+ print $fh &quot; &quot; x $l ,$_,&quot;***Error: $errormessage\n&quot;;
+ }
+ if ($comments_on) { #print to output file file
+ print OUT &quot;%% *** $curr_in_file&quot;, &quot;Line $error_line: $A\n&quot;;
+ print OUT &quot;%% *** &quot;,&quot; &quot; x $l ,$_,&quot;%% ... Error: $errormessage\n&quot;;
+ }
+ $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>&lt;subroutine <tt>PrintWarningMessage</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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 $fh &quot;$curr_in_file&quot;, &quot;Line $warning_line: $A\n&quot;;
+ print $fh &quot; &quot; x $l ,$_,&quot;***Warning: $warningMessage\n&quot;;
+ }
+ if ($comments_on) { #print to output file file
+ print OUT &quot;%% *** $curr_in_file&quot;, &quot;Line $warning_line: $A\n&quot;;
+ print OUT &quot;%% *** &quot;,&quot; &quot; x $l ,$_,&quot;%% ... Warning: $warningMessage\n&quot;;
+ }
+ }
+
+</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>&lt;subroutine <tt>PrintFatalError</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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 &quot;$curr_in_file&quot;, &quot;Line $fatal_line: $A\n&quot; .
+ (&quot; &quot; x $l) . $_ . &quot;***Fatal Error: $FatalMessage\n&quot;;
+ }
+
+</pre><p><a name="NWD21HcNW-E">The subroutine </a><tt>chk_lparen</tt> accepts two arguments: the name
+of the token that should be immediately before the left parenthesis (variable
+<code>$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>&lt;subroutine <tt>chk_lparen</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_lparen {
+ my $token = $_[0];
+ my $lc = $_[1];
+ s/\s*//;
+ if (/^[^\(]/) {
+ PrintErrorMessage(&quot;Missing ( after $token&quot;,$lc);
+ }
+ else {
+ s/^\(\s*//;
+ }
+}
+
+</pre><p><a name="NWD21HcNW-F">The subroutine </a><tt>chk_rparen</tt> accepts two parameters: the name
+of the token that should be immediately after a right parenthesis (variable
+<code>$token</code>), and the current line number (variable <code>$lc</code>). Initially, we
+skip any leading white space and then we check whether the next input
+token is a right parenthesis. If it is not we issue a error message and
+return, otherwise we skip the parenthesis and any trailing white space.
+
+<pre><a name="NW21HcNW-3fTYkz-1" href="#NWD21HcNW-F"><dfn>&lt;subroutine <tt>chk_rparen</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_rparen {
+ my $token = $_[0];
+ my $lc = $_[1];
+ s/\s*//;
+ if (s/^\)//) {
+ s/\s*//;
+ }
+ else {
+ PrintErrorMessage(&quot;Missing ) after $token&quot;,$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>&lt;subroutine <tt>chk_lcb</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_lcb {
+ my $token = $_[0];
+ my $lc = $_[1];
+ s/\s*//;
+ if ($_ !~ /^\{/) {
+ PrintErrorMessage(&quot;Missing { after $token&quot;,$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>&lt;subroutine <tt>chk_rcb</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_rcb {
+ my $token = $_[0];
+ my $lc = $_[1];
+ if ($_ !~ /^\s*\}/) {
+ PrintErrorMessage(&quot;Missing } after $token&quot;,$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>&lt;subroutine <tt>chk_lsb</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_lsb {
+ my $token = $_[0];
+ my $lc = $_[1];
+
+ s/\s*//;
+ if ($_ !~ /^\[/) {
+ PrintErrorMessage(&quot;Missing [ after $token&quot;,$lc);
+ }
+ else {
+ s/^\[\s*//;
+ }
+}
+
+</pre><p><a name="NWD21HcNW-J">Subroutine </a><tt>chk_rsb</tt> behaves in a similar way to the subroutine
+<tt>chk_rparen</tt>.
+
+<pre><a name="NW21HcNW-ma6zf-1" href="#NWD21HcNW-J"><dfn>&lt;subroutine <tt>chk_rsb</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_rsb {
+ my $token = $_[0];
+ my $lc = $_[1];
+
+ s/\s*//;
+ if ($_ !~ /^\]/) {
+ PrintErrorMessage(&quot;Missing ] after $token&quot;,$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>&lt;subroutine <tt>chk_comma</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_comma {
+ my $lc = $_[0];
+
+ s/\s*//;
+ if (/^[^,]/) {
+ PrintErrorMessage(&quot;Did not find expected comma&quot;,$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>&lt;subroutine <tt>chk_comment</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub chk_comment {
+ my $lc = $_[0];
+
+ s/\s*//;
+ if (/^%/) {
+ # do nothing!
+ }
+ elsif (/^[^%]/) {
+ PrintWarningMessage(&quot;Trailing text is ignored&quot;,$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>&lt;subroutine <tt>print_headers</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub print_headers
+ {
+ my ($sec,$min,$hour,$mday,$mon,$year,$wday,$yday,$isdst) = localtime;
+ $year+=1900;
+ $mon+=1;
+ $now_string = &quot;$year/&quot; . ($mon&gt;9 ? &quot;$mon/&quot; : &quot;0$mon/&quot;) .
+ ($mday&gt;9 ? &quot;$mday &quot; : &quot;0$mday &quot;) .
+ ($hour&gt;9 ? &quot;$hour:&quot; : &quot;0$hour:&quot;) .
+ ($min&gt;9 ? &quot;$min:&quot; : &quot;0$min:&quot;) .
+ ($sec&gt;9 ? &quot;$sec&quot; : &quot;0$sec&quot;);
+ print OUT &quot;%* -----------------------------------------------\n&quot;;
+ print OUT &quot;%* mathspic (Perl version $version_number)\n&quot;;
+ print OUT &quot;%* A filter program for use with PiCTeX\n&quot;;
+ print OUT &quot;%* Copyright (c) 2005 A Syropoulos &amp; RWD Nickalls \n&quot;;
+ print OUT &quot;%* Command line: $0 $commandLineArgs\n&quot;;
+ print OUT &quot;%* Input filename : $source_file\n&quot;;
+ print OUT &quot;%* Output filename: $out_file\n&quot;;
+ print OUT &quot;%* Date &amp; time: $now_string\n&quot;;
+ print OUT &quot;%* -----------------------------------------------\n&quot;;
+ #
+ print LOG &quot;----\n&quot;;
+ print LOG &quot;$now_string\n&quot;;
+ print LOG &quot;mathspic (Perl version $version_number)\n&quot;;
+ print LOG &quot;Copyright (c) 2005 A Syropoulos &amp; RWD Nickalls \n&quot;;
+ print LOG &quot;Input file = $source_file\n&quot;;
+ print LOG &quot;Output file = $out_file\n&quot;;
+ print LOG &quot;Log file = $log_file\n&quot;;
+ print LOG &quot;----\n&quot;;
+ }
+
+</pre><p><a name="NWD21HcNW-N">The subroutine </a><code>get_point</code> parses an individual point name.
+If the next token is also a point name then it returns the point name
+ (but only if the only if
+the point name exists in the PointTable). In all other cases it returns
+the string <code>_undef_</code> to indicate that something is wrong.
+
+<pre><a name="NW21HcNW-1h5ef9-1" href="#NWD21HcNW-N"><dfn>&lt;subroutine <tt>get_point</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub get_point {
+
+ my ($lc) = $_[0];
+ my ($PointName);
+
+ if (s/^([^\W\d_]\d{0,3})\s*//i) { #point name
+ $PointName = $1;
+ if (!exists($PointTable{lc($PointName)})) {
+ PrintErrorMessage(&quot;Undefined point $PointName&quot;,$lc);
+ return &quot;_undef_&quot;;
+ }
+ else {
+ return lc($PointName);
+ }
+ }
+ else {
+ PrintErrorMessage(&quot;Point name expected&quot;,$lc);
+ return &quot;_undef_&quot;;
+ }
+ }
+
+</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>&lt;subroutine <tt>perpendicular</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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) &lt; 0.0000001;
+ $deltay = $yA - $yB;
+ return ($xP, $yA) if abs($deltay) &lt; 0.0000001;
+ $m1 = $deltay / $deltax;
+ eval { $m2 = (-1) / $m1;};
+ PrintFatalError(&quot;Division by zero&quot;,$lc) if $@;
+ $c1 = $yA - $m1 * $xA;
+ $c2 = $yP - $m2 * $xP;
+ eval { $factor = 1 / ($m1 - $m2)};
+ PrintFatalError(&quot;Division by zero&quot;,$lc) if $@;
+ return (($c2 - $c1) * $factor, ($m1 * $c2 - $m2 * $c1) * $factor);
+ }
+
+</pre><p> <a name="NWD21HcNW-P">The subroutine </a><code>Length</code> computes the distance between two points A and B.
+Notice, that the name of the subroutine starts with a capital L, just
+to avoid conflict with the predefined Perl function. The subroutine
+requires four parameters which are the coordinates of the two points.
+
+<pre><a name="NW21HcNW-4XEuZg-1" href="#NWD21HcNW-P"><dfn>&lt;subroutine <tt>Length</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub Length {
+ my ($xA, $yA, $xB, $yB)=@_;
+ return sqrt(($xB - $xA)**2 + ($yB - $yA)**2);
+ }
+
+</pre><p><a name="NWD21HcNW-Q">The subroutine </a><code>triangleArea</code> computes the area of a triangle by using
+Heron's formula, i.e., given a triangle ABC, we first compute
+s=(AB+BC+CA)/2 and then the area of the triangle is equal to the
+square root of s times (s-AB) times (s-BC) times (s-BA), where AB, BC, and CA
+are the lengths of the three sides of the triangle. The subroutine accepts 6
+parameters, which correspond to the coordinates of three points that define
+the triangle.
+
+<pre><a name="NW21HcNW-4DwBs6-1" href="#NWD21HcNW-Q"><dfn>&lt;subroutine <tt>triangleArea</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub triangleArea {
+ my ($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 - $lenCA));
+ }
+
+</pre><p><a name="NWD21HcNW-R">The subroutine </a><code>poinOnLine</code> accepts five arguments: the coordinates of two
+points and the decimal number which corresponds to the distance from the
+first point towards the second one. The way we compute the coordinates of
+the point is fairly simple.
+
+<pre><a name="NW21HcNW-VFnEE-1" href="#NWD21HcNW-R"><dfn>&lt;subroutine <tt>pointOnLine</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub pointOnLine {
+ my ($xA, $yA, $xB, $yB, $dist)=@_;
+ my ($deltax, $deltay, $xPol, $yPol);
+
+ $deltax = $xB - $xA;
+ $deltay = $yB - $yA;
+ $xPol = $xA + ($dist * $deltax / &amp;Length($xA,$yA,$xB,$yB));
+ $yPol = $yA + ($dist * $deltay / &amp;Length($xA,$yA,$xB,$yB));
+ return ($xPol, $yPol);
+ }
+
+
+</pre><p>As we have mentioned above the subroutine <code>circumCircleCenter</code> takes six
+arguments that correspond to the coordinates of three points that
+define a triangle. The subroutine computes the coordinates of
+the center of a circle that passes through these three points, and the radius of
+the circle. We now describe how the subroutine computes the center
+of the circle and its radius. Let the triangle points be <code>t1</code>, <code>t2</code>
+and <code>t3</code>. We use the two pairs of points to define two sides,
+i.e., <code>t1t2</code> and <code>t2t3</code>. For each
+<a name="NWD21HcNW-S">side we locate the midpoints and get the their coordinates. We check</a>
+whether either of these two lines is either vertical or horizontal. If this
+is true, we know that one of the coordinates of the center of the circumcircle
+is the same as that of the midpoints of the horizontal or vertical line.
+Next, we determine the slopes of the lines <code>t1t2</code> and <code>t2t3</code>.
+We now determine the slope of lines at right-angles to these lines. We solve the
+resulting equations and obtain the center of the circumcircle. Now we get the
+radius, and then we are done.
+
+<pre><a name="NW21HcNW-lKNKf-1" href="#NWD21HcNW-S"><dfn>&lt;subroutine <tt>circumCircleCenter</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+
+ sub circumCircleCenter {
+ my ($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, $yC)) &lt; 0.0000001)
+ {
+ PrintErrorMessage(&quot;Area of triangle is zero!&quot;,$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) &lt; 0.0000001)
+ {
+ $xcc = $xs12;
+ if (abs($deltax23) &lt; 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) &lt; 0.0000001)
+ {
+ $ycc = $ys12;
+ if (abs($deltay23) &lt; 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) &lt; 0.0000001)
+ {
+ $xcc = $xs23;
+ if (abs($deltax12) &lt; 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) &lt; 0.0000001)
+ {
+ $ycc = $ys23;
+ if (abs($deltay12) &lt; 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);
+ }
+ #
+ $sideA = &amp;Length($xA,$yA,$xB,$yB);
+ $sideB = &amp;Length($xB,$yB,$xC,$yC);
+ $sideC = &amp;Length($xC,$yC,$xA,$yA);
+ $a = triangleArea($xA, $yA, $xB, $yB, $xC, $yC);
+ $radius = ($sideA * $sideB * $sideC) / (4 * $a);
+ #
+ return ($xcc, $ycc, $radius);
+ }
+
+</pre><p>The subroutine <code>ComputeDist</code> is used to compute a distance that is
+specified by either a float number, a pair of points, or a variable
+name. In case we have a pair of identifiers, we check whether the first
+one is a point. If it isn't a point we assume we have a variable followed
+by a keyword. Otherwise, i.e., if it is a point name, we check whether
+the second identifier is also a point name. If it is, we simply return
+the distance between them, otherwise we issue an error message.
+<a name="NWD21HcNW-T">If we have only a single identifier, we check whether it is a</a>
+variable that has already been defined, and if so we return its value.
+ Since, this
+subroutine is heavily used, it actually returns a pair of numbers:
+the first one being the computed distance and the second one being an
+error indicator. If the value of this indicator is 0, then there is no
+error. If its value is 1, then there is an error. Moreover, in case there
+is an error the distance is assumed to be equal to zero.
+
+<pre><a name="NW21HcNW-3GSnCT-1" href="#NWD21HcNW-T"><dfn>&lt;subroutine <tt>ComputeDist</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub ComputeDist {
+ my ($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(&quot;Point $v1 has not been defined&quot;, $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(&quot;Point $v2 has not been defined&quot;, $lc);
+ return (0,0);
+ }
+ $v2 = lc($v2);
+ my ($x1,$y1,$pSV1,$pS1) = unpack(&quot;d3A*&quot;,$PointTable{$v1});
+ my ($x2,$y2,$pSV2,$pS2) = unpack(&quot;d3A*&quot;,$PointTable{$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(&quot;Variable $v1 has not been defined&quot;, $lc);
+ return (0,0);
+ }
+ return ($VarTable{lc($v1)}, 1);
+ }
+ else
+ {
+ PrintErrorMessage(&quot;Unexpected token&quot;, $lc);
+ return (0,0);
+ }
+ }
+
+</pre><p><a name="NWD21HcNW-U">The subroutine </a><code>intersection4points</code> has 8 parameters that correspond to the
+coordinates of four points that uniquely determine two lines, and computes the
+the point of intersection of these two lines.
+
+<pre><a name="NW21HcNW-106ivL-1" href="#NWD21HcNW-U"><dfn>&lt;subroutine <tt>intersection4points</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub intersection4points {
+ my ($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) &lt; 0.0000001)
+ {
+ $ycc = $y1;
+ if (abs($deltax34) &lt; 0.0000001)
+ {
+ $xcc = $x3;
+ last I4PXYLINE;
+ }
+ else
+ {
+ $m34 = $deltay34 / $deltax34;
+ $c34 = $y3 - $m34 * $x3;
+ $xcc = ($ycc - $c34) / $m34;
+ last I4PXYLINE;
+ }
+ }
+ if (abs($deltax12) &lt; 0.0000001)
+ {
+ $xcc = $x1;
+ if (abs($deltay34) &lt; 0.0000001)
+ {
+ $ycc = $y3;
+ last I4PXYLINE;
+ }
+ else
+ {
+ $m34 = $deltay34 / $deltax34;
+ $c34 = $y3 - $m34 * $x3;
+ $ycc = $m34 * $xcc + $c34;
+ last I4PXYLINE;
+ }
+ }
+ if (abs($deltay34) &lt; 0.0000001)
+ {
+ $ycc = $y3;
+ if (abs($deltax12) &lt; 0.0000001)
+ {
+ $xcc = $x1;
+ last I4PXYLINE;
+ }
+ else
+ {
+ $m12 = $deltay12 / $deltax12;
+ $c12 = $y1 - $m12 * $x1;
+ $xcc = ($ycc - $c12) / $m12;
+ last I4PXYLINE;
+ }
+ }
+ if (abs($deltax34) &lt; 0.0000001)
+ {
+ $xcc = $x3;
+ if (abs($deltay12) &lt; 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, $ycc);
+ }
+
+</pre><p>The subroutine <code>IncircleCenter</code> computes the center and the
+radius of the circle that is inside a triangle and touches the sides of
+the triangle. The subroutine has six arguments that correspond to the
+coordinates of three points that uniquely determine the triangle. Here are
+the details:
+<ul>
+<li> Let the triangle points be A, B, C and sides a, b, c, where side B
+is opposite angle B, etc. </li>
+<li> Use angles A and B only.</li>
+<li> Let the bisector of angle A meet side a in point A1, and let the
+distance of A1 from B be designated BA1</li>
+<li> Using the sine rule, one gets: BA1/c = a/(b+c), that is
+BA1 = c * a/(b+c).</li>
+<li> Now do the same for side b, and determine equivalent point B1.
+<a name="NWD21HcNW-V">CB1/a = b/(b+c), that is CB1 = a * b/(b+c).</a></li>
+<li> We can now find the intersection of the line from point A to point A1,
+and the line from point B to point B1. We have four points, so we use the
+mathspic internal <code>intersection4points</code> subroutine to return the
+coordinates of the intersection X<sub>i</sub>, Y<sub>i</sub>.</li>
+<li> Now get the radius: R=(area of triangle)/(a+b+c)/2</li>
+<li>Finally, return the radius and the coordinates of the center.
+</ul>
+
+<pre><a name="NW21HcNW-Kxdzt-1" href="#NWD21HcNW-V"><dfn>&lt;subroutine <tt>IncircleCenter</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub IncircleCenter {
+ my ($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, $ycenter) = &amp;intersection4points($Ax, $Ay, $xA1, $yA1,
+ $Bx, $By, $xB1, $yB1);
+ # get radius
+ $a = &amp;triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy);
+ $s = ($sideA + $sideB +$sideC) / 2;
+ $r = $a / $s;
+ return ($xcenter, $ycenter, $r);
+ }
+
+</pre><p><a name="NWD21HcNW-W">The subroutine </a><code>Angle</code> takes six arguments which correspond to the
+coordinates of three points that define an angle. The subroutine computes
+the opening of the angle in degrees. In case there is an error it returns
+the number -500. ****EXPLAIN THE ALGORITHM****
+
+<pre><a name="NW21HcNW-3xteda-1" href="#NWD21HcNW-W"><dfn>&lt;subroutine <tt>Angle</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub Angle {
+ my ($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 &lt; 0.0000001)
+ {
+ return -500;
+ }
+ $deltax = $RBx - $RCx;
+ $deltay = $RBy - $RCy;
+ $lineBC = sqrt($deltax*$deltax + $deltay*$deltay);
+ if ($lineBC &lt; 0.0000001)
+ {
+ return -500;
+ }
+ $deltax = $RAx - $RCx;
+ $deltay = $RAy - $RCy;
+ $lineAC = sqrt($deltax*$deltax + $deltay*$deltay);
+ if ($lineAC &lt; 0.0000001)
+ {
+ return -500;
+ }
+ $k = ($lineBA*$lineBA + $lineBC*$lineBC - $lineAC*$lineAC ) /
+ (2 * $lineBA * $lineBC);
+ $k = -1 if $k &lt; -0.99999;
+ $k = 1 if $k &gt; 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 $angle * 180 / PI;
+ }
+
+</pre><p>The subroutine <code>excircle</code> computes the center and the radius of a circle that
+externally touches a given side (4th and 5th arguments) of triangle (determined
+by the 1rst, the 2nd and 3rd argument). Here are the details:
+<ul>
+<li> Let the triangle points be A, B, C, and the given side be BC.</li>
+<li> Now calculate the radius of Excircle = (triangle area)/(s - side length),
+where s = (a+b+c)/2</li>
+<li><a name="NWD21HcNW-X">Calculate the distance from the angle (A) (opposite the given side BC)</a>
+ to the excircle center = radius/sin(A/2)</li>
+<li> Now determine the the Excircle center by locating it on the angle bisector
+(i.e., same line that the IncircleCenter is on), but at distance d further
+away from angle A. So, we now have the Incircle center (I),
+ determine deltaX and deltaY from I to A, calculate the distance AI,
+ and then extend the line from I by distance d to Excenter Xc, Yc.</li>
+</ul>
+
+<pre><a name="NW21HcNW-cchrT-1" href="#NWD21HcNW-X"><dfn>&lt;subroutine <tt>excircle</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub excircle {
+ my ($A, $B, $C, $D, $E) = @_;
+ my ($Ax,$Ay,$Bx,$By,$Dx,$Dy,$Ex,$Ey,$ASVA,$ASA);
+ ($Ax,$Ay,$ASVA,$ASA)=unpack(&quot;d3A*&quot;,$PointTable{$A});
+ ($Bx,$By,$ASVA,$ASA)=unpack(&quot;d3A*&quot;,$PointTable{$B});
+ ($Cx,$Cy,$ASVA,$ASA)=unpack(&quot;d3A*&quot;,$PointTable{$C});
+ ($Dx,$Dy,$ASVA,$ASA)=unpack(&quot;d3A*&quot;,$PointTable{$D});
+ ($Ex,$Ey,$ASVA,$ASA)=unpack(&quot;d3A*&quot;,$PointTable{$E});
+ my ($sideA, $sideB, $sideC, $s, $R, $theAdeg, $d);
+ my ($Xmypoint, $Ymypoint, $deltax, $deltay, $mylength, $xc, $yc);
+
+ $sideA = &amp;Length($Bx, $By, $Cx, $Cy);
+ $sideB = &amp;Length($Cx, $Cy, $Ax, $Ay);
+ $sideC = &amp;Length($Ax, $Ay, $Bx, $By);
+ $s = ($sideA + $sideB + $sideC) / 2;
+ $R = triangleArea($Ax, $Ay, $Bx, $By, $Cx, $Cy) /
+ ($s - &amp;Length($Dx, $Dy, $Ex, $Ey));
+ if (($D eq $A &amp;&amp; $E eq $B) || ($D eq $B &amp;&amp; $E eq $A))
+ {
+ $theAdeg = &amp;Angle($Bx, $By, $Cx, $Cy, $Ax, $Ay);
+ $Xmypoint = $Cx;
+ $Ymypoint = $Cy;
+ }
+ elsif (($D eq $B &amp;&amp; $E eq $C) || ($D eq $C &amp;&amp; $E eq $B))
+ {
+ $theAdeg = &amp;Angle($Cx, $Cy, $Ax, $Ay, $Bx, $By);
+ $Xmypoint = $Ax;
+ $Ymypoint = $Ay;
+ }
+ elsif (($D eq $C &amp;&amp; $E eq $A) || ($D eq $A &amp;&amp; $E eq $C))
+ {
+ $theAdeg = &amp;Angle($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, $rin) = &amp;IncircleCenter($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>&lt;subroutine <tt>DrawLineOrArrow</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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 ($lineLength &lt;= 0) {
+# PrintErrorMessage(&quot;length must greater than zero&quot;,$lc);
+# $lineLength = -1;
+# }
+# chk_rsb(&quot;optional part&quot;,$lc);
+# }
+# }
+ chk_lparen(&quot;$cmd&quot;,$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(&quot;Undefined point $P&quot;,$lc);
+ }
+ else {
+ push (@PP,$P);
+ }
+ }
+ else {
+ $stacklen = @PP;
+ if ($draw_Line != 2) {
+ if ($stacklen &lt;= 1) {
+ PrintErrorMessage(&quot;Wrong number of points&quot;,$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 &lt; 2) {
+ PrintErrorMessage(&quot;Wrong number of points&quot;,$lc);
+ }
+ elsif ($stacklen % 2 == 0) {
+ PrintErrorMessage(&quot;Number of points must be odd&quot;,$lc);
+ }
+ else {
+ drawCurve(@PP);
+ }
+ }
+ chk_rparen(&quot;arguments of $cmd&quot;,$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>$arrowAngleC</code> * <code>d2r</code> / 2).
+
+<pre><a name="NW21HcNW-4STZZz-1" href="#NWD21HcNW-Z"><dfn>&lt;subroutine <tt>drawarrows</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub drawarrows {
+ my ($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 &lt; $NumberOfPoints - 1; $i++)
+ {
+ $p = $_[$i];
+ $q = $_[$i+1];
+ ($px,$py,$pSV,$pS) = unpack(&quot;d3A*&quot;,$PointTable{lc($p)});
+ ($qx,$qy,$qSV,$qS) = unpack(&quot;d3A*&quot;,$PointTable{lc($q)});
+ $pSV = $defaultLFradius if $pSV == 0;
+ $qSV = $defaultLFradius if $qSV == 0;
+ $r12 = $pSV + $qSV;
+ $d12 = Length($px,$py,$qx,$qy);
+ if ($d12 &lt;= $r12)
+ {
+ if($d12 == 0)
+ {
+ PrintErrorMessage(&quot;points $p and $q are the same&quot;, $lc);
+ next LOOP;
+ }
+ PrintWarningMessage(&quot;arrow $p$q not drawn: points too close or &quot;.
+ &quot;radii too big&quot;, $lc);
+ next LOOP;
+ }
+ ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV &gt; 0;
+ ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV &gt; 0;
+ my ($beta, $gamma);
+ $beta = tan($arrowAngleB * D2R / 2);
+ $gamma = 2 * tan($arrowAngleC * D2R / 2);
+ printf OUT &quot;\\arrow &lt;%.5f%s&gt; [%.5f,%.5f] from %.5f %.5f to %.5f %.5f\n&quot;,
+ $arrowLength, $arrowLengthUnits, $beta, $gamma, $px, $py, $qx, $qy;
+ }
+ }
+
+</pre><p>The subroutine <code>drawlines</code> is used to draw one or more lines. The subroutine
+accepts as argument an array which contains the names of the points which
+define the lines, plus the current program line number. If there are only
+two points (i.e., only one line), then we output the following PiCTeX code:
+<center>
+<tt> \plot x1 y1 x2 y2 / %% pointname1 pointname2</tt>
+</center>
+If there are more than two points, then we need to write the PiCTeX code in
+pairs with two points on each line (just to keep things simple) as follows:
+<center>
+<tt> \plot x1 y1 x2 y2 / %% pointname1 pointname2</tt>
+<tt> \plot x2 y2 x3 y3 / %% pointname2 pointname3</tt>
+<tt> \plot x3 y3 x4 y4 / %% pointname3 pointname4</tt>
+</center>
+<a name="NWD21HcNW-a">An important part of the subroutine is devoted to checking whether either</a>
+or both of the pairs of points are associated with a line-free zone, and if
+so, then we must take care not to draw the line inside the line-free zone. If
+a point does have a line-free zone, then we use the <code>pointOnLine</code>
+subroutine to determine the point on the line which is just on the line-free
+boundary, and draw the line to the that point instead of to the exact
+point-location.
+
+<pre><a name="NW21HcNW-3KtTfB-1" href="#NWD21HcNW-a"><dfn>&lt;subroutine <tt>drawlines</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub drawlines {
+ my ($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 &lt; $NumberOfPoints - 1; $i++)
+ {
+ $p = $_[$i];
+ $q = $_[$i+1];
+ ($px,$py,$pSV,$pS) = unpack(&quot;d3A*&quot;,$PointTable{lc($p)});
+ ($qx,$qy,$qSV,$qS) = unpack(&quot;d3A*&quot;,$PointTable{lc($q)});
+ $pSV = $defaultLFradius if $pSV == 0;
+ $qSV = $defaultLFradius if $qSV == 0;
+ $r12 = $pSV + $qSV;
+ $d12 = Length($px,$py,$qx,$qy);
+ if ($d12 &lt;= $r12)
+ {
+ if($d12 == 0)
+ {
+ PrintErrorMessage(&quot;points $p and $q are the same&quot;, $lc);
+ next LOOP;
+ }
+ PrintWarningMessage(&quot;line $p$q not drawn: points too close or &quot;.
+ &quot;radii too big&quot;, $lc);
+ next LOOP;
+ }
+ ($px, $py) = pointOnLine($px, $py, $qx, $qy, $pSV) if $pSV &gt; 0;
+ ($qx, $qy) = pointOnLine($qx, $qy, $px, $py, $qSV) if $qSV &gt; 0;
+ if ($px == $qx || $py == $qy)
+ {
+ printf OUT &quot;\\putrule from %.5f %.5f to %.5f %.5f %%%% %s%s\n&quot;,
+ $px,$py,$qx,$qy,$p,$q;
+ }
+ else
+ {
+ printf OUT &quot;\\plot %.5f %.5f\t%.5f %.5f / %%%% %s%s\n&quot;,
+ $px, $py,$qx,$qy,$p,$q;
+ }
+ }
+ }
+
+</pre><p>The subroutine <code>drawCurve</code> is used to draw a curve that passes through an odd
+number of points. The subroutine has as argument an array which contains the names of the
+points which define the lines plus the current program line number. The subroutine
+emits code that has the following general form:
+<pre>
+ <a name="NWD21HcNW-b">\setquadratic</a>
+ \plot
+ X1 Y1
+ X2 Y2
+ X3 Y3
+ \setlinear
+</pre>
+
+
+<pre><a name="NW21HcNW-3c2Tgd-1" href="#NWD21HcNW-b"><dfn>&lt;subroutine <tt>drawCurve</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub drawCurve {
+ my ($NoArgs);
+ $NoArgs = @_;
+ my ($lc) = $_[$NoArgs-1]; #line number is the last argument
+ my ($NumberOfPoints, $p);
+
+ $NumberOfPoints = $NoArgs - 1;
+ print OUT &quot;\\setquadratic\n\\plot\n&quot;;
+ for(my $i=0; $i &lt;= $NumberOfPoints; $i++)
+ {
+ $p = $_[$i];
+ my ($px,$py,$pSV,$pS) = unpack(&quot;d3A*&quot;,$PointTable{lc($p)});
+ printf OUT &quot;\t%0.5f %0.5f&quot;, $px, $py;
+ print OUT (($i == $NumberOfPoints) ? &quot; / %$p\n&quot; : &quot; %$p\n&quot;);
+ }
+ print OUT &quot;\\setlinear\n&quot;;
+ }
+
+</pre><p>The subroutine <code>drawpoints</code> is used to draw one or more points. The subroutine
+<a name="NWD21HcNW-c">has as arguments a list of points. For each point we produce code that has</a>
+the following general form:
+<center>
+<tt> \put {SYMBOL} at Px PY</tt>
+</center>
+where <code>SYMBOL</code> is either the default plot symbol, i.e., <code>$\bullet$</code>,
+whatever the user has set with the <code>PointSymbol</code> command, or the plot
+symbol specified in the definition of the point.
+
+<pre><a name="NW21HcNW-1NgToL-1" href="#NWD21HcNW-c"><dfn>&lt;subroutine <tt>drawpoints</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub drawpoints {
+ my ($NumberOfPoints,$p);
+ $NumberOfPoints = @_;
+ my ($px,$py,$pSV,$pS);
+
+ for($i=0; $i &lt; $NumberOfPoints; $i++)
+ {
+ $p = $_[$i];
+ ($px,$py,$pSV,$pS) = unpack(&quot;d3A*&quot;,$PointTable{lc($p)});
+ if ($pS eq &quot;&quot; and $defaultsymbol =~ /circle|square/) {
+ $pS = $defaultsymbol;
+ }
+ POINTSWITCH: {
+ if ($pS eq &quot;&quot;) # no plot symbol specified
+ {
+ printf OUT &quot;\\put {%s} at %.5f %.5f %%%% %s\n&quot;,
+ $defaultsymbol, $px, $py, $p;
+ last POINTSWITCH;
+ }
+ if ($pS eq &quot;circle&quot;) # plot symbol is a circle
+ {
+ my $radius = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} :
+ $GlobalDimOfPoints;
+ if ($radius &gt; 0) # draw a circle using the current units
+ {
+ if ($radius == 1.5) # use \bigcirc
+ {
+ printf OUT &quot;\\put {\$\\bigcirc\$} at %.5f %.5f %%%% %s\n&quot;,
+ $px, $py, $p;
+ }
+ else
+ {
+ printf OUT &quot;\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f %%%% %s\n&quot;,
+ $px+$radius, $py, $px, $py, $p;
+ }
+ }
+ else #use \circ symbol
+ {
+ printf OUT &quot;\\put {\$\\circ\$} at %.5f %.5f %%%% %s\n&quot;,
+ $px,$py,$p;
+ }
+ last POINTSWITCH;
+ }
+ if ($pS eq &quot;square&quot;)
+ {
+ my $side = (defined($DimOfPoint{lc($p)})) ? $DimOfPoint{lc($p)} :
+ $GlobalDimOfPoints;
+ printf OUT &quot;\\put {%s} at %.5f %.5f %%%% %s\n&quot;,
+ drawsquare($side), $px, $py, $p;
+ last POINTSWITCH;
+ }
+ printf OUT &quot;\\put {%s} at %.5f %.5f %%%% %s\n&quot;, $pS,$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>&lt;subroutine <tt>drawAngleArc</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub drawAngleArc {
+ my ($P1, $P2, $P3, $radius, $inout, $direction) = @_;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$P1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$P2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$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 $code = &quot;&quot;;
+ if ($inout eq &quot;internal&quot; and $direction eq &quot;clockwise&quot; ) {
+ $code = sprintf &quot;\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ -1 * $internalAngle, $x, $y, $x2, $y2;
+ }
+ elsif ($inout eq &quot;internal&quot; and $direction eq &quot;anticlockwise&quot; ) {
+ $code = sprintf &quot;\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ $internalAngle, $x, $y, $x2, $y2;
+ }
+ elsif ($inout eq &quot;external&quot; and $direction eq &quot;clockwise&quot; ) {
+ $code = sprintf &quot;\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ -1 * $externalAngle, $x, $y, $x2, $y2;
+ }
+ elsif ($inout eq &quot;external&quot; and $direction eq &quot;anticlockwise&quot; ) {
+ $code = sprintf &quot;\\circulararc %.5f degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ $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>&lt;subroutine <tt>drawAngleArrow</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub drawAngleArrow {
+ my ($P1, $P2, $P3, $radius, $inout, $direction) = @_;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$P1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$P2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$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) &lt; 0.00001) {
+ if ($deltax &gt; 0 ) {$thetaqr = 0 }
+ elsif ($deltax &lt; 0) {$thetaqr = -180}
+ }
+ else {
+ if (abs($deltax) &lt; 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) &lt; 0.00001) {
+ if ($deltay &gt; 0) { $thetaqr = 90 }
+ elsif ($deltay &lt; 0) { $thetaqr = - 90 }
+ last LINE2;
+ }
+ else {
+ $thetaqr = atan2($deltay / $deltax, 1) * R2D;
+ }
+ if (abs($deltay) &lt; 0.00001) {
+ if ($deltax &gt; 0) { $thetaqr = 0 }
+ elsif ($deltax &lt; 0) { $thetaqr = -180 }
+ last LINE2;
+ }
+ else {
+ $thetaqr = atan2($deltay / $deltax, 1) * R2D;
+ }
+ if ($deltax &lt; 0 and $deltay &gt; 0) { $thetaqr += 180 }
+ elsif ($deltax &lt; 0 and $deltay &lt; 0) { $thetaqr += 180 }
+ elsif ($deltax &gt; 0 and $deltay &lt; 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 &quot;internal&quot; and $direction eq &quot;clockwise&quot;) {
+ $code .= sprintf &quot;\\arrow &lt;1.5mm&gt; [0.5, 1] from %.5f %.5f to %.5f %.5f\n&quot;,
+ $xqrleft, $yqrleft, $xqr, $yqr;
+ }
+ elsif ($inout eq &quot;internal&quot; and $direction eq &quot;anticlockwise&quot;) {
+ $code .= sprintf &quot;\\arrow &lt;1.5mm&gt; [0.5, 1] from %.5f %.5f to %.5f %.5f\n&quot;,
+ $xqrright, $yqrright, $xqr, $yqr;
+ }
+ elsif ($inout eq &quot;external&quot; and $direction eq &quot;clockwise&quot;) {
+ $code .= sprintf &quot;\\arrow &lt;1.5mm&gt; [0.5, 1] from %.5f %.5f to %.5f %.5f\n&quot;,
+ $xqrleft, $yqrleft, $xqr, $yqr;
+ }
+ elsif ($inout eq &quot;external&quot; and $direction eq &quot;anticlockwise&quot;) {
+ $code .= sprintf &quot;\\arrow &lt;1.5mm&gt; [0.5, 1] from %.5f %.5f to %.5f %.5f\n&quot;,
+ $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>&lt;subroutine <tt>expr</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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/^([+-])// &amp;&amp; $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(&quot;Division by zero&quot;, $lc) if $@;
+ }
+ else {
+ eval {$left /= $right};
+ PrintFatalError(&quot;Division by zero&quot;, $lc) if $@;
+ }
+ }
+ return $left;
+}
+
+sub mulop {
+ (s#^([*/])## || s/^(rem)//i) &amp;&amp; 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(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^-//) { # is it a negated primitive
+ $val = - primitive();
+ }
+ elsif (s/^\+//) { # is it a positive primitive
+ $val = primitive();
+ }
+ elsif (s/^angledeg//i) {
+ chk_lparen(&quot;angledeg&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $point_3 = get_point($lc);
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point_3});
+ my $d12 = Length($x1, $y1, $x2, $y2);
+ my $d23 = Length($x2, $y2, $x3, $y3);
+ my $d31 = Length($x3, $y3, $x1, $y1);
+ if ( $d12 == 0 ) {
+ PrintErrorMessage(&quot;points `$point_1' and `$point_2' are the same&quot;, $lc);
+ $val = 0;
+ }
+ elsif ( $d23 == 0 ) {
+ PrintErrorMessage(&quot;points `$point_2' and `$point_3' are the same&quot;, $lc);
+ $val = 0;
+ }
+ elsif ( $d31 == 0 ) {
+ PrintErrorMessage(&quot;points `$point_1' and `$point_3' are the same&quot;, $lc);
+ $val = 0;
+ }
+ else {
+ $val = Angle($x1, $y1, $x2, $y2, $x3, $y3);
+ $val = 0 if $val == -500;
+ }
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^angle//i) {
+ chk_lparen(&quot;angle&quot;.$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $point_3 = get_point($lc);
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point_3});
+ my $d12 = Length($x1, $y1, $x2, $y2);
+ my $d23 = Length($x2, $y2, $x3, $y3);
+ my $d31 = Length($x3, $y3, $x1, $y1);
+ if ( $d12 == 0 ) {
+ PrintErrorMessage(&quot;points `$point_1' and `$point_2' are the same&quot;, $lc);
+ $val = 0;
+ }
+ elsif ( $d23 == 0 ) {
+ PrintErrorMessage(&quot;points `$point_2' and `$point_3' are the same&quot;, $lc);
+ $val = 0;
+ }
+ elsif ( $d31 == 0 ) {
+ PrintErrorMessage(&quot;points `$point_1' and `$point_3' are the same&quot;, $lc);
+ $val = 0;
+ }
+ else {
+ $val = Angle($x1, $y1, $x2, $y2, $x3, $y3);
+ if ($val == -500) {
+ $val = 0;
+ }
+ else {
+ $val = D2R * $val;
+ }
+ }
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^area//i) {
+ chk_lparen(&quot;angledeg&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $point_3 = get_point($lc);
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point_3});
+ $val = triangleArea($x1, $y1, $x2, $y2, $x3, $y3);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^asin//i) {
+ chk_lparen(&quot;asin&quot;);
+ $val = expr();
+ PrintFatalError(&quot;Can't take asin of $val&quot;, $lc) if $val &lt; -1 || $val &gt; 1;
+ $val = asin($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^acos//i) {
+ chk_lparen(&quot;acos&quot;);
+ $val = expr();
+ PrintFatalError(&quot;Can't take acos of $val&quot;, $lc) if $val &lt; -1 || $val &gt; 1 ;
+ $val = acos($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^atan//i) {
+ chk_lparen(&quot;atan&quot;);
+ $val = expr();
+ $val = atan($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^cos//i) {
+ chk_lparen(&quot;cos&quot;);
+ $val = expr();
+ $val = cos($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^directiondeg//i) {
+ chk_lparen(&quot;directiondeg&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $x3 = $x1+1;
+ if ( ($y2 - $y1) &gt;= 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(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^direction//i) {
+ chk_lparen(&quot;direction&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $x3 = $x1+1;
+ if ( ($y2 - $y1) &gt;= 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(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^exp//i) {
+ chk_lparen(&quot;exp&quot;);
+ $val = expr();
+ $val = exp($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^int//i) {
+ chk_lparen(&quot;int&quot;);
+ $val = expr();
+ $val = int($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^log//i) {
+ chk_lparen(&quot;log&quot;);
+ $val = expr();
+ PrintFatalError(&quot;Can't take log of $val&quot;, $lc) if $val &lt;= 0;
+ $val = log($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^sin//i) {
+ chk_lparen(&quot;sin&quot;);
+ $val = expr();
+ $val = sin($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^sgn//i) {
+ chk_lparen(&quot;sgn&quot;);
+ $val = expr();
+ if ($val &gt; 0) {
+ $val = 1;
+ }
+ elsif ($val == 0) {
+ $val = 0;
+ }
+ else {
+ $val = -1;
+ }
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^sqrt//i) {
+ chk_lparen(&quot;sqrt&quot;);
+ $val = expr();
+ $val = sqrt($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^tan//i) {
+ chk_lparen(&quot;tan&quot;);
+ $val = expr();
+ $val = sin($val)/cos($val);
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^xcoord//i) {
+ chk_lparen(&quot;xcoord&quot;);
+ my $point_name = get_point;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_name});
+ $val = $x1;
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+ }
+ elsif (s/^ycoord//i) {
+ chk_lparen(&quot;ycoord&quot;);
+ my $point_name = get_point;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_name});
+ $val = $y1;
+ chk_rparen(&quot;Missing right parenthesis&quot;, $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>&lt;subroutine <tt>memberOf</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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>&lt;subroutine <tt>tand</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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>&quot;</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>&lt;subroutine <tt>get_string</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub get_string {
+ my $string = shift;
+ my $lc = shift;
+
+ $string =~ s/^\s+//;
+ if ($string !~ s/^\&quot;//) {
+ PrintErrorMessage(&quot;No starting \&quot; found&quot;,$lc);
+ return (1,$string,$string);
+ }
+ my @ch = split //,$string;
+ my @cmd;
+ while (@ch and $ch[0] ne &quot;\&quot;&quot;) {
+ if ($ch[0] eq &quot;\\&quot; and (defined $ch[1]) and $ch[1] eq &quot;\&quot;&quot;) {
+ shift @ch;
+ push @cmd, $ch[0];
+ shift @ch;
+ }
+ else {
+ push @cmd, $ch[0];
+ shift @ch;
+ }
+ }
+ if (! defined $ch[0]) {
+ PrintErrorMessage(&quot;No closing \&quot; found&quot;,$lc);
+ return (1,join(&quot;&quot;,@cmd), join(&quot;&quot;,@ch))
+ }
+ else {
+ shift @ch;
+ return (0, join(&quot;&quot;,@cmd), join(&quot;&quot;,@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>&lt;subroutine <tt>is_tainted</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub is_tainted {
+ my $arg = shift;
+ my $nada = substr($arg,0,0);
+ local $@;
+ eval { eval &quot;# $nada&quot;};
+ return length($@) != 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>&lt;subroutine <tt>noOfDigits</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-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>&lt;subroutine <tt>drawsquare</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub drawsquare {
+ my $s = $_[0];
+ #$s *= sqrt(2);
+ $s = sprintf &quot;%.5f&quot;, $s;
+ my $code = &quot;\\setlength{\\unitlength}{$xunits}%\n&quot;;
+ $code .= &quot;\\begin{picture}($s,$s)\\put(0,0)&quot; .
+ &quot;{\\framebox($s,$s){}}\\end{picture}&quot;;
+ 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>&lt;subroutine <tt>X2sp</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub X2sp {
+ my $LT = shift;
+ my $units = shift;
+
+ if ($units eq &quot;pc&quot;) {
+ return $LT * 786432;
+ }
+ elsif ($units eq &quot;pt&quot;) {
+ return $LT * 65536;
+ }
+ elsif ($units eq &quot;in&quot;) {
+ return $LT * 4736286.72;
+ }
+ elsif ($units eq &quot;bp&quot;) {
+ return $LT * 65781.76;
+ }
+ elsif ($units eq &quot;cm&quot;) {
+ return $LT * 1864679.811023622;
+ }
+ elsif ($units eq &quot;mm&quot;) {
+ return $LT * 186467.981102362;
+ }
+ elsif ($units eq &quot;dd&quot;) {
+ return $LT * 70124.086430424;
+ }
+ elsif ($units eq &quot;cc&quot;) {
+ return $LT * 841489.037165082;
+ }
+ elsif ($units eq &quot;sp&quot;) {
+ 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>&lt;subroutine <tt>sp2X</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub sp2X {
+ my $LT = shift;
+ my $units = shift;
+
+ if ($units eq &quot;pc&quot;) {
+ return $LT / 786432;
+ }
+ elsif ($units eq &quot;pt&quot;) {
+ return $LT / 65536;
+ }
+ elsif ($units eq &quot;in&quot;) {
+ return $LT / 4736286.72;
+ }
+ elsif ($units eq &quot;bp&quot;) {
+ return $LT / 65781.76;
+ }
+ elsif ($units eq &quot;cm&quot;) {
+ return $LT / 1864679.811023622;
+ }
+ elsif ($units eq &quot;mm&quot;) {
+ return $LT / 186467.981102362;
+ }
+ elsif ($units eq &quot;dd&quot;) {
+ return $LT / 70124.086430424;
+ }
+ elsif ($units eq &quot;cc&quot;) {
+ return $LT / 841489.037165082;
+ }
+ elsif ($units eq &quot;sp&quot;) {
+ 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>&lt;subroutine <tt>setLineThickness</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+sub setLineThickness {
+ my $Xunits = shift;
+ my $LT = shift;
+ $Xunits =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//;
+ my $xlength = &quot;$1&quot;;
+ $Xunits =~ s/^\s*($units)//;
+ my $x_in_units = $1;
+ $LT =~ s/^((\+|-)?\d+(\.\d+)?([eE](\+|-)?\d+)?)//;
+ my $LTlength = &quot;$1&quot;;
+ $LT =~ s/^\s*($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>$no_output</code> to 1,
+print a comment to the output file and continue with the next input line.
+If the first token is <code>endSkip</code>, we check whether we are in a no-process
+mode. If this is the case, we revert to process mode; otherwise we print
+an error message. Finally, depending on whether we are in process or no-process
+mode we process the input text or simply printed commented out to the output
+file. Note, that we don't allow nested comment blocks, as this makes really
+no sense!
+
+<pre><a name="NW21HcNW-1RrLPF-1" href="#NWD21HcNW-p"><dfn>&lt;subroutine <tt>process_input</tt> &gt;=</dfn></a> <b>(<a href="#NWD21HcNW-9">&lt;-U</a>)</b>
+ sub process_input {
+ my ($INFILE,$currInFile) = @_;
+ my $lc = 0;
+ my $no_output = 0;
+ $curr_in_file = $currInFile;
+ LINE: while(&lt;$INFILE&gt;) {
+ $lc++;
+ chomp($command = $_);
+ s/^\s+//;
+ if (/^beginSkip\s*/i) {
+ $no_output = 1;
+ print OUT &quot;%%$_&quot; if $comments_on;
+ next LINE;
+ }
+ elsif (/^endSkip\s*/i) {
+ if ($no_output == 0) {
+ PrintErrorMessage(&quot;endSkip without beginSkip&quot;,$lc);
+ }
+ else {
+ $no_output = 0;
+ }
+ print OUT &quot;%%$_&quot; 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
+ $_ = &quot;$out_line\n&quot;;
+ }
+ <a name="NW21HcNW-1RrLPF-1-u1" href="#NWD21HcNW-q"><i>&lt;process input line&gt;</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>&lt;process input line&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-p">&lt;-U</a>)</b>
+
+ if (/^\s*%/)
+ {
+ print OUT &quot;$_&quot; if $comments_on;
+ }
+ elsif (s/^\s*(beginloop(?=\W))//i) {
+ s/\s+//;
+ my $times = expr($lc);
+ print OUT &quot;%% BEGINLOOP $times\n&quot; if $comments_on;
+ my @C = ();
+ REPEATCOMMS: while (&lt;$INFILE&gt;) {
+ if (/^\s*endloop/i) {
+ last REPEATCOMMS;
+ }
+ else {
+ push @C, $_;
+ }
+ }
+ if (! /^\s*endloop/i) {
+ PrintFatalError(&quot;unexpected end of file&quot;,$lc);
+ }
+ else {
+ s/^\s*endloop//i;
+ for(my $i=1; $i&lt;=$times; $i++) {
+ tie *DUMMY, 'DummyFH', \@C;
+ process_input(DUMMY, $currInFile);
+ untie *DUMMY;
+ }
+ print OUT &quot;%% ENDLOOP\n&quot; if $comments_on;
+ }
+ }
+ elsif (s/^\s*(ArrowShape(?=\W))//i)
+ {
+ my $cmd = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u1" href="#NWD21HcNW-1V"><i>&lt;process <tt>ArrowShape</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(const(?=\W))//i)
+ {
+ print OUT &quot;%% $1$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u2" href="#NWD21HcNW-1b"><i>&lt;process <tt>const</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(dasharray(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u3" href="#NWD21HcNW-r"><i>&lt;process <tt>dasharray</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawAngleArc(?=\W))//i or s/^\s*(drawAngleArrow(?=\W))//i )
+ {
+ my $cmd = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u4" href="#NWD21HcNW-s"><i>&lt;process <tt>drawAngleArcOrArrow</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawArrow(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ DrawLineOrArrow(0,$lc);
+ }
+ elsif (s/^\s*(drawcircle(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u5" href="#NWD21HcNW-v"><i>&lt;process <tt>drawcircle</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawcurve(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ DrawLineOrArrow(2,$lc);
+ }
+ elsif (s/^\s*(drawcircumcircle(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u6" href="#NWD21HcNW-w"><i>&lt;process <tt>drawcircumcircle</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawexcircle(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u7" href="#NWD21HcNW-x"><i>&lt;process <tt>drawexcircle</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawincircle(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u8" href="#NWD21HcNW-y"><i>&lt;process <tt>drawincircle</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawline(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ DrawLineOrArrow(1,$lc);
+ }
+ elsif (s/^\s*(drawthickarrow(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ print OUT &quot;\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n&quot;;
+ print OUT &quot;{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n&quot;;
+ print OUT &quot; \\global\\linethickness=0.31\\wd1}%\n&quot;;
+ DrawLineOrArrow(0,$lc);
+ print OUT &quot;\\setlength{\\linethickness}{0.4pt}%\n&quot;;
+ print OUT &quot;\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n&quot;;
+ }
+ elsif (s/^\s*(drawthickline(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ print OUT &quot;\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\large .})%\n&quot;;
+ print OUT &quot;{\\setbox1=\\hbox{\\usefont{OT1}{cmr}{m}{n}\\large .}%\n&quot;;
+ print OUT &quot; \\global\\linethickness=0.31\\wd1}%\n&quot;;
+ DrawLineOrArrow(1,$lc);
+ print OUT &quot;\\setlength{\\linethickness}{0.4pt}%\n&quot;;
+ print OUT &quot;\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n&quot;;
+ }
+ elsif (s/^\s*(drawperpendicular(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u9" href="#NWD21HcNW-z"><i>&lt;process <tt>drawPerpendicular</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawpoint(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u10" href="#NWD21HcNW-10"><i>&lt;process <tt>drawpoint</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawRightAngle(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u11" href="#NWD21HcNW-11"><i>&lt;process <tt>drawRightAngle</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(drawsquare(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u12" href="#NWD21HcNW-12"><i>&lt;process <tt>drawsquare</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*inputfile\*//i)
+ {
+ <a name="NW21HcNW-RKDir-1-u13" href="#NWD21HcNW-13"><i>&lt;process <tt>inputfile*</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(inputfile(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u14" href="#NWD21HcNW-14"><i>&lt;process <tt>inputfile</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(linethickness(?=\W))//i)
+ {
+ my $cmd = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u15" href="#NWD21HcNW-15"><i>&lt;process <tt>linethickness</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(paper(?=\W))//i)
+ {
+ my ($cmd) = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u16" href="#NWD21HcNW-16"><i>&lt;process <tt>paper</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(PointSymbol(?=\W))//i)
+ {
+ my $cmd = $1;
+ print OUT &quot;%% $cmd$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u17" href="#NWD21HcNW-1W"><i>&lt;process <tt>PointSymbol</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*point(?=\W)//i)
+ {
+ my ($Point_Line);
+ chomp($Point_Line=$_);
+ <a name="NW21HcNW-RKDir-1-u18" href="#NWD21HcNW-1H"><i>&lt;process <tt>point/point*</tt> commands&gt;</i></a>
+ }
+ elsif (/^\s*setPointNumber(?=\W)/i)
+ {
+ PrintWarningMessage(&quot;Command setPointNumber is ignored&quot;,$lc);
+ next LINE;
+ }
+ elsif (s/^\s*(showAngle(?=\W))//i)
+ {
+ <a name="NW21HcNW-RKDir-1-u19" href="#NWD21HcNW-1A"><i>&lt;process <tt>showAngle</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(showArea(?=\W))//i)
+ {
+ <a name="NW21HcNW-RKDir-1-u20" href="#NWD21HcNW-1B"><i>&lt;process <tt>showArea</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(showLength(?=\W))//i)
+ {
+ <a name="NW21HcNW-RKDir-1-u21" href="#NWD21HcNW-1C"><i>&lt;process <tt>showLength</tt> command&gt;</i></a>
+ }
+ elsif (/^\s*showPoints(?=\W)/i)
+ {
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ print OUT &quot;%% L I S T O F P O I N T S \n&quot;;
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ foreach my $p (keys(%PointTable)) {
+ my ($x, $y, $pSV, $pS) = unpack(&quot;d3A*&quot;,$PointTable{$p});
+ printf OUT &quot;%%%%\t%s\t= ( %.5f, %.5f ), LF-radius = %.5f, symbol = %s\n&quot;,
+ $p, $x, $y, $pSV, $pS;
+ }
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ print OUT &quot;%% E N D O F L I S T O F P O I N T S \n&quot;;
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ next LINE;
+ }
+ elsif (/^\s*showVariables(?=\W)/i)
+ {
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ print OUT &quot;%% L I S T O F V A R I A B L E S \n&quot;;
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ foreach my $var (keys(%VarTable)) {
+ print OUT &quot;%%\t&quot;, $var, &quot;\t=\t&quot;, $VarTable{$var}, &quot;\n&quot;;
+ }
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ print OUT &quot;%% E N D O F L I S T O F V A R I A B L E S \n&quot;;
+ print OUT &quot;%%-------------------------------------------------\n&quot;;
+ next LINE;
+ }
+ elsif (s/^\s*(system(?=\W))//i)
+ {
+ print OUT &quot;%% $1$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u22" href="#NWD21HcNW-1X"><i>&lt;process <tt>system</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(text(?=\W))//i)
+ {
+ print OUT &quot;%% $1$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u23" href="#NWD21HcNW-1Y"><i>&lt;process <tt>text</tt> command&gt;</i></a>
+ }
+ elsif (s/^\s*(var(?=\W))//i)
+ {
+ print OUT &quot;%% $1$_&quot; if $comments_on;
+ <a name="NW21HcNW-RKDir-1-u24" href="#NWD21HcNW-1c"><i>&lt;process <tt>var</tt> command&gt;</i></a>
+ }
+ elsif (/^\s*\\(.+)/)
+ {
+ my $line = $1;
+ if ($line =~ /^\s+(.+)/)
+ {
+ print OUT &quot; $line\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\$line\n&quot;;
+ }
+ next LINE;
+ }
+ elsif (0==length) #empty line
+ {
+ next LINE;
+ }
+ else {
+ PrintErrorMessage(&quot;command not recognized&quot;,$lc);
+ next LINE;
+ }
+
+</pre><p>Command <code>dasharray</code> takes an arbitrary number of arguments that are used to
+specify a dash pattern. Its general syntax follows:
+<center>
+ <tt> "dasharray" "(" d<sub>1</sub> "," g<sub>1</sub> "," d<sub>2</sub> ","
+ g<sub>2</sub> "," ... ")"</tt>
+</center>
+where <tt>d<sub>i</sub></tt> denotes the length of a dash and <tt>g<sub>i</sub></tt>
+<a name="NWD21HcNW-r">denotes the length of gap between two consecutive dashes. Each </a><tt>d<sub>i</sub></tt>
+and <tt>g<sub>i</sub></tt> is a length (i.e., a number accompanied by a length of unit).
+Since we do not a priori know the number of arguments, we push them onto a stack and
+then we produce a command of the form
+<center>
+ <tt> \setdashpattern &lt; d<sub>1</sub>, g<sub>1</sub>, d<sub>2</sub>,
+ g<sub>2</sub>, ...&gt;</tt>
+</center>
+
+<pre><a name="NW21HcNW-19jqyn-1" href="#NWD21HcNW-r"><dfn>&lt;process <tt>dasharray</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen($cmd,$lc);
+ my @DashArray = ();
+ my $dash = &quot;&quot;;
+ my $dashpattern = &quot;&quot;;
+ PATTERN: while (1) {
+ $dash = sprintf(&quot;%.5f&quot;, expr($lc));
+ if (s/^\s*($units)//i) {
+ push (@DashArray, &quot;$dash$1&quot;);
+ }
+ else {
+ PrintErrorMessage(&quot;Did not found unit after expression&quot;, $lc);
+ }
+ s/\s*//;
+ if (/^[^,]/) {
+ last PATTERN;
+ }
+ else {
+ s/^,\s*//;
+ }
+ }
+ print OUT &quot;\\setdashpattern &lt;&quot;;
+ while (@DashArray) {
+ $dashpattern .= shift @DashArray;
+ $dashpattern .= &quot;,&quot;;
+ }
+ $dashpattern =~ s/,$//;
+ print OUT $dashpattern, &quot;&gt;\n&quot;;
+ chk_rparen(&quot;arguments of $cmd&quot;,$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>$cmd</code> we call either the subroutine <code>drawAngleArc</code> or the
+subroutine <code>drawAngleArrow</code>. These subroutines return the code that will be
+finally output to the output file.
+
+<pre><a name="NW21HcNW-12lwO-1" href="#NWD21HcNW-s"><dfn>&lt;process <tt>drawAngleArcOrArrow</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lcb($cmd,$lc);
+ <a name="NW21HcNW-12lwO-1-u1" href="#NWD21HcNW-t"><i>&lt;process <tt>angle</tt> part of command&gt;</i></a>
+ s/^,\s*// or s/\s*//; #parse optional comma
+ <a name="NW21HcNW-12lwO-1-u2" href="#NWD21HcNW-u"><i>&lt;process <tt>radius</tt> part of command&gt;</i></a>
+ s/^,\s*// or s/\s*//; #parse optional comma
+ my $inout = &quot;&quot;;
+ if (s/^(internal(?=\W))//i or s/^(external(?=\W))//i) {
+ $inout = $1;
+ }
+ else {
+ PrintErrorMessage(&quot;Did not find expected 'internal' specifier&quot;, $lc);
+ next LINE;
+ }
+ s/^,\s*// or s/\s*//; #parse optional comma
+ my $direction = &quot;&quot;;
+ if (s/^(clockwise(?=\W))//i or s/^(anticlockwise(?=\W))//i) {
+ $direction = $1;
+ }
+ else {
+ PrintErrorMessage(&quot;Did not find expected 'direction' specifier&quot;, $lc);
+ next LINE;
+ }
+ chk_rcb(&quot;arguments of $cmd&quot;,$lc);
+ chk_comment($lc);
+ my $code;
+ if (lc($cmd) eq &quot;drawanglearc&quot;) {
+ $code = drawAngleArc($P1, $P2, $P3, $radius, $inout, $direction);
+ }
+ else {
+ $code = drawAngleArrow($P1, $P2, $P3, $radius, $inout, $direction);
+ }
+ print OUT $code if $code ne &quot;&quot;;
+
+</pre><p><a name="NWD21HcNW-t">We first check whether the first token is the word </a><code>angle</code>. In case it
+isn't, this yields an unrecoverable error. In case the expected word is
+there, we check for a left parenthesis. Next, we parse the three points that
+must follow. For this purpose we use the user-defined subroutine
+<code>get_point</code>. Now we check that the angle has a reasonable value, i.e., if
+it is less than -400 or equal to zero, the value yields an unrecoverable error.
+We finish by checking whether there is a right parenthesis.
+
+<pre><a name="NW21HcNW-4X9wPg-1" href="#NWD21HcNW-t"><dfn>&lt;process <tt>angle</tt> part of command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-s">&lt;-U</a>)</b>
+ my ($P1, $P2, $P3);
+ if (s/^angle(?=\W)//i) {
+ chk_lparen(&quot;token angle of command $cmd&quot;,$lc);
+ $P1 = get_point($lc);
+ next LINE if $P1 eq &quot;_undef_&quot;;
+ $P2 = get_point($lc);
+ next LINE if $P2 eq &quot;_undef_&quot;;
+ $P3 = get_point($lc);
+ next LINE if $P3 eq &quot;_undef_&quot;;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$P1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$P2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$P3});
+ my $Angle = Angle($x1, $y1, $x2, $y2, $x3, $y3);
+ if ($Angle &lt;= 0) {
+ if ($Angle == 0) {
+ PrintErrorMessage(&quot;Angle is equal to zero&quot;,$lc);
+ next LINE;
+ }
+ elsif ($Angle &lt; -400) {
+ PrintErrorMessage(&quot;Something is wrong with the points&quot;,$lc);
+ next LINE;
+ }
+ }
+ chk_rparen(&quot;angle part of command $cmd&quot;,$lc);
+ }
+ else {
+ PrintErrorMessage(&quot;Did not find expected angle part&quot;,$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>&lt;process <tt>radius</tt> part of command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-s">&lt;-U</a>)</b>
+
+ my $radius;
+ if (s/^radius(?=\W)//i) {
+ chk_lparen(&quot;token radius of command $cmd&quot;,$lc);
+ $radius = expr($lc);
+ chk_rparen(&quot;radius part of command $cmd&quot;,$lc);
+ }
+ else {
+ PrintErrorMessage(&quot;Did not found expected angle part&quot;,$lc);
+ next LINE;
+ }
+
+</pre><p>Command <code>drawcircle</code> accepts two arguments--a point name that is
+used to specify the center of the circle and the radius of the circle.
+The radius is simply an expression, whose value must be greater than zero.
+Otherwise, we print an error message and continue with the next input line.
+The general syntax of the command is as follows:
+<pre>
+ "drawcircle" "(" point-name "," rad ")"
+</pre>
+The code we emit for a point with coordinates <code>x</code> and <code>y</code> and for radius
+equal to <code>R</code> is:
+<pre>
+ \circulararc 360 degrees from X y center at x y
+</pre>
+where <code>X = x+R</code>.<p>
+<a name="NWD21HcNW-v">Initially, we check whether there is an opening left parenthesis. Next,</a>
+we get the point name by using the subroutine <code>get_point</code> which
+issues an error message if the point hasn't been defined. In this
+case we stop processing the command, as there is absolutely no reason to
+do otherwise. Next, we parse the comma and then the radius by using
+the subroutine <code>ComputeDist</code>. If there is no problem, we emit the code
+and finally we check for a closing right parenthesis and for
+possible garbage that may follow the command.
+
+<pre><a name="NW21HcNW-EIAAh-1" href="#NWD21HcNW-v"><dfn>&lt;process <tt>drawcircle</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;drawcircle&quot;,$lc);
+ my $Point = get_point($lc);
+ next LINE if $Point eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ my $R = expr($lc);
+ if ($R &lt;= 0) {
+ PrintErrorMessage(&quot;Radius must be greater than zero&quot;,$lc);
+ next LINE;
+ }
+ my ($x,$y,$pSV,$pS)=unpack(&quot;d3A*&quot;,$PointTable{lc($Point)});
+ printf OUT &quot;\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ $x+$R, $y, $x, $y;
+ chk_rparen(&quot;arguments of $cmd&quot;,$lc);
+ chk_comment($lc);
+
+</pre><p>Command <code>drawcircumcircle</code> is used to draw the circumcircle of triangle
+specified by three points which are the arguments of the command. We start
+by parsing the opening left parenthesis. Next, we get the three points
+that define the triangle. We are now able to compute the center and
+the radius of the circumcircle by calling the subroutine <code>circumCircleCenter</code>.
+If the triangle area is equal to zero, then this subroutine will return
+the array <code>(0,0,0)</code> to indicate this fact.
+We now have all necessary information to draw the circumcircle. We use the
+<a name="NWD21HcNW-w">following code to do the job:</a>
+<pre>
+ \circulararc 360 degrees from X y center x y
+</pre>
+where <code>x</code> and <code>y</code> are the coordinates of the center, <code>R</code> its
+radius and <code>X=x+R</code>. What is left is to check whether there is a
+closing right parenthesis and any trailing garbage.
+
+
+<pre><a name="NW21HcNW-1HqG4z-1" href="#NWD21HcNW-w"><dfn>&lt;process <tt>drawcircumcircle</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;drawcircumcircle&quot;,$lc);
+ my $point1 = get_point($lc);
+ next LINE if $point1 eq &quot;_undef_&quot;;
+ my $point2 = get_point($lc);
+ next LINE if $point2 eq &quot;_undef_&quot;;
+ my $point3 = get_point($lc);
+ next LINE if $point3 eq &quot;_undef_&quot;;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point3});
+ my ($xc, $yc,$r) = circumCircleCenter($x1,$y1,$x2,$y2,$x3,$y3,$lc);
+ next LINE if $xc == 0 and $yc == 0 and $r == 0;
+ print OUT &quot;%% circumcircle center = ($xc,$yc), radius = $r\n&quot; if $comments_on;
+ printf OUT &quot;\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ $xc+$r, $yc, $xc, $yc;
+ chk_rparen(&quot;arguments of $cmd&quot;,$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>&lt;process <tt>drawexcircle</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;drawexcircle&quot;,$lc);
+ my $point1 = get_point($lc);
+ next LINE if $point1 eq &quot;_undef_&quot;;
+ my $point2 = get_point($lc);
+ next LINE if $point2 eq &quot;_undef_&quot;;
+ my $point3 = get_point($lc);
+ next LINE if $point3 eq &quot;_undef_&quot;;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point3});
+ if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) &lt; 0.0001) {
+ PrintErrorMessage(&quot;Area of triangle is zero!&quot;,$lc);
+ next LINE;
+ }
+ chk_comma($lc);
+ my $point4 = get_point($lc);
+ if (!memberOf($point4, $point1, $point2, $point3)) {
+ PrintErrorMessage(&quot;Current point isn't a side point&quot;,$lc);
+ next LINE;
+ }
+ next LINE if $point4 eq &quot;_undef_&quot;;
+ my $point5 = get_point($lc);
+ next LINE if $point5 eq &quot;_undef_&quot;;
+ if (!memberOf($point5, $point1, $point2, $point3)) {
+ PrintErrorMessage(&quot;Current point isn't a side point&quot;,$lc);
+ next LINE;
+ }
+ if ($point4 eq $point5) {
+ PrintErrorMessage(&quot;Side points are identical&quot;,$lc);
+ next LINE;
+ }
+ chk_rparen(&quot;arguments of $cmd&quot;,$lc);
+ my ($xc, $yc, $r) = excircle($point1, $point2, $point3,
+ $point4, $point5);
+ my $R=$r;
+ if (s/^\s*\[\s*//) {
+ $R += expr($lc);
+ if ($R &lt; 0.0001) {
+ PrintErrorMessage(&quot;Radius has become equal to zero!&quot;,$lc);
+ next LINE;
+ }
+ chk_rsb($lc);
+ }
+ if ($R &gt; (500 / 2.845)) {
+ PrintErrorMessage(&quot;Radius is greater than 175mm!&quot;,$lc);
+ next LINE;
+ }
+ print OUT &quot;%% excircle center = ($xc,$yc) radius = $R\n&quot; if $comments_on;
+ printf OUT &quot;\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ $xc+$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>$R</code>. At this point we check whether the sum of the
+radius plus the optional part is equal to zero and if it is we continue with
+the next input line. Next, we check for a closing right square bracket.
+<a name="NWD21HcNW-y">We are now ready to emit the source code. The first thing we must check is</a>
+that the radius is not too big for PiCTeX, i.e., not greater than 500/2.845.
+Then we print some informative text to the output file and of course the
+actual code. We use the following code to do the job:
+<pre>
+ \circulararc 360 degrees from (xc+R) yc center xc yc
+</pre>
+The last thing we check is whether there is some trailing garbage.
+
+<pre><a name="NW21HcNW-3GJ2p7-1" href="#NWD21HcNW-y"><dfn>&lt;process <tt>drawincircle</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;drawincircle&quot;,$lc);
+ my $point1 = get_point($lc);
+ next LINE if $point1 eq &quot;_undef_&quot;;
+ my $point2 = get_point($lc);
+ next LINE if $point2 eq &quot;_undef_&quot;;
+ my $point3 = get_point($lc);
+ next LINE if $point3 eq &quot;_undef_&quot;;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point3});
+ if (triangleArea($x1, $y1, $x2, $y2, $x3, $y3) &lt; 0.0001) {
+ PrintErrorMessage(&quot;Area of triangle is zero!&quot;,$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 ($R &lt; 0.0001) {
+ PrintErrorMessage(&quot;Radius has become equal to zero!&quot;,$lc);
+ next LINE;
+ }
+ chk_rsb($lc);
+ }
+ if ($R &gt; (500 / 2.845)) {
+ PrintErrorMessage(&quot;Radius is greater than 175mm!&quot;,$lc);
+ next LINE;
+ }
+ print OUT &quot;%% incircle center = ($xc,$yc) radius = $R\n&quot; if $comments_on;
+ printf OUT &quot;\\circulararc 360 degrees from %.5f %.5f center at %.5f %.5f\n&quot;,
+ $xc+$R, $yc, $xc, $yc;
+ chk_rparen(&quot;arguments of $cmd&quot;,$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$</code>. If this point is undefined
+we print an error message and continue with the next line. Next, we parse
+the expected leading comma and the names of the other two points. Certainly,
+in case either of these two points has not been defined, we simply print an
+error message and continue with the next input line. Finally, we check for
+a closing right parenthesis and a possible trailing comment. Now we are
+ready to compute the coordinates of the foot of the
+perpendicular line. We do so my calling subroutine
+<code><a name="NWD21HcNW-z">perpendicular</a></code>. Certainly, before we do this we have to get the
+coordinates of the points that we have parsed. Finally, we output the
+PiCTeX code:
+<pre>
+ \plot x1 y1 xF xY /
+</pre>
+where <code>x1</code> and <code>y1</code> are coordinates of the point A and <code>xF</code> and <code>yF</code>
+the coordinates of the foot.
+
+<pre><a name="NW21HcNW-4OiWfi-1" href="#NWD21HcNW-z"><dfn>&lt;process <tt>drawPerpendicular</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen($cmd,$lc);
+ my $A = get_point($lc);
+ next LINE if $A eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ my $B = get_point($lc);
+ next LINE if $A eq &quot;_undef_&quot;;
+ s/\s*//; #ignore white space
+ my $C = get_point($lc);
+ next LINE if $A eq &quot;_undef_&quot;;
+ chk_rparen(&quot;arguments of $cmd&quot;,$lc);
+ chk_comment($lc);
+ #
+ #start actual computation
+ #
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$A});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$B});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$C});
+ my ($xF, $yF) = perpendicular($x1, $y1, $x2, $y2, $x3, $y3);
+ printf OUT &quot;\\plot %.5f %.5f %.5f %.5f /\n&quot;,
+ $x1, $y1, $xF, $yF;
+
+</pre><p>The <code>drawpoint</code> command has a number of points as arguments and produces
+PiCTeX code that draws a plot symbol at the coordinates of each point. The
+syntax of the command is as follows:
+<pre>
+ drawpoint ::= "drawpoint" "(" Point { separator Point } ")"
+</pre>
+The <code>while</code> loop is used to consume all points that are
+<a name="NWD21HcNW-10">between an opening left parenthesis and a closing right parenthesis. All</a>
+points are pushed on the local array <code>PP</code>. When we have parsed the lists
+of points, we call the subroutine <code>drawpoints</code> to emit the actual PiCTeX code.
+Finally, we check whether there is a closing parenthesis
+parenthesis, and whether
+there is some trailing text that makes no sense. In case there are no points
+between the parentheses, then we issue an appropriate error message and
+we continue with the next input line.
+
+<pre><a name="NW21HcNW-2EC5Ei-1" href="#NWD21HcNW-10"><dfn>&lt;process <tt>drawpoint</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ my ($stacklen);
+ chk_lparen(&quot;$cmd&quot;,$lc);
+ if (/^\)/) {
+ PrintErrorMessage(&quot;There are no point to draw&quot;,$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(&quot;Undefined point $P&quot;,$lc);
+ next DRAWPOINTS;
+ }
+ else {
+ push (@PP,$P);
+ s/\s*//;
+ }
+ }
+ else {
+ last DRAWPOINTS;
+ }
+ }
+ drawpoints(@PP);
+ chk_rparen(&quot;arguments of $cmd&quot;,$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>&lt;process <tt>drawRightAngle</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;drawRightAngle&quot;,lc);
+ my $point1 = get_point($lc);
+ next LINE if $point1 eq &quot;_undef_&quot;;
+ my $point2 = get_point($lc);
+ next LINE if $point2 eq &quot;_undef_&quot;;
+ my $point3 = get_point($lc);
+ next LINE if $point3 eq &quot;_undef_&quot;;
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point1});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point2});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point3});
+ chk_comma($lc);
+ my $dist = expr($lc);
+ chk_rparen(&quot;arguments of $cmd&quot;,$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 &quot;\\plot %.5f %.5f %.5f %.5f /\n&quot;,
+ $xS1, $yS1, $xS2, $yS2;
+ ($xS1, $yS1) = pointOnLine($x2, $y2, $x1, $y1, $dist);
+ printf OUT &quot;\\plot %.5f %.5f %.5f %.5f /\n&quot;,
+ $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>&lt;process <tt>drawsquare</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;drawSquare&quot;,$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(&quot;d3A*&quot;,$PointTable{$p});
+ printf OUT &quot;\\put {%s} at %.5f %.5f %%drawsquare\n&quot;, drawsquare($side), $x, $y;
+ chk_rparen(&quot;arguments of $cmd&quot;,$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>&lt;process <tt>inputfile*</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;inputfile*&quot;,$lc);
+ my $row_in = &quot;&quot;;
+ if (s/^((\w|-|\.)+)//) {
+ $row_in = $1;
+ }
+ else {
+ PrintErrorMessage(&quot;No input file name found&quot;,$lc);
+ next LINE;
+ }
+ if (!(-e $row_in)) {
+ PrintErrorMessage(&quot;File $row_in does not exist&quot;,$lc);
+ next LINE;
+ }
+ open(ROW, &quot;$row_in&quot;)|| die &quot;Can't open file $row_in\n&quot;;
+ while (defined($in_line=&lt;ROW&gt;)) { print OUT $in_line; }
+ print OUT &quot;%% ... end of input file &lt;$row_in&gt;\n&quot;;
+ close ROW;
+ chk_rparen(&quot;input file name&quot;,$lc);
+ chk_comment($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>&lt;process <tt>inputfile</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;inputfile&quot;,$lc);
+ my $comm_in = &quot;&quot;;
+ if (s/^((\w|-|\.)+)//) {
+ $comm_in = $1;
+ }
+ else {
+ PrintErrorMessage(&quot;No input file name found&quot;,$lc);
+ next LINE;
+ }
+ if (!(-e $comm_in)) {
+ PrintErrorMessage(&quot;File $comm_in does not exist&quot;,$lc);
+ next LINE;
+ }
+ chk_rparen(&quot;input file name&quot;,$lc);
+ my $input_times = 1; #default value
+ if (s/^\[//) {
+ $input_times = expr($lc);
+ chk_rsb(&quot;optional argument&quot;,$lc);
+ }
+ print OUT &quot;%% ... start of file &lt;$comm_in&gt; loop [$input_times]\n&quot;;
+ for (my $i=0; $i&lt;int($input_times); $i++) {
+ open(COMM,&quot;$comm_in&quot;) or die &quot;Can't open file $comm_in\n&quot;;
+ print OUT &quot;%%% Iteration number: &quot;,$i+1,&quot;\n&quot;;
+ my $old_file_name = $curr_in_file;
+ process_input(COMM,&quot;File $comm_in, &quot;);
+ $curr_in_file = $old_file_name;
+ close COMM;
+ }
+ print OUT &quot;%% ... end of file &lt;$comm_in&gt; loop [$input_times]\n&quot;;
+ chk_comment($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>&lt;process <tt>linethickness</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;linethickness&quot;, $lc);
+ if (s/^default//i) {
+ print OUT &quot;\\linethickness=0.4pt\\Linethickness{0.4pt}%%\n&quot;;
+ print OUT &quot;\\setplotsymbol ({\\usefont{OT1}{cmr}{m}{n}\\tiny .})%\n&quot;;
+ $LineThickness = setLineThickness($xunits,&quot;0.4pt&quot;);
+ }
+ else {
+ my $length = expr($lc);
+ if (s/^\s*($units)//i) {
+ my $units = $1;
+ printf OUT &quot;\\linethickness=%.5f%s\\Linethickness{%.5f%s}%%\n&quot;,
+ $length, $units, $length, $units;
+ $LineThickness = setLineThickness($xunits,&quot;$length$units&quot;);
+ my $mag;
+ if ($units eq &quot;pc&quot;) {
+ $mag = $length * 12;
+ }
+ elsif ($units eq &quot;in&quot;) {
+ $mag = $length * 72.27;
+ }
+ elsif ($units eq &quot;bp&quot;) {
+ $mag = $length * 1.00375;
+ }
+ elsif ($units eq &quot;cm&quot;) {
+ $mag = $length * 28.45275;
+ }
+ elsif ($units eq &quot;mm&quot;) {
+ $mag = $length * 2.845275;
+ }
+ elsif ($units eq &quot;dd&quot;) {
+ $mag = $length * 1.07001;
+ }
+ elsif ($units eq &quot;cc&quot;) {
+ $mag = $length * 0.08917;
+ }
+ elsif ($units eq &quot;sp&quot;) {
+ $mag = $length * 0.000015259;
+ }
+ elsif ($units eq &quot;pt&quot;) {
+ $mag = $length;
+ }
+ $mag = 10 * $mag / 1.00278219;
+ printf OUT &quot;\\font\\CM=cmr10 at %.5fpt%%\n&quot;, $mag;
+ print OUT &quot;\\setplotsymbol ({\\CM .})%\n&quot;;
+ }
+ else {
+ PrintErrorMessage(&quot;Did not found expect units part&quot;,$lc);
+ }
+ }
+ chk_rparen(&quot;linethickness&quot;, $lc);
+ chk_comment($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>&lt;process <tt>paper</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lcb(&quot;paper&quot;, $lc);
+ if (s/^units(?=\W)//i)
+ {
+ <a name="NW21HcNW-1Pby5X-1-u1" href="#NWD21HcNW-17"><i>&lt;process <tt>unit</tt> part&gt;</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>&lt;process <tt>xrange</tt> part&gt;</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>&lt;process <tt>yrange</tt> part&gt;</i></a>
+ $noyrange = 0;
+ }
+ else
+ {
+ $noyrange = 1;
+ }
+ <a name="NW21HcNW-1Pby5X-1-u4" href="#NWD21HcNW-1D"><i>&lt;generate plot area related commands&gt;</i></a>
+ s/^,\s*// or s/\s*//;
+ $axis = &quot;&quot;;
+ if (s/^ax[ei]s(?=\W)//i)
+ {
+ <a name="NW21HcNW-1Pby5X-1-u5" href="#NWD21HcNW-1E"><i>&lt;process <tt>axis</tt> part&gt;</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>&lt;process <tt>ticks</tt> part&gt;</i></a>
+ }
+ else
+ {
+ $xticks = $yticks = 0;
+ }
+ chk_rcb(&quot;paper&quot;, $lc);
+ <a name="NW21HcNW-1Pby5X-1-u7" href="#NWD21HcNW-1G"><i>&lt;generate the rest of the code for the <tt>paper</tt> command&gt;</i></a>
+ chk_comment($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>&lt;process <tt>unit</tt> part&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;units&quot;,$lc);
+ if(s/^\)//)
+ {
+ PrintWarningMessage(&quot;Missing value in \&quot;units\&quot;--default is 1pt&quot;,
+ $lc);
+ $xunits = &quot;1pt&quot;;
+ }
+ else {
+ $xunits = expr($lc);
+ s/\s*//;
+ if (s/^($units)//i) {
+ $xunits .= &quot;$1&quot;;
+ $LineThickness = setLineThickness($xunits,&quot;0.4pt&quot;);
+ }
+ elsif(s/^(\w)+//i) {
+ PrintErrorMessage(&quot;$1 is not a valid mathspic unit&quot;,$lc);
+ $xunits = &quot;1pt&quot;;
+ }
+ else {
+ PrintErrorMessage(&quot;No x-units found&quot;,$lc);
+ $xunits = &quot;1pt&quot;;
+ }
+ 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 .= &quot;$1&quot;;
+ }
+ elsif(s/^(\w)+//i) {
+ PrintErrorMessage(&quot;$1 is not a valid mathspic unit&quot;,$lc);
+ $yunits = &quot;1pt&quot;;
+ }
+ else {
+ PrintErrorMessage(&quot;No y-units found&quot;,$lc);
+ $yunits = $xunits;
+ }
+ }
+ else {
+ $yunits = $xunits;
+ }
+ chk_rparen(&quot;units&quot;,$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>&lt;process <tt>xrange</tt> part&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;xrange&quot;,$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 &gt;= $xhigh)
+ {
+ PrintErrorMessage(&quot;xlow &gt;= xhigh in xrange&quot;,$lc);
+ next LINE;
+ }
+ chk_rparen(&quot;$xhigh&quot;,$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>&lt;process <tt>yrange</tt> part&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;yrange&quot;,$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 &gt;= $yhigh)
+ {
+ PrintErrorMessage(&quot;ylow &gt;= yhigh in yrange&quot;,$lc);
+ next LINE;
+ }
+ chk_rparen(&quot;$yhigh&quot;,$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>&lt;process <tt>showAngle</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;showangle&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $point_3 = get_point($lc);
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point_3});
+ my $angle = Angle($x1, $y1, $x2, $y2, $x3, $y3);
+ $angle = 0 if $angle == -500;
+ printf OUT &quot;%%%% angle(%s%s%s) = %.5f deg ( %.5f rad)\n&quot;, $point_1,
+ $point_2, $point_3, $angle, $angle*D2R;
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+
+</pre><p><a name="NWD21HcNW-1B">The </a><code>showArea</code> command has three arguments that correspond to three distinct
+points and emits a comment of the form:
+<center>
+<tt>%% area(ABC) = 45</tt>
+</center>
+Note that the computed angle is expressed in degrees.
+
+<pre><a name="NW21HcNW-2THNRJ-1" href="#NWD21HcNW-1B"><dfn>&lt;process <tt>showArea</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;showarea&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ my $point_3 = get_point($lc);
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$point_3});
+ print OUT &quot;%% area($point_1$point_2$point_3) = &quot;,
+ triangleArea($x1, $y1, $x2, $y2, $x3, $y3), &quot;\n&quot;;
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+
+</pre><p><a name="NWD21HcNW-1C">The </a><code>showLength</code> command has two arguments that correspond to two distinct
+points and emits a comment of the form:
+<center>
+<tt>%% length(AB) = 45</tt>
+</center>
+Note that the computed angle is expressed in degrees.
+
+<pre><a name="NW21HcNW-Ofe1b-1" href="#NWD21HcNW-1C"><dfn>&lt;process <tt>showLength</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ chk_lparen(&quot;showlength&quot;,$lc);
+ my $point_1 = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$point_1});
+ my $point_2 = get_point($lc);
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$point_2});
+ print OUT &quot;%% length($point_1$point_2) = &quot;,
+ Length($x1, $y1, $x2, $y2), &quot;\n&quot;;
+ chk_rparen(&quot;Missing right parenthesis&quot;, $lc);
+
+
+</pre><p><a name="NWD21HcNW-1D">If the user hasn't specified units then we use the previous values to</a>
+set the coordinate system. If the user hasn't specified either the
+<code>xunits</code> part or the <code>yunits</code>, then we don't emit code. In case he/she
+has specified both parts we generate the command that sets the plot area.
+
+<pre><a name="NW21HcNW-2SitZA-1" href="#NWD21HcNW-1D"><dfn>&lt;generate plot area related commands&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+
+ if (!$nounits)
+ {
+ printf OUT &quot;\\setcoordinatesystem units &lt;%s,%s&gt;\n&quot;,
+ $xunits,$yunits;
+ }
+ if(!$noxrange &amp;&amp; !$noyrange)
+ {
+ printf OUT &quot;\\setplotarea x from %.5f to %.5f, y from %.5f to %.5f\n&quot;,
+ $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>&lt;process <tt>axis</tt> part&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;axis&quot;,$lc);
+ while(/^[^\)]/)
+ {
+ if (s/^([lrtbxy]{1}\*?)//i)
+ {
+ $axis .= $1;
+ }
+ elsif (s/^([^lrtbxy])//i)
+ {
+ PrintErrorMessage(&quot;Non-valid character \&quot;$1\&quot; in axis()&quot;,$lc);
+ }
+ s/\s*//;
+ }
+ chk_rparen(&quot;axis(arguments&quot;,$lc);
+
+</pre><p>As usual we start by skipping white space. Next we check whether there is
+<a name="NWD21HcNW-1F">an opening left parenthesis. Now, we expect two numbers/variables/pair of</a>
+point representing the <code>ticks</code> increment value. These <code>ticks</code> increment
+values must be separated by a comma (and possibly some white space around
+them). We use the subroutine <code>ComputeDist</code> to get the value of the <code>ticks</code>
+increment value and we assign to the variables <code>$xticks</code> and <code>$yticks</code>
+the value of x-ticks and y-ticks increment value. In case there is a
+problem we issue an error message and continue with the next line. The last
+thing we check is whether there is a closing right parenthesis.
+
+<pre><a name="NW21HcNW-1isLLJ-1" href="#NWD21HcNW-1F"><dfn>&lt;process <tt>ticks</tt> part&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+ chk_lparen(&quot;ticks&quot;,$lc);
+ my $ec;
+ ($xticks,$ec) = ComputeDist($lc);
+ next LINE if $ec == 0;
+ chk_comma($lc);
+ ($yticks,$ec) = ComputeDist($lc);
+ next LINE if $ec == 0;
+ chk_rparen(&quot;ticks(arguments&quot;,$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>&lt;generate the rest of the code for the <tt>paper</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-16">&lt;-U</a>)</b>
+YBRANCH: {
+ if (index($axis, &quot;Y&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;Y*&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis left shiftedto x=0 / \n&quot;;
+ last YBRANCH;
+ }
+ if ($yticks &gt; 0)
+ {
+ if (index($axis, &quot;T&quot;)&gt;-1 &amp;&amp; index($axis, &quot;B&quot;)==-1)
+ {
+ print OUT &quot;\\axis left shiftedto x=0 ticks numbered from &quot;;
+ print OUT &quot;$ylow to -$yticks by $yticks\n from $yticks to &quot;;
+ print OUT $yhigh-$yticks,&quot; by $yticks /\n&quot;;
+ }
+ elsif (index($axis, &quot;T&quot;)==-1 &amp;&amp; index($axis, &quot;B&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis left shiftedto x=0 ticks numbered from &quot;;
+ print OUT $ylow+$yticks,&quot; to -$yticks by $yticks\n from &quot;;
+ print OUT &quot;$yticks to $yhigh by $yticks /\n&quot;;
+ }
+ elsif (index($axis, &quot;T&quot;)&gt;-1 &amp;&amp; index($axis, &quot;B&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis left shiftedto x=0 ticks numbered from &quot;;
+ print OUT $ylow+$yticks,&quot; to -$yticks by $yticks\n from &quot;;
+ print OUT &quot;$yticks to &quot;,$yhigh-$yticks,&quot; by $yticks /\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\axis left shiftedto x=0 ticks numbered from &quot;;
+ print OUT &quot;$ylow to -$yticks by $yticks\n from &quot;;
+ print OUT &quot;$yticks to $yhigh by $yticks /\n&quot;;
+ }
+ }
+ else
+ {
+ print OUT &quot;\\axis left shiftedto x=0 /\n&quot;;
+ }
+ }
+ }
+ XBRANCH: { if (index($axis, &quot;X&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;X*&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis bottom shiftedto y=0 /\n&quot;;
+ last XBRANCH;
+ }
+ if ($xticks &gt; 0)
+ {
+ if (index($axis, &quot;L&quot;)&gt;-1 &amp;&amp; index($axis, &quot;R&quot;)==1)
+ {
+ print OUT &quot;\\axis bottom shiftedto y=0 ticks numbered from &quot;;
+ print OUT $xlow + $xticks,&quot; to -$xticks by $xticks\n from&quot;;
+ print OUT &quot; $xticks to $xhigh by $xticks /\n&quot;;
+ }
+ elsif (index($axis, &quot;L&quot;)==-1 &amp;&amp; index($axis, &quot;R&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis bottom shiftedto y=0 ticks numbered from &quot;;
+ print OUT &quot;$xlow to -$xticks by $xticks\n from &quot;;
+ print OUT &quot;$xticks to &quot;,$xhigh-$xticks,&quot; by $xticks /\n&quot;;
+ }
+ elsif (index($axis, &quot;L&quot;)&gt;-1 &amp;&amp; index($axis, &quot;R&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis bottom shiftedto y=0 ticks numbered from &quot;;
+ print OUT $xlow + $xticks,&quot; to -$xticks by $xticks\n from &quot;;
+ print OUT &quot;$xticks to &quot;,$xhigh - $xticks,&quot; by $xticks /\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\axis bottom shiftedto y=0 ticks numbered from &quot;;
+ print OUT &quot;$xlow to -$xticks by $xticks\n from &quot;;
+ print OUT &quot;$xticks to $xhigh by $xticks /\n&quot;;
+ }
+ }
+ else
+ {
+ print OUT &quot;\\axis bottom shiftedto y=0 /\n&quot;;
+ }
+ } }
+ LBRANCH: {if (index($axis, &quot;L&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;L&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;L*&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis left /\n&quot;;
+ last LBRANCH;
+ }
+ if ($yticks &gt; 0)
+ {
+ print OUT &quot;\\axis left ticks numbered from &quot;;
+ print OUT &quot;$ylow to $yhigh by $yticks /\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\axis left /\n&quot;;
+ }
+ }
+ } }
+ RBRANCH: { if (index($axis, &quot;R&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;R*&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis right /\n&quot;;
+ last RBRANCH;
+ }
+ if ($yticks &gt; 0)
+ {
+ print OUT &quot;\\axis right ticks numbered from $ylow to $yhigh by &quot;;
+ print OUT &quot;$yticks /\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\axis right /\n&quot;;
+ }
+ } }
+ TBRANCH: { if (index($axis, &quot;T&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;T*&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis top /\n&quot;;
+ last TBRANCH;
+ }
+ if ($xticks &gt; 0)
+ {
+ print OUT &quot;\\axis top ticks numbered from $xlow to $xhigh by &quot;;
+ print OUT &quot;$xticks /\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\axis top /\n&quot;;
+ }
+ } }
+ BBRANCH: { if (index($axis, &quot;B&quot;)&gt;-1)
+ {
+ if (index($axis, &quot;B*&quot;)&gt;-1)
+ {
+ print OUT &quot;\\axis bottom /\n&quot;;
+ last BBRANCH;
+ }
+ if ($xticks &gt; 0)
+ {
+ print OUT &quot;\\axis bottom ticks numbered from $xlow to $xhigh by &quot;;
+ print OUT &quot;$xticks /\n&quot;;
+ }
+ else
+ {
+ print OUT &quot;\\axis bottom /\n&quot;;
+ }
+ } }
+
+
+</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>&lt;process <tt>point/point*</tt> commands&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ my ($pointStar, $PointName, $origPN);
+ $pointStar = 0; # default value: he have a point command
+ $pointStar = 1 if s/^\*//;
+ chk_lparen(&quot;point&quot; . (($pointStar)?&quot;*&quot;:&quot;&quot;),$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($1);
+ }
+ else {
+ PrintErrorMessage(&quot;Invalid point name&quot;,$lc);
+ next LINE;
+ }
+ #if ($pointStar and !exists($PointTable{$PointName})) {
+ # PrintWarningMessage(&quot;Point $origPN has not been defined&quot;,$lc);
+ #}
+ if (!$pointStar and exists($PointTable{$PointName})) {
+ PrintWarningMessage(&quot;Point $origPN has been used already&quot;,$lc);
+ }
+ chk_rparen(&quot;point&quot; . (($pointStar)?&quot;*&quot;:&quot;&quot;). &quot;($origPN&quot;,$lc);
+ chk_lcb(&quot;point&quot; . (($pointStar)?&quot;*&quot;:&quot;&quot;). &quot;($origPN)&quot;,$lc);
+ my ($Px, $Py);
+ <a name="NW21HcNW-2bvYBY-1-u1" href="#NWD21HcNW-1I"><i>&lt;process coordinates&gt;</i></a>
+ chk_rcb(&quot;coordinates part&quot;,$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>&lt;process optional point shape part&gt;</i></a>
+ chk_rsb(&quot;optional part&quot;,$lc);
+ }
+ # to avoid truncation problems introduced by the pack function, we
+ # round each number up to five decimal digits
+ $Px = sprintf(&quot;%.5f&quot;, $Px);
+ $Py = sprintf(&quot;%.5f&quot;, $Py);
+ print OUT &quot;%% point$Point_Line \t$origPN = ($Px, $Py)\n&quot; if $comments_on;
+ chk_comment($lc);
+ $PointTable{$PointName} = pack(&quot;d3A*&quot;,$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>&lt;process coordinates&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1H">&lt;-U</a>)</b>
+ if (s/^perpendicular(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u1" href="#NWD21HcNW-1J"><i>&lt;process <tt>perpendicular</tt> case&gt;</i></a>
+ }
+ elsif (s/^intersection(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u2" href="#NWD21HcNW-1K"><i>&lt;process <tt>intersection</tt> case&gt;</i></a>
+ }
+ elsif (s/^midpoint(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u3" href="#NWD21HcNW-1L"><i>&lt;process <tt>midpoint</tt> case&gt;</i></a>
+ }
+ elsif (s/^pointonline(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u4" href="#NWD21HcNW-1M"><i>&lt;process <tt>pointonline</tt> case&gt;</i></a>
+ }
+ elsif (s/^circumcircleCenter(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u5" href="#NWD21HcNW-1N"><i>&lt;process <tt>circumcircleCenter</tt> case&gt;</i></a>
+ }
+ elsif (s/^IncircleCenter(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u6" href="#NWD21HcNW-1O"><i>&lt;process <tt>IncircleCenter</tt> case&gt;</i></a>
+ }
+ elsif (s/^ExcircleCenter(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u7" href="#NWD21HcNW-1P"><i>&lt;process <tt>ExcircleCenter</tt> case&gt;</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(&quot;d3A*&quot;,$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>&lt;process <tt>shift</tt> case&gt;</i></a>
+ }
+ elsif (s/^polar(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u9" href="#NWD21HcNW-1R"><i>&lt;process <tt>polar</tt> case&gt;</i></a>
+ }
+ elsif (s/^rotate(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u10" href="#NWD21HcNW-1S"><i>&lt;process <tt>rotate</tt> case&gt;</i></a>
+ }
+ elsif (s/^vector(?=\W)//i) {
+ <a name="NW21HcNW-3bnmlP-1-u11" href="#NWD21HcNW-1T"><i>&lt;process <tt>vector</tt> case&gt;</i></a>
+ }
+ else {
+ PrintErrorMessage(&quot;unexpected token&quot;,$lc);
+ next LINE;
+ }
+ }
+ else {
+ my ($xA,$yA,$pSVA,$pSA)=unpack(&quot;d3A*&quot;,$PointTable{lc($PointA)});
+ $Px = $xA;
+ $Py = $yA;
+ }
+ }
+ else {
+ PrintErrorMessage(&quot;Undefined point $PointA&quot;,$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>&lt;process <tt>perpendicular</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;perpendicular&quot;,$lc);
+ my $FirstPoint = &amp;get_point($lc);
+ next LINE if $FirstPoint eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ my $SecondPoint = &amp;get_point($lc);
+ next LINE if $SecondPoint eq &quot;_undef_&quot;;
+ my $ThirdPoint = &amp;get_point($lc);
+ next LINE if $ThirdPoint eq &quot;_undef_&quot;;
+ chk_rparen(&quot;No closing parenthesis found&quot;,$lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$FirstPoint});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$SecondPoint});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$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>&lt;process <tt>intersection</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;intersection&quot;,$lc);
+ my $FirstPoint = get_point($lc);
+ next LINE if $FirstPoint eq &quot;_undef_&quot;;
+ my $SecondPoint = get_point($lc);
+ next LINE if $SecondPoint eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ my $ThirdPoint = get_point($lc);
+ next LINE if $ThirdPoint eq &quot;_undef_&quot;;
+ my $ForthPoint = get_point($lc);
+ next LINE if $ForthPoint eq &quot;_undef_&quot;;
+ chk_rparen(&quot;No closing parenthesis found&quot;,$lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$FirstPoint});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$SecondPoint});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$ThirdPoint});
+ my ($x4,$y4,$pSV4,$pS4)=unpack(&quot;d3A*&quot;,$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>&lt;process <tt>midpoint</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;midpoint&quot;,$lc);
+ my $FirstPoint = &amp;get_point($lc);
+ next LINE if $FirstPoint eq &quot;_undef_&quot;;
+ my $SecondPoint = &amp;get_point($lc);
+ next LINE if $SecondPoint eq &quot;_undef_&quot;;
+ chk_rparen(&quot;No closing parenthesis found&quot;,$lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$FirstPoint});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$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>&lt;process <tt>pointonline</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;pointonline&quot;,$lc);
+ my $FirstPoint = &amp;get_point($lc);
+ next LINE if $FirstPoint eq &quot;_undef_&quot;;
+ my $SecondPoint = &amp;get_point($lc);
+ next LINE if $SecondPoint eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ # now get the distance
+ my $distance = expr($lc);
+ chk_rparen(&quot;No closing parenthesis found&quot;,$lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$FirstPoint});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$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>&lt;process <tt>circumcircleCenter</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;circumCircleCenter&quot;,$lc);
+ my $FirstPoint = &amp;get_point($lc);
+ next LINE if $FirstPoint eq &quot;_undef_&quot;;
+ my $SecondPoint = &amp;get_point($lc);
+ next LINE if $SecondPoint eq &quot;_undef_&quot;;
+ my $ThirdPoint = &amp;get_point($lc);
+ next LINE if $ThirdPoint eq &quot;_undef_&quot;;
+ chk_rparen(&quot;No closing parenthesis found&quot;,$lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$FirstPoint});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$SecondPoint});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$PointTable{$ThirdPoint});
+ ($Px, $Py,$r) = &amp;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>&lt;process <tt>IncircleCenter</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;IncircleCenter&quot;,$lc);
+ my $FirstPoint = &amp;get_point($lc);
+ next LINE if $FirstPoint eq &quot;_undef_&quot;;
+ my $SecondPoint = &amp;get_point($lc);
+ next LINE if $SecondPoint eq &quot;_undef_&quot;;
+ my $ThirdPoint = &amp;get_point($lc);
+ next LINE if $ThirdPoint eq &quot;_undef_&quot;;
+ chk_rparen(&quot;No closing parenthesis found&quot;,$lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$FirstPoint});
+ my ($x2,$y2,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$PointTable{$SecondPoint});
+ my ($x3,$y3,$pSV3,$pS3)=unpack(&quot;d3A*&quot;,$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>&lt;process <tt>ExcircleCenter</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;ExcircleCenter&quot;,$lc);
+ my $PointA = get_point($lc);
+ next LINE if $PointA eq &quot;_undef_&quot;;
+ my $PointB = get_point($lc);
+ next LINE if $PointB eq &quot;_undef_&quot;;
+ my $PointC = get_point($lc);
+ next LINE if $PointC eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ my $PointD = &amp;get_point($lc);
+ next LINE if $PointD eq &quot;_undef_&quot;;
+ if (!memberOf($PointD, $PointA, $PointB, $PointC)) {
+ PrintErrorMessage(&quot;Current point isn't a side point&quot;,$lc);
+ next LINE;
+ }
+ my $PointE = get_point($lc);
+ next LINE if $PointE eq &quot;_undef_&quot;;
+ if (!memberOf($PointE, $PointA, $PointB, $PointC)) {
+ PrintErrorMessage(&quot;Current point isn't a side point&quot;,$lc);
+ next LINE;
+ }
+ if ($PointD eq $PointE) {
+ PrintErrorMessage(&quot;Side points are identical&quot;,$lc);
+ next LINE;
+ }
+ ($Px, $Py, $r) = excircle($PointA, $PointB, $PointC,
+ $PointD, $PointE);
+ chk_rparen(&quot;after coordinates part&quot;,$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>&lt;process <tt>shift</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a> <a href="#NWD21HcNW-1Z">U-&gt;</a>)</b>
+
+ chk_lparen(&quot;shift&quot;,$lc);
+ my $dist1 = expr($lc);
+ chk_comma($lc);
+ my $dist2 = expr($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{lc($PointA)});
+ $Px = $x1 + $dist1;
+ $Py = $y1 + $dist2;
+ chk_rparen(&quot;shift part&quot;,$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>&lt;process <tt>polar</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a> <a href="#NWD21HcNW-1Z">U-&gt;</a>)</b>
+ chk_lparen(&quot;polar&quot;,$lc);
+ my ($R1, $Theta1);
+ $R1 = expr($lc);
+ chk_comma($lc);
+ $Theta1 = expr($lc);
+ my ($x1,$y1,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$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(&quot;after polar part&quot;,$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>&lt;process <tt>rotate</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;rotate&quot;,$lc);
+ my $Q = lc($PointA);
+ my $P = get_point($lc);
+ next LINE if $P eq &quot;_undef_&quot;;
+ chk_comma($lc);
+ my $Theta1 = expr($lc);
+ my ($xP,$yP,$pSV1,$pS1)=unpack(&quot;d3A*&quot;,$PointTable{$P});
+ my ($xQ,$yQ,$pSV2,$pS2)=unpack(&quot;d3A*&quot;,$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(&quot;after rotate part&quot;,$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>&lt;process <tt>vector</tt> case&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1I">&lt;-U</a>)</b>
+ chk_lparen(&quot;vector&quot;,$lc);
+ my ($x0,$y0,$pSV0,$pS0) = unpack(&quot;d3A*&quot;,$PointTable{lc($PointA)});
+ my $P = get_point($lc);
+ my $Q = get_point($lc);
+ my ($x1,$y1,$pSV1,$pS1) = unpack(&quot;d3A*&quot;,$PointTable{$P});
+ my ($x2,$y2,$pSV2,$pS2) = unpack(&quot;d3A*&quot;,$PointTable{$Q});
+ $Px = $x0 + $x2 - $x1;
+ $Py = $y0 + $y2 - $y1;
+ chk_rparen(&quot;vector part&quot;,$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>&lt;process optional point shape part&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1H">&lt;-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 &lt;= 2) {
+ my $option = lc($1);
+ if (s/^=\s*//) {
+ if (memberOf($option,@previous_options)) {
+ PrintErrorMessage(&quot;Option \&quot;$option\&quot; has been already defined&quot;, $lc);
+ my $dummy = expr($lc);
+ }
+ elsif ($option eq &quot;radius&quot;) {
+ $sh = expr($lc);
+ $sv = $defaultsymbol if ! $symbol_set;
+ }
+ elsif ($option eq &quot;symbol&quot;) {
+ if (s/^circle\s*//i) {
+ $sv = &quot;circle&quot;;
+ chk_lparen(&quot;after token circle&quot;,$lc);
+ $side_or_radius = expr($lc);
+ chk_rparen(&quot;expression&quot;,$lc);
+ }
+ elsif (s/^square\s*//i) {
+ $sv = &quot;square&quot;;
+ chk_lparen(&quot;after token square&quot;,$lc);
+ $side_or_radius = expr($lc);
+ chk_rparen(&quot;expression&quot;,$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(&quot;unexpected token&quot;, $lc);
+ next LINE;
+ }
+ $number_of_options++;
+ push (@previous_options, $option);
+ s/^,\s*//;
+ }
+ }
+ else {
+ PrintErrorMessage(&quot;unexpected token&quot;, $lc);
+ next LINE;
+ }
+
+</pre><p>The <code>ArrowShape</code> command has either one or three arguments. If the only argument of
+the command is the token <code>default</code>, then the parameters associated with the
+arrow shape resume their default values. Now, if there are three arguments, these are
+used to specify the shape of an arrow. The command actually sets the three global variables
+<code>$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>&lt;process <tt>ArrowShape</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;$cmd&quot;,$lc);
+ if (s/^default//i) {
+ $arrowLength = 2;
+ $arrowLengthUnits = &quot;mm&quot;;
+ $arrowAngleB = 30;
+ $arrowAngleC = 40;
+ }
+ else {
+ my ($LocalArrowLength, $LocalArrowAngleB ,$LocalArrowAngleC) = (0,0,0);
+ $LocalArrowLength = expr($lc);
+ if (s/^\s*($units)//i) {
+ $arrowLengthUnits = &quot;$1&quot;;
+ }
+ else {
+ $xunits =~ /(\d+(\.\d+)?)\s*($units)/;
+ $LocalArrowLength *= $1;
+ $arrowLengthUnits = &quot;$3&quot;;
+ }
+ chk_comma($lc);
+ $LocalArrowAngleB = expr($lc);
+ chk_comma($lc);
+ $LocalArrowAngleC = expr($lc);
+ $arrowLength = ($LocalArrowLength == 0 ? 2 : $LocalArrowLength);
+ $arrowLengthUnits = ($LocalArrowLength == 0 ? &quot;mm&quot; : $arrowLengthUnits);
+ $arrowAngleB = ($LocalArrowAngleB == 0 ? 30 : $LocalArrowAngleB);
+ $arrowAngleC = ($LocalArrowAngleC == 0 ? 40 : $LocalArrowAngleC);
+ }
+ chk_rparen(&quot;after $cmd arguments&quot;,$lc);
+ chk_comment(&quot;after $cmd command&quot;,$lc);
+ print OUT &quot;%% arrowLength = $arrowLength$arrowLengthUnits, &quot;,
+ &quot;arrowAngleB = $arrowAngleB &quot;,
+ &quot;and arrowAngleC = $arrowAngleC\n&quot; 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>&lt;process <tt>PointSymbol</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;$cmd&quot;,$lc);
+ if (s/^default//i) #default point symbol
+ {
+ $defaultsymbol = &quot;\$\\bullet\$&quot;;
+ }
+ elsif (s/^(circle|square)//i) {
+ $defaultsymbol = $1;
+ chk_lparen($defaultsymbol, $lc);
+ $GlobalDimOfPoints = expr($lc);
+ chk_rparen(&quot;expression&quot;, $lc);
+ }
+ elsif (s/^(((\\,){1}|(\\\)){1}|(\\\s){1}|[^\),\s])+)//) #arbitrary LaTeX point
+ {
+ $defaultsymbol = $1;
+ $defaultsymbol=~ s/\\\)/\)/g;
+ $defaultsymbol=~ s/\\,/,/g;
+ $defaultsymbol=~ s/\\ / /g;
+ }
+ else
+ {
+ PrintErrorMessage(&quot;unrecognized point symbol&quot;,$lc);
+ }
+ if (s/\s*,\s*//) {
+ $defaultLFradius = expr($lc);
+ }
+ chk_rparen(&quot;after $cmd arguments&quot;,$lc);
+ chk_comment(&quot;after $cmd command&quot;,$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>&lt;process <tt>system</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;$cmd&quot;,$lc);
+ my ($error, $command, $rest) = get_string($_);
+ next LINE if $error == 1;
+ $_ = $rest;
+ if (! is_tainted($command)) {
+ system($command);
+ }
+ else {
+ PrintErrorMessage(&quot;String \&quot;$command\&quot; has tainted data&quot;, $lc);
+ next LINE;
+ }
+ chk_rparen(&quot;after $cmd arguments&quot;,$lc);
+ chk_comment(&quot;after $cmd command&quot;,$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>&lt;process <tt>text</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+
+ chk_lparen(&quot;text&quot;,$lc);
+ my ($level,$text)=(1,&quot;&quot;);
+ TEXTLOOP: while (1)
+ {
+ $level++ if /^\(/;
+ $level-- if /^\)/;
+ s/^(.)//;
+ last TEXTLOOP if $level==0;
+ $text .= $1;
+ }
+ chk_lcb(&quot;text part&quot;,$lc);
+ my ($Px, $Py,$dummy,$pos);
+ $pos=&quot;&quot;;
+ s/\s*//;
+ <a name="NW21HcNW-z25eX-1-u1" href="#NWD21HcNW-1Z"><i>&lt;process coordinates part of text command&gt;</i></a>
+ chk_rcb(&quot;coordinates part of text command&quot;,$lc);
+ if (s/^\[//)
+ {
+ s/\s*//;
+ <a name="NW21HcNW-z25eX-1-u2" href="#NWD21HcNW-1a"><i>&lt;process optional part of text command&gt;</i></a>
+ s/\s*//;
+ chk_rsb(&quot;optional part of text command&quot;,$lc);
+ }
+ chk_comment($lc);
+ if ($pos eq &quot;&quot;)
+ {
+ printf OUT &quot;\\put {%s} at %f %f\n&quot;, $text, $Px, $Py;
+ }
+ else
+ {
+ printf OUT &quot;\\put {%s} [%s] at %f %f\n&quot;, $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>&lt;process coordinates part of text command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1Y">&lt;-U</a>)</b>
+
+ if (/^[^\W\d_]\d{0,3}\s*[^,\w]/) {
+ my $Tcoord = get_point($lc);
+ my ($x,$y,$pSV,$pS)=unpack(&quot;d3A*&quot;,$PointTable{$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($PointA)})) {
+ s/\s*//;
+ if (s/^,//) {
+ s/\s*//;
+ if (s/^shift(?=\W)//i) {
+ <a name="NW21HcNW-Ee8Ug-1-u1" href="#NWD21HcNW-1Q"><i>&lt;process <tt>shift</tt> case&gt;</i></a>
+ }
+ elsif (s/^polar(?=\W)//i) {
+ <a name="NW21HcNW-Ee8Ug-1-u2" href="#NWD21HcNW-1R"><i>&lt;process <tt>polar</tt> case&gt;</i></a>
+ }
+ }
+ }
+ else {
+ PrintErrorMessage(&quot;undefined point/var&quot;,$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>&lt;process optional part of text command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-1Y">&lt;-U</a>)</b>
+
+ if (s/^(\w{1})\s*//) {
+ $pos .= $1;
+ if (memberOf($pos, &quot;l&quot;, &quot;r&quot;)) {
+ if (s/^(\w{1})\s*//) {
+ my $np = $1;
+ if (memberOf($np, &quot;t&quot;, &quot;b&quot;, &quot;B&quot;)) {
+ $pos .= $np;
+ }
+ else {
+ if (memberOf($np, &quot;l&quot;, &quot;r&quot;)) {
+ PrintErrorMessage(&quot;$np can't follow 'l' or 'r'&quot;, $lc);
+ }
+ else {
+ PrintErrorMessage(&quot;$np is not a valid positioning option&quot;, $lc);
+ }
+ next LINE;
+ }
+ }
+ }
+ elsif (memberOf($pos, &quot;t&quot;, &quot;b&quot;, &quot;B&quot;)) {
+ if (s/^(\w{1})\s*//) {
+ my $np = $1;
+ if (memberOf($np, &quot;l&quot;, &quot;r&quot;)) {
+ $pos .= $np;
+ }
+ else {
+ if (memberOf($np, &quot;t&quot;, &quot;b&quot;, &quot;B&quot;)) {
+ PrintErrorMessage(&quot;$np can't follow 't', 'b', or 'B'&quot;, $lc);
+ }
+ else {
+ PrintErrorMessage(&quot;$np is not a valid positioning option&quot;, $lc);
+ }
+ next LINE;
+ }
+ }
+ }
+ else {
+ PrintErrorMessage(&quot;$pos is not a valid positioning option&quot;, $lc);
+ next LINE;
+ }
+ }
+ else {
+ PrintErrorMessage(&quot;illegal token in optional part of text command&quot;,$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>&lt;process <tt>const</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ do{
+ s/\s*//;
+ PrintErrorMessage(&quot;no identifier found after token const&quot;,$lc)
+ if $_ !~ s/^([^\W\d_]\d{0,3})//i;
+ my $Constname = $1;
+ my $constname = lc($Constname);
+ if (exists $ConstTable{$constname}) {
+ PrintErrorMessage(&quot;Redefinition of constant $constname&quot;,$lc);
+ }
+ s/\s*//; #remove leading white space
+ PrintErrorMessage(&quot;did not find expected = sign&quot;,$lc)
+ if $_ !~ s/^[=]//i;
+ my $val = expr($lc);
+ $VarTable{$constname} = $val;
+ $ConstTable{$constname} = 1;
+ print OUT &quot;%% $Constname = $val\n&quot; if $comments_on;
+ }while (s/^,//);
+ chk_comment($lc);
+ s/\s*//;
+ if (/^[^%]/) {
+ PrintWarningMessage(&quot;Trailing text is ignored&quot;,$lc);
+ }
+
+</pre><p>The <code>var</code> command is used to store values into a comma separated
+list of named variables. Variable names have the same format as point names,
+<a name="NWD21HcNW-1c">i.e., they start with a letter and are followed by up to two digits. The</a>
+whole operation is performed by a <code>do-while</code> construct that checks that
+there is a valid variable name, a <code>=</code> sign, and an expression. The
+<code>do-while</code> construct terminates if the next token isn't a comma. The variable
+<code>$Varname</code> is used to store the initial variable name, while we store
+in the variable <code>$varname</code> the lowercase version of the variable name.
+The last thing we do is to check whether there is a trailing comment.
+In case there, we simply ignore itl; otherwise we print a warning message.
+
+<pre><a name="NW21HcNW-2NFa6I-1" href="#NWD21HcNW-1c"><dfn>&lt;process <tt>var</tt> command&gt;=</dfn></a> <b>(<a href="#NWD21HcNW-q">&lt;-U</a>)</b>
+ do{
+ s/\s*//;
+ PrintErrorMessage(&quot;no identifier found after token var&quot;,$lc)
+ if $_ !~ s/^([^\W\d_]\d{0,3})//i;
+ my $Varname = $1;
+ my $varname = lc($Varname);
+ if (exists $ConstTable{$varname}) {
+ PrintErrorMessage(&quot;Redefinition of constant $varname&quot;,$lc);
+ }
+ s/\s*//; #remove leading white space
+ PrintErrorMessage(&quot;did not find expected = sign&quot;,$lc)
+ if $_ !~ s/^[=]//i;
+ my $val = expr($lc);
+ $VarTable{$varname} = $val;
+ print OUT &quot;%% $Varname = $val\n&quot; if $comments_on;
+ }while (s/^,//);
+ chk_comment($lc);
+ s/\s*//;
+ if (/^[^%]/) {
+ PrintWarningMessage(&quot;Trailing text is ignored&quot;,$lc);
+ }
+</pre>
+
+<ul>
+<li><a href="#NWD21HcNW-2"><i>&lt;*&gt;</i></a>: <a href="#NWD21HcNW-2">D1</a>
+<li><a href="#NWD21HcNW-4"><i>&lt;Check for command line arguments&gt;</i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-4">D2</a>
+<li><a href="#NWD21HcNW-6"><i>&lt;Check if .m file exists&gt;</i></a>: <a href="#NWD21HcNW-4">U1</a>, <a href="#NWD21HcNW-6">D2</a>
+<li><a href="#NWD21HcNW-8"><i>&lt;Define global variables&gt;</i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-8">D2</a>
+<li><a href="#NWD21HcNW-1D"><i>&lt;generate plot area related commands&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1D">D2</a>
+<li><a href="#NWD21HcNW-1G"><i>&lt;generate the rest of the code for the <tt>paper</tt> command&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1G">D2</a>
+<li><a href="#NWD21HcNW-3"><i>&lt;package <tt>DummyFH</tt> &gt;</i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-3">D2</a>
+<li><a href="#NWD21HcNW-t"><i>&lt;process <tt>angle</tt> part of command&gt;</i></a>: <a href="#NWD21HcNW-s">U1</a>, <a href="#NWD21HcNW-t">D2</a>
+<li><a href="#NWD21HcNW-1V"><i>&lt;process <tt>ArrowShape</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1V">D2</a>
+<li><a href="#NWD21HcNW-1E"><i>&lt;process <tt>axis</tt> part&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1E">D2</a>
+<li><a href="#NWD21HcNW-1N"><i>&lt;process <tt>circumcircleCenter</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1N">D2</a>
+<li><a href="#NWD21HcNW-1b"><i>&lt;process <tt>const</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1b">D2</a>
+<li><a href="#NWD21HcNW-r"><i>&lt;process <tt>dasharray</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-r">D2</a>
+<li><a href="#NWD21HcNW-s"><i>&lt;process <tt>drawAngleArcOrArrow</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-s">D2</a>
+<li><a href="#NWD21HcNW-v"><i>&lt;process <tt>drawcircle</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-v">D2</a>
+<li><a href="#NWD21HcNW-w"><i>&lt;process <tt>drawcircumcircle</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-w">D2</a>
+<li><a href="#NWD21HcNW-x"><i>&lt;process <tt>drawexcircle</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-x">D2</a>
+<li><a href="#NWD21HcNW-y"><i>&lt;process <tt>drawincircle</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-y">D2</a>
+<li><a href="#NWD21HcNW-z"><i>&lt;process <tt>drawPerpendicular</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-z">D2</a>
+<li><a href="#NWD21HcNW-10"><i>&lt;process <tt>drawpoint</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-10">D2</a>
+<li><a href="#NWD21HcNW-11"><i>&lt;process <tt>drawRightAngle</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-11">D2</a>
+<li><a href="#NWD21HcNW-12"><i>&lt;process <tt>drawsquare</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-12">D2</a>
+<li><a href="#NWD21HcNW-1P"><i>&lt;process <tt>ExcircleCenter</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1P">D2</a>
+<li><a href="#NWD21HcNW-1O"><i>&lt;process <tt>IncircleCenter</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1O">D2</a>
+<li><a href="#NWD21HcNW-13"><i>&lt;process <tt>inputfile*</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-13">D2</a>
+<li><a href="#NWD21HcNW-14"><i>&lt;process <tt>inputfile</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-14">D2</a>
+<li><a href="#NWD21HcNW-1K"><i>&lt;process <tt>intersection</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1K">D2</a>
+<li><a href="#NWD21HcNW-15"><i>&lt;process <tt>linethickness</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-15">D2</a>
+<li><a href="#NWD21HcNW-1L"><i>&lt;process <tt>midpoint</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1L">D2</a>
+<li><a href="#NWD21HcNW-16"><i>&lt;process <tt>paper</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-16">D2</a>
+<li><a href="#NWD21HcNW-1J"><i>&lt;process <tt>perpendicular</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1J">D2</a>
+<li><a href="#NWD21HcNW-1H"><i>&lt;process <tt>point/point*</tt> commands&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1H">D2</a>
+<li><a href="#NWD21HcNW-1M"><i>&lt;process <tt>pointonline</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1M">D2</a>
+<li><a href="#NWD21HcNW-1W"><i>&lt;process <tt>PointSymbol</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1W">D2</a>
+<li><a href="#NWD21HcNW-1R"><i>&lt;process <tt>polar</tt> case&gt;</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>&lt;process <tt>radius</tt> part of command&gt;</i></a>: <a href="#NWD21HcNW-s">U1</a>, <a href="#NWD21HcNW-u">D2</a>
+<li><a href="#NWD21HcNW-1S"><i>&lt;process <tt>rotate</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1S">D2</a>
+<li><a href="#NWD21HcNW-1Q"><i>&lt;process <tt>shift</tt> case&gt;</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>&lt;process <tt>showAngle</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1A">D2</a>
+<li><a href="#NWD21HcNW-1B"><i>&lt;process <tt>showArea</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1B">D2</a>
+<li><a href="#NWD21HcNW-1C"><i>&lt;process <tt>showLength</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1C">D2</a>
+<li><a href="#NWD21HcNW-1X"><i>&lt;process <tt>system</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1X">D2</a>
+<li><a href="#NWD21HcNW-1Y"><i>&lt;process <tt>text</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1Y">D2</a>
+<li><a href="#NWD21HcNW-1F"><i>&lt;process <tt>ticks</tt> part&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-1F">D2</a>
+<li><a href="#NWD21HcNW-17"><i>&lt;process <tt>unit</tt> part&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-17">D2</a>
+<li><a href="#NWD21HcNW-1c"><i>&lt;process <tt>var</tt> command&gt;</i></a>: <a href="#NWD21HcNW-q">U1</a>, <a href="#NWD21HcNW-1c">D2</a>
+<li><a href="#NWD21HcNW-1T"><i>&lt;process <tt>vector</tt> case&gt;</i></a>: <a href="#NWD21HcNW-1I">U1</a>, <a href="#NWD21HcNW-1T">D2</a>
+<li><a href="#NWD21HcNW-18"><i>&lt;process <tt>xrange</tt> part&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-18">D2</a>
+<li><a href="#NWD21HcNW-19"><i>&lt;process <tt>yrange</tt> part&gt;</i></a>: <a href="#NWD21HcNW-16">U1</a>, <a href="#NWD21HcNW-19">D2</a>
+<li><a href="#NWD21HcNW-5"><i>&lt;Process command line arguments&gt;</i></a>: <a href="#NWD21HcNW-4">U1</a>, <a href="#NWD21HcNW-5">D2</a>
+<li><a href="#NWD21HcNW-1I"><i>&lt;process coordinates&gt;</i></a>: <a href="#NWD21HcNW-1H">U1</a>, <a href="#NWD21HcNW-1I">D2</a>
+<li><a href="#NWD21HcNW-1Z"><i>&lt;process coordinates part of text command&gt;</i></a>: <a href="#NWD21HcNW-1Y">U1</a>, <a href="#NWD21HcNW-1Z">D2</a>
+<li><a href="#NWD21HcNW-7"><i>&lt;process file&gt;</i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-7">D2</a>
+<li><a href="#NWD21HcNW-q"><i>&lt;process input line&gt;</i></a>: <a href="#NWD21HcNW-p">U1</a>, <a href="#NWD21HcNW-q">D2</a>
+<li><a href="#NWD21HcNW-1a"><i>&lt;process optional part of text command&gt;</i></a>: <a href="#NWD21HcNW-1Y">U1</a>, <a href="#NWD21HcNW-1a">D2</a>
+<li><a href="#NWD21HcNW-1U"><i>&lt;process optional point shape part&gt;</i></a>: <a href="#NWD21HcNW-1H">U1</a>, <a href="#NWD21HcNW-1U">D2</a>
+<li><a href="#NWD21HcNW-W"><i>&lt;subroutine <tt>Angle</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-W">D2</a>
+<li><a href="#NWD21HcNW-K"><i>&lt;subroutine <tt>chk_comma</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-K">D2</a>
+<li><a href="#NWD21HcNW-L"><i>&lt;subroutine <tt>chk_comment</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-L">D2</a>
+<li><a href="#NWD21HcNW-G"><i>&lt;subroutine <tt>chk_lcb</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-G">D2</a>
+<li><a href="#NWD21HcNW-E"><i>&lt;subroutine <tt>chk_lparen</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-E">D2</a>
+<li><a href="#NWD21HcNW-I"><i>&lt;subroutine <tt>chk_lsb</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-I">D2</a>
+<li><a href="#NWD21HcNW-H"><i>&lt;subroutine <tt>chk_rcb</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-H">D2</a>
+<li><a href="#NWD21HcNW-F"><i>&lt;subroutine <tt>chk_rparen</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-F">D2</a>
+<li><a href="#NWD21HcNW-J"><i>&lt;subroutine <tt>chk_rsb</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-J">D2</a>
+<li><a href="#NWD21HcNW-S"><i>&lt;subroutine <tt>circumCircleCenter</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-S">D2</a>
+<li><a href="#NWD21HcNW-T"><i>&lt;subroutine <tt>ComputeDist</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-T">D2</a>
+<li><a href="#NWD21HcNW-d"><i>&lt;subroutine <tt>drawAngleArc</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-d">D2</a>
+<li><a href="#NWD21HcNW-e"><i>&lt;subroutine <tt>drawAngleArrow</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-e">D2</a>
+<li><a href="#NWD21HcNW-Z"><i>&lt;subroutine <tt>drawarrows</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-Z">D2</a>
+<li><a href="#NWD21HcNW-b"><i>&lt;subroutine <tt>drawCurve</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-b">D2</a>
+<li><a href="#NWD21HcNW-Y"><i>&lt;subroutine <tt>DrawLineOrArrow</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-Y">D2</a>
+<li><a href="#NWD21HcNW-a"><i>&lt;subroutine <tt>drawlines</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-a">D2</a>
+<li><a href="#NWD21HcNW-c"><i>&lt;subroutine <tt>drawpoints</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-c">D2</a>
+<li><a href="#NWD21HcNW-l"><i>&lt;subroutine <tt>drawsquare</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-l">D2</a>
+<li><a href="#NWD21HcNW-X"><i>&lt;subroutine <tt>excircle</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-X">D2</a>
+<li><a href="#NWD21HcNW-f"><i>&lt;subroutine <tt>expr</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-f">D2</a>
+<li><a href="#NWD21HcNW-N"><i>&lt;subroutine <tt>get_point</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-N">D2</a>
+<li><a href="#NWD21HcNW-i"><i>&lt;subroutine <tt>get_string</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-i">D2</a>
+<li><a href="#NWD21HcNW-V"><i>&lt;subroutine <tt>IncircleCenter</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-V">D2</a>
+<li><a href="#NWD21HcNW-U"><i>&lt;subroutine <tt>intersection4points</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-U">D2</a>
+<li><a href="#NWD21HcNW-j"><i>&lt;subroutine <tt>is_tainted</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-j">D2</a>
+<li><a href="#NWD21HcNW-P"><i>&lt;subroutine <tt>Length</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-P">D2</a>
+<li><a href="#NWD21HcNW-g"><i>&lt;subroutine <tt>memberOf</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-g">D2</a>
+<li><a href="#NWD21HcNW-A"><i>&lt;subroutine <tt>mpp</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-A">D2</a>
+<li><a href="#NWD21HcNW-k"><i>&lt;subroutine <tt>noOfDigits</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-k">D2</a>
+<li><a href="#NWD21HcNW-O"><i>&lt;subroutine <tt>perpendicular</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-O">D2</a>
+<li><a href="#NWD21HcNW-R"><i>&lt;subroutine <tt>pointOnLine</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-R">D2</a>
+<li><a href="#NWD21HcNW-M"><i>&lt;subroutine <tt>print_headers</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-M">D2</a>
+<li><a href="#NWD21HcNW-B"><i>&lt;subroutine <tt>PrintErrorMessage</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-B">D2</a>
+<li><a href="#NWD21HcNW-D"><i>&lt;subroutine <tt>PrintFatalError</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-D">D2</a>
+<li><a href="#NWD21HcNW-C"><i>&lt;subroutine <tt>PrintWarningMessage</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-C">D2</a>
+<li><a href="#NWD21HcNW-p"><i>&lt;subroutine <tt>process_input</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-p">D2</a>
+<li><a href="#NWD21HcNW-o"><i>&lt;subroutine <tt>setLineThickness</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-o">D2</a>
+<li><a href="#NWD21HcNW-n"><i>&lt;subroutine <tt>sp2X</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-n">D2</a>
+<li><a href="#NWD21HcNW-h"><i>&lt;subroutine <tt>tand</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-h">D2</a>
+<li><a href="#NWD21HcNW-Q"><i>&lt;subroutine <tt>triangleArea</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-Q">D2</a>
+<li><a href="#NWD21HcNW-m"><i>&lt;subroutine <tt>X2sp</tt> &gt;</i></a>: <a href="#NWD21HcNW-9">U1</a>, <a href="#NWD21HcNW-m">D2</a>
+<li><a href="#NWD21HcNW-9"><i>&lt;subroutine definitions&gt;</i></a>: <a href="#NWD21HcNW-2">U1</a>, <a href="#NWD21HcNW-9">D2</a>
+</ul>
+</body></html>
+