#!/usr/bin/perl -w # CABpict.pl # (c) Copyright 2006 by H. Moeller (mollerh@math.uni-muenster.de). # Version 1.2 for Cabri-gˇom¸tre II with MacOS 9.x, Virtual Printer as PostScript driver, MacPerl 5.6, and LATEX-packages 'pict2e' and 'ebezier'. # This program may be distributed and/or modified under the conditions of the LaTeX Project Public License, either version 1.3 of this license or (at your option) any later version. # The latest version of this license is in http://www.latex-project.org/lppl.txt. # This program has the LPPL maintenance status "maintained". The Current Maintainer of this program is H. Möller. # use POSIX('ceil','floor'); #________________________________________________________ # Definable by the user: # Unitlength in pt: $ul = 1.0; # Fill factor (for filling with magnification up to 500%) $fillf = 5; # Point factor: $pointf = 0.3; # Flag for the dotting of parabolic arcs (1: Dotting) $Qbezflag = 0; #________________________________________________________ # Constants: # Color names: $yellow = "0.9843900.9511410.020249"; $orange = "1.0000000.3927370.009949"; $red = "0.8649270.0342110.025910"; $purple = "0.9486080.0325630.519234"; $violet = "0.2769050.0000000.645487"; $navy = "0.0000000.0000000.828138"; $blue = "0.0088040.6692610.917967"; $green = "0.1215990.7170980.078874"; $darkgreen = "0.0000000.3933010.069093"; $darkbrown = "0.3359430.1742730.020081"; $brown = "0.5657890.4428780.227359"; #________________________________________________________ # Further Constants: # Pi: $Pi = "3.14159265358979"; # Floor of the tenth part of the greatest integer of Perl $gi = 214748364; # Constants in dotted figures: $uli = sp(4 / $ul); $ule = sp(0.8 / $ul); #________________________________________________________ @lines = <>; do { $_ = $lines[$i++]; if (/ setrgbcolor \s/o) { s/ //go; s/setrgbcolor\s/ /o; $c = $_; $_ = $lines[$i++]; s/ moveto//o; s/lineto stroke/stroke/o; s/curveto stroke/curveto/o; s/ setlinewidth stroke//o; s/ lineto//go; if (/stroke/o) { $line[++$#line] = $c.$_; } elsif (/closepath fill/o) { $vector[++$#vector] = $c.$_; } elsif (/arc /o) { $circle[++$#circle] = $c.$_; } elsif (/arcn/o) { $arc[++$#arc] = $c.$_; } elsif (/curveto/o) { do { $conic[++$#conic] = $c.$_; $_ = $lines[$i++]; s/ moveto//o; s/curveto stroke/curveto/o; } until $_ !~ /curveto/o; } } } until $i == $#lines; # $pflag = 1; $sflag = 1; $thicknessflag = 1; $coun = 0; $xtex = ""; $mtex = ""; #________________________________________________________ # Lines and polygons $cflag = 1; foreach (@line) { @coo = split; $co0 = $coo[0]; $co2 = (-1) * $coo[2]; $co4 = (-1) * $coo[4]; if (($co0 ne $violet) and ($co0 ne $yellow)) { if ($cflag) { $xtex .= "%Lines, arrows, polygons and Bezier curves\n"; $cflag = 0; } if ($co0 ne $blue) { bound($coo[1],$co2); bound($coo[3],$co4); } if (($co0 ne $red) and ($co0 ne $blue) and ($co0 ne $brown) and ($co0 ne $darkbrown) and ($co0 ne $navy)) { lin($co0,$coo[1],$co2,$coo[3],$co4); } if (($co0 ne $green) and ($co0 ne $darkgreen)) { if ($pflag) { $cb1 = $coo[1]; $cb2 = $co2; $pol = $co0." ".$cb1." ".$cb2; $pflag = 0; } else { $pol .= " ".$coo[1]." ".$co2; if (abs($coo[3] - $cb1) + abs($co4 - $cb2) < 2.0E-6) { $poly[++$#poly] = $pol; $pflag = 1; } } } } if ($co0 eq $violet) { $xtex .= "%Arrow\n"; bound($coo[1],$co2); bound($coo[3],$co4); $dx = $coo[3] - $coo[1]; $dy = $co4 - $co2; $len = sp(abs($dx)); if ($len > 1.0E-3) { @p = best(abs($dy / $dx)); $psx = sp($p[1]) * ($dx <=> 0); $psy = sp($p[0]) * ($dy <=> 0); } else { $psx = 0; $psy = ($dy <=> 0); $len = sp(abs($dy)); } $xb = sp($coo[1]); $yb = sp($co2); if (not $thicknessflag) { $xtex .= "\\linethickness{0.8pt}\n"; $thicknessflag = 1; } $xtex .= "\\put(".$xb.",".$yb."){\\vector(".$psx.",".$psy."){".$len."}}\n"; } } # foreach (@poly) { @po = split; $p0 = $po[0]; $pon = $#po; if (($p0 eq $red) or ($p0 eq $purple) or ($p0 eq $darkbrown) or ($p0 eq $orange) or ($p0 eq $brown)) { if ($pon == 6) { tri($p0,$po[1],$po[2],$po[3],$po[4],$po[5],$po[6]); } elsif ($pon == 8) { ($p0,$u1,$v1,$u2,$v2,$u3,$v3,$u4,$v4) = @po; $s1 = abs($u1 - $u4) + abs($u2 - $u3) + abs($v1 - $v2) + abs($v3 -$v4); $s2 = abs($u1 - $u2) + abs($u3 - $u4) + abs($v1 - $v4) + abs($v2 -$v3); if (($s1 < 4.0E-6) or ($s2 < 4.0E-6)) { bound($u1,$v1); bound($u3,$v3); rect($p0,$u1,$v1,$u2,$v2,$u3,$v3,$u4,$v4); } else { bound($u1,$v1); bound($u2,$v2); bound($u3,$v3); bound($u4,$v4); tri($p0,$u1,$v1,$u2,$v2,$u3,$v3); tri($p0,$u1,$v1,$u3,$v3,$u4,$v4); } } elsif ($pon > 8) { bound($po[1],$po[2]); for (my $j = 3; $j <= $pon - 3; $j += 2) { bound($po[$j],$po[$j + 1]); tri($p0,$po[1],$po[2],$po[$j],$po[$j + 1],$po[$j + 2],$po[$j + 3]); } bound($po[$pon - 1],$po[$pon]); } } elsif ($p0 eq $navy) { for (my $j = 1; $j <= $pon - 3; $j +=2) { lin($p0,$po[$j],$po[$j + 1],$po[$j + 2],$po[$j + 3]); } } elsif ($p0 eq $blue) { if ($pon == 4) { # Text marker and Bezier curves $coun++; $bo3 = $po[1] + ($po[3] - $po[1]) / $ul; $bo4 = $po[2] + ($po[4] - $po[2]) / $ul; bound($po[1],$po[2]); bound($bo3,$bo4); $po1 = sp($po[1]); $po2 = sp($po[2]); $mtex .= "\\put(".$po1.",".$po2."){".$coun."}\n"; } elsif ($pon == 6) { $xtex .= "%Quadratic Bezier curve\n"; qbez($po[1],$po[2],$po[3],$po[4],$po[5],$po[6]); } elsif ($pon == 8) { $xtex .= "%Cubic Bezier curve\n"; cbez($po[1],$po[2],$po[3],$po[4],$po[5],$po[6],$po[7],$po[8]); } } } #________________________________________________________ # Arrows foreach (@vector) { @ve = split; if ($ve[0] eq $darkgreen) { if ($cflag) { $xtex .= "%Arrow\n"; $cflag = 0; } $ve[2] = (-1) * $ve[2]; $ve[4] = (-1) * $ve[4]; $ve[6] = (-1) * $ve[6]; $ve[8] = (-1) * $ve[8]; bound($ve[1],$ve[2]); bound($ve[3],$ve[4]); bound($ve[7],$ve[8]); $vu0 = $ve[5] + ($ve[1] - $ve[5]) / $ul; $vu1 = $ve[6] + ($ve[2] - $ve[6]) / $ul; $vu2 = $ve[5] + ($ve[3] - $ve[5]) / $ul; $vu3 = $ve[6] + ($ve[4] - $ve[6]) / $ul; $vu6 = $ve[5] + ($ve[7] - $ve[5]) / $ul; $vu7 = $ve[6] + ($ve[8] - $ve[6]) / $ul; tri($red,$vu0,$vu1,$vu2,$vu3,$ve[5],$ve[6]); tri($red,$vu0,$vu1,$vu6,$vu7,$ve[5],$ve[6]); } } #________________________________________________________ # Conics $cflag = 1; foreach (@conic) { @po = split; $p0 = $po[0]; if ($p0 ne $yellow) { if ($cflag) { $xtex .= "%Conics\n"; $cflag = 0; } $po[2] = (-1) * $po[2]; $po[4] = (-1) * $po[4]; $po[6] = (-1) * $po[6]; $po[8] = (-1) * $po[8]; cbez($po[1],$po[2],$po[3],$po[4],$po[5],$po[6],$po[7],$po[8]); } } #________________________________________________________ # Circles, halves and quarters of circles $cflag = 1; $aflag = 1; foreach (@circle) { @po = split; $p0 = $po[0]; if ($p0 ne $yellow) { $po[2] = (-1) * $po[2]; $di = 2 * $po[3]; if ($po[4] > 1.0E-3 or abs($po[5] - 360) > 1.0E-3) { if ($aflag) { $xtex .= "%Arcs\n"; $aflag = 0; } $arce = ($po[4] > 0) ? 360 - $po[4] : 0; $arcb = ($po[5] > 0) ? 360 - $po[5] : 0; $darc = $arce - $arcb; if ($darc < 0) {$darc += 360} $quar = int($darc / 90); if ($quar > 0) { for (my $k = 1; $k <= $quar; $k++) { arc($p0,$po[1],$po[2],$po[3],$arcb,$arcb + 90); $arcb += 90; if ($arcb > 360) {$arcb -= 360} } } if ($darc > $quar * 90) { arc($p0,$po[1],$po[2],$po[3],$arcb,$arce); } } else { if ($cflag) { $xtex .= "%Circles, halves and quarters of circles\n"; $cflag = 0; } if ($p0 eq $navy) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\circle{".$di."}}\n"; bound($po[1] + $po[3],$po[2] + $po[3]); bound($po[1] + $po[3],$po[2] - $po[3]); bound($po[1] - $po[3],$po[2] + $po[3]); bound($po[1] - $po[3],$po[2] - $po[3]); } elsif ($p0 eq $purple) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[l]}\n"; bound($po[1],$po[2] + $po[3]); bound($po[1] - $po[3],$po[2] - $po[3]); } elsif ($p0 eq $red) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[r]}\n"; bound($po[1],$po[2] - $po[3]); bound($po[1] + $po[3],$po[2] + $po[3]); } elsif ($p0 eq $orange) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[b]}\n"; bound($po[1] - $po[3],$po[2] - $po[3]); bound($po[1] + $po[3],$po[2]); } elsif ($p0 eq $darkbrown) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[t]}\n"; bound($po[1] - $po[3],$po[2]); bound($po[1] + $po[3],$po[2] + $po[3]); } elsif ($p0 eq $blue) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[bl]}\n"; bound($po[1] - $po[3],$po[2]); bound($po[1],$po[2] - $po[3]); } elsif ($p0 eq $green) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[tl]}\n"; bound($po[1] - $po[3],$po[2]); bound($po[1],$po[2] + $po[3]); } elsif ($p0 eq $brown) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[br]}\n"; bound($po[1],$po[2] - $po[3]); bound($po[1] + $po[3],$po[2]); } elsif ($p0 eq $violet) { $xtex .= "\\put(".$po[1].",".$po[2]."){\\oval[".$di."](".$di.",".$di.")[tr]}\n"; bound($po[1] + $po[3],$po[2]); bound($po[1],$po[2] + $po[3]); } elsif ($p0 eq $darkgreen) { $r = $po[3]; $le = int(2 * $pointf * $ul * $Pi * $r); $xtex .= "\\cCircle[".$le."](".$po[1].",".$po[2]."){".$r."}[f]\n"; bound($po[1] + $r,$po[2] + $r); bound($po[1] + $r,$po[2] - $r); bound($po[1] - $r,$po[2] + $r); bound($po[1] - $r,$po[2] - $r); } } } } #________________________________________________________ # Arcs $aflag = 1; foreach (@arc) { @po = split; if ($aflag) { $xtex .= "%Arcs\n"; $aflag = 0; } $po[2] = (-1) * $po[2]; $arcb = ($po[4] > 0) ? 360 - $po[4] : 0; $arce = ($po[5] > 0) ? 360 - $po[5] : 0; $darc = $arce - $arcb; if ($darc < 0) {$darc += 360} $quar = int($darc / 90); if ($quar > 0) { for (my $k = 1; $k <= $quar; $k++) { arc($po[0],$po[1],$po[2],$po[3],$arcb,$arcb + 90); $arcb += 90; if ($arcb > 360) {$arcb -= 360} } } if ($darc > $quar * 90) { arc($po[0],$po[1],$po[2],$po[3],$arcb,$arce); } } #________________________________________________________ # Frame if ($xtex . $mtex ne "") { $xtex = "\\documentclass{article}\n\\usepackage{ebezier}\n". "\\usepackage[pstarrows]{pict2e}\n\n\\begin{document}\n\n". "\\setlength{\\unitlength}{".$ul."pt}\n". "\\begin{picture}(".ceil(($xmax - $xmin)).",". ceil(($ymax - $ymin)).")(".floor($xmin).",".floor($ymin).")\n". "\\linethickness{0.8pt}\n"."\\thicklines\n".$xtex; $xtex .= $mtex."\\end{picture}\n\n\\end{document}"; } print $xtex."\n"; #________________________________________________________ # Best pair for the slope of a line sub best { my $x = shift; if ($x > 1000) { return (1,0); } elsif ($x < 1.0E-3) { return (0,1); } else { if ($x =~ (/^\d+$/)) { return ($x,1); } else { $num1 = floor($x); $den1 = 1; $y = $x; while (($y =~ (/\D+/)) and ($num1 <= $gi) and ($den1 <= $gi)) { $y *= 10; $num1 = floor($y); $den1 *= 10; } $r0 = $num1; $r1 = $den1; $q1 = 1; @li = (0); while ($r1 != 0) { $q1 = floor($r0 / $r1); $r2 = ($r0 % $r1); $r0 = $r1; $r1 = $r2; $li[++$#li] = $q1; } $num1 = $num1 / $r0; $den1 = $den1 / $r0; if ($num1 <= 1000 and $den1 <= 1000) { return ($num1,$den1); } else { $n = $#li; @num = (1,$li[1]); @den = (0,1); $bnum = $li[1]; $bden = 1; $i = 2; $numh = 0; $denh = 0; while (($numh <= 1000 and $denh <= 1000) and $i <= $n) { $c = ($li[$i] >> 1); if (($li[$i] % 2) == 1) { $c++; } else { $j = 1; while (($i - $j >= 1 and $i + $j <= $n) and $li[$i - $j] == $li[$i + $j]) { $j++; } $dj = $i - $j; $sj = $i + $j; if (($dj >= 1 and $sj <= $n) and $li[$dj] != $li[$sj]) { $c += (($j + (($li[$sj] < $li[$dj]) ? 0 : 1)) % 2); } elsif ($dj == 0 and $sj <= $n) { $c += ($j % 2); } elsif ($dj >= 1 and $sj == $n + 1) { $c += (($j + 1) % 2); } elsif (($dj == 0 and $sj == $n + 1) or ($dj == 2 and $sj == $n and $li[1] == 1 and $li[2] + 1 == $li[$n]) or ($dj == 1 and $sj == $n - 1 and $li[$n] == 1 and $li[$n - 1] + 1 == $li[1])) { $c++; } } $k = $c; while ($k <= $li[$i]) { $numh = $k * $num[$i - 1] + $num[$i - 2]; $denh = $k * $den[$i - 1] + $den[$i - 2]; if ($numh > 1000 or $denh > 1000) { last; } $bnum = $numh; $bden = $denh; if ($k == $li[$i]) { $num[$i] = $numh; $den[$i] = $denh; } $k++; } $i++; } return ($bnum,$bden); } } } } #________________________________________________________ # Lines sub lin { my ($c,$xb,$yb,$xe,$ye) = @_; if (($c eq $green) or ($c eq $orange) or ($c eq $purple) or ($c eq $navy)) { $dx = $xe - $xb; $dy = $ye - $yb; $le = abs($dx); if ($le > 1.0E-3) { @p = best(abs($dy / $dx)); $psx = sp($p[1]) * ($dx <=> 0); $psy = sp($p[0]) * ($dy <=> 0); } else { $psx = 0; $psy = ($dy <=> 0); $le = abs($dy); } $xbu = sp($xb); $ybu = sp($yb); $leu = sp($le); $xtex .= "\\put(".$xbu.",".$ybu."){\\line(".$psx.",".$psy."){".$leu."}}\n"; } elsif ($c eq $darkgreen) { # Dotted line if ($thicknessflag) { $xtex .= "%Dotted line\n\\linethickness{1.2pt}\n"; $thicknessflag = 0; } $le = floor($pointf * $ul * (sqrt(($xe - $xb)**2 + ($ye - $yb)**2))); if ($le > 0) { $xbu = sp($xb); $ybu = sp($yb); $xeu = sp($xe); $yeu = sp($ye); $xtex .= "\\Lbezier[".$le."](".$xbu.",".$ybu.")(".$xeu.",".$yeu.")\n"; } } } #________________________________________________________ # Triangles sub tri { my ($q0,$qx1,$qy1,$qx2,$qy2,$qx3,$qy3) = @_; $qx1 = $qx1 * $ul; $qy1 = $qy1 * $ul; $qx2 = $qx2 * $ul; $qy2 = $qy2 * $ul; $qx3 = $qx3 * $ul; $qy3 = $qy3 * $ul; if ($q0 eq $red) { # Filled triangle %ha = ($qx1,$qy1,$qx2+1e-07,$qy2+1e-07,$qx3+2e-07,$qy3+2e-07); @hb = (); @hc = (); foreach (sort { $ha{$a} <=> $ha{$b} } keys %ha) { $hb[++$#hb] = $_; $hc[++$#hc] = $ha{$_}; } ($qx1,$qx2,$qx3) = @hb; ($qy1,$qy2,$qy3) = @hc; $lin = int(($qy3 - $qy1) * $fillf); $xtex .= "%Filled triangle\n\\linethickness{0.1pt}\n"; $si = ($qy3 - $qy1) * $qx2 - ($qx3 - $qx1) * $qy2 - $qx1 * $qy3 + $qx3 * $qy1 <=> 0; $dex = ($qx3 - $qx1) / ($qy3 - $qy1) / $fillf; $d1 = $qy2 - $qy1; $d2 = $qy3 - $qy2; if ($d1 >= 1.0E-3) { $fx1 = ($qx2 - $qx1) / $d1; $sx1 = $qx1 - $qy1 * $fx1; } if ($d2 >= 1.0E-3) { $fx2 = ($qx3 - $qx2) / $d2; $sx2 = $qx2 - $qy2 * $fx2; } for ($k = 1; $k <= $lin; $k++) { $xb = $qx1 + $k * $dex; $yb = $qy1 + $k / $fillf; if ($yb <= $qy2) { if ($d1 >= 1.0E-3) { $leu = sp((abs($sx1 + $yb * $fx1 - $xb) + 0.5)/ $ul); } else { $leu = sp((abs($qx2 - $qx1) + 0.5)/ $ul); } } else { if ($d2 >= 1.0E-3) { $leu = sp((abs($sx2 + $yb * $fx2 - $xb) + 0.5)/ $ul); } else { $leu = sp((abs($qx3 - $qx2) + 0.5)/ $ul); } } if ($si > 0) { $xbu = sp($xb / $ul); } else { $xbu = sp($xb / $ul); } $ybu = sp($yb / $ul); $xtex .= "\\put(".$xbu.",".$ybu."){\\line(".$si.",0){".$leu."}}\n"; } $xtex .= "\\linethickness{0.8pt}\n"; } elsif (($q0 eq $purple) or ($q0 eq $darkbrown)) { # Dotted triangle %ha = ($qx1,$qy1,$qx2+1e-07,$qy2+1e-07,$qx3+2e-07,$qy3+2e-07); @hb = (); @hc = (); foreach (sort { $ha{$a} <=> $ha{$b} } keys %ha) { $hb[++$#hb] = $_; $hc[++$#hc] = $ha{$_}; } ($qx1,$qx2,$qx3) = @hb; ($qy1,$qy2,$qy3) = @hc; $xtex .= "%Dotted triangle\n"; $si = ($qy3 - $qy1) * $qx2 - ($qx3 - $qx1) * $qy2 - $qx1 * $qy3 + $qx3 * $qy1 <=> 0; $dy1 = 2 * ceil($qy1 / 2); $dy3 = 2 * floor($qy3 / 2); $lin = $dy3 - $dy1; $dex = ($qx3 - $qx1) / ($qy3 - $qy1); $xbh = $qx1 + ($dy1 - $qy1 - 2.0) * $dex; $dex = 2 * $dex; $d1 = $qy2 - $qy1; $d2 = $qy3 - $qy2; if ($d1 >= 1.0E-3) { $fx1 = ($qx2 - $qx1) / $d1; $sx1 = $qx1 + ($dy1 - $qy1) * $fx1; } if ($d2 >= 1.0E-3) { $fx2 = ($qx3 - $qx2) / $d2; $sx2 = $qx2 + ($dy1 - $qy2) * $fx2; } for ($k = 0; $k <= $lin; $k += 2) { $qy = $dy1 + $k; $xbh = $xbh + $dex; ($si > 0) ? ($xb = $xbh) : ($xe = $xbh); if ($qy <= $qy2) { ($d1 >= 1.0E-3) ? ($xeh = $sx1 + $k * $fx1) : ($xeh = $qx1); } else { ($d2 >= 1.0E-3) ? ($xeh = $sx2 + $k * $fx2) : ($xeh = $qx2); } ($si > 0) ? ($xe = $xeh) : ($xb = $xeh); $xb = 2 * ceil($xb / 2); $xbd = $xb + (($xb + $qy) % 4); ($xe >= $xbd) ? ($num = floor(($xe - $xbd) / 4) + 1) : ($num = 0); if (not $thicknessflag) { $xtex .= "\\linethickness{0.8pt}\n"; $thicknessflag = 1; } $xbu = sp($xbd / $ul); $qyu = sp($qy / $ul); $xtex .= "\\multiput(".$xbu.",".$qyu.")(".$uli.",0){".$num; $xtex .= "}{\\line(1,0){".$ule."}}\n"; } } elsif (($q0 eq $orange) or ($q0 eq $brown)) { # Hatched triangle $xtex .= "%Hatched triangle\n"; $d1 = $qx1 - $qy1; $d2 = $qx2 - $qy2; $d3 = $qx3 - $qy3; $qd1 = $d1; $qd2 = $d2; $qd3 = $d3; %ha = ($qx1,$qd1,$qx2+1e-07,$qd2+1e-07,$qx3+2e-07,$qd3+2e-07); @hb = (); foreach (sort { $ha{$a} <=> $ha{$b} } keys %ha) { $hb[++$#hb] = $_; } ($qx1,$qx2,$qx3) = @hb; %ha = ($qy1,$qd1,$qy2+1e-07,$qd2+1e-07,$qy3+2e-07,$qd3+2e-07); @hb = (); @hc = (); foreach (sort { $ha{$a} <=> $ha{$b} } keys %ha) { $hb[++$#hb] = $_; $hc[++$#hc] = $ha{$_}; } ($qy1,$qy2,$qy3) = @hb; ($d1,$d2,$d3) = @hc; $si = (-$qy3 + $qy1) * $qx2 + ($qx3 - $qx1) * $qy2 + $qx1 * $qy3 - $qx3 * $qy1 <=> 0; $p1 = 4 * ceil($d1 / 4); $p2 = 4 * floor($d2 / 4); $p3 = 4 * floor($d3 / 4); $fx1 = ($qx1 - $qx3) / ($d3 - $d1); $sx1 = $qx3 + $fx1 * $d3; $fy1 = ($qy1 - $qy3) / ($d3 - $d1); $sy1 = $qy3 + $fy1 * $d3; $d21 = $d2 - $d1; $d32 = $d3 - $d2; if ($d21 >= 1.0E-3) { $fx2 = ($qx1 - $qx2) / $d21; $sx2 = $qx2 + $fx2 * $d2; } if ($d32 >= 1.0E-3) { $fx3 = ($qx2 - $qx3) / $d32; $sx3 = $qx3 + $fx3 * $d3; } for ($k = $p1; $k <= $p3; $k += 4) { $xbk = $sx1 - $k * $fx1; $ybk = $sy1 - $k * $fy1; if ($k <= $p2) { ($d21 < 1.0E-3) ? ($le = abs($qx2 - $qx1)) : ($le = abs($sx2 - $k * $fx2 - $xbk)); } else { ($d32 < 1.0E-3) ? ($le = abs($qx3 - $qx2)) : ($le = abs($sx3 - $k * $fx3 - $xbk)); } $xbk = sp($xbk / $ul); $ybk = sp($ybk / $ul); $le = sp($le / $ul); $xtex .= "\\put(".$xbk.",".$ybk."){\\line(".$si.",".$si."){".$le."}}\n"; } } } #________________________________________________________ # Rectangles sub rect { my ($q0,$x1,$y1,$x2,$y2,$x3,$y3,$x4,$y4) = @_; $dx = abs($x2 - $x1); $dx = ($dx < 1.0E-6) ? abs($x3 -$x2) : $dx; $dx = $dx * $ul; $xb = ($x1 < $x2) ? (($x1 < $x3) ? $x1 : $x3) : (($x2 < $x3) ? $x2 : $x3); $xb = $xb * $ul; $dy = abs($y2 - $y1); $dy = ($dy < 1.0E-6) ? abs($y3 -$y2) : $dy; $dy = $dy * $ul; $yb = ($y1 < $y2) ? (($y1 < $y3) ? $y1 : $y3) : (($y2 < $y3) ? $y2 : $y3); $yb = $yb * $ul; $xe = $xb + $dx; $ye = $yb + $dy; # Filled rectangle if ($q0 eq $red) { $xtex .= "%Filled rectangle\n\\linethickness{0.1pt}\n"; $lin = 5 * $dx; if ($dy <= $dx) { $ybf = $yb - 0.2; $xbu = sp($xb / $ul); $dxu = sp($dx / $ul); for ($k = 0; $k <= $lin; $k++) { $ybf += 0.2; $ybu = sp($ybf / $ul); $xtex .= "\\put(".$xbu.",".$ybu."){\\line(1,0){".$dxu."}}\n"; } } else { $xbf = $xb - 0.2; $ybu = sp($yb / $ul); $dyu = sp($dy / $ul); for ($k = 0; $k <= $lin; $k++) { $xbf += 0.2; $xbu = sp($xbf / $ul); $xtex .= "\\put(".$xbu.",".$ybu."){\\line(0,1){".$dyu."}}\n"; } } $xtex .= "\\linethickness{0.8pt}\n"; } # Dotted rectangle elsif (($q0 eq $purple) or ($q0 eq $darkbrown)) { $xtex .= "%Dotted rectangle\n"; $xbb = 2 * ceil($xb / 2); $ybb = 2 * ceil($yb / 2); for ($k = 0; $k <= 2; $k += 2) { $ybd = $ybb + $k; $xbd = $xbb + (($xbb + $ybd) % 4); $numx = floor(($xe - 0.13 - $xbd) / 4) + 1; $numy = floor(($ye - 0.13 - $ybd) / 4) + 1; $xbu = sp($xbd / $ul); $ybu = sp($ybd / $ul); $xtex .= "\\multiput(".$xbu.",".$ybu.")(".$uli.",0){".$numx."}\n"; $xtex .= "{\\begin{picture}(0,0)\\multiput(0,0)(0,".$uli."){"; $xtex .= $numy."}\n{\\line(1,0){".$ule."}}\\end{picture}}\n"; } } # Hatched rectangle elsif (($q0 eq $orange) or ($q0 eq $brown)) { $xtex .= "%Hatched rectangle\n"; $p1 = 4 * ceil(($xb - $ye) / 4); if ($dx >= $dy) { $p2 = 4 * floor(($xb - $yb) / 4) + 4; $p3 = 4 * floor(($xe - $ye) / 4) + 4; $xp = $yb + $p2; $yp = $yb; $lp = $dy; $ip1 = 4; $ip2 = 0; } else { $p3 = 4 * floor(($xb - $yb) / 4) + 4; $p2 = 4 * floor(($xe - $ye) / 4) + 4; $xp = $xb; $yp = $xb - $p2; $lp = $dx; $ip1 = 0; $ip2 = -4; } $p4 = 4 * floor(($xe - $yb) / 4); for ($k = $p1; $k <= $p2 - 4; $k += 4) { $xbu = sp($xb / $ul); $ybu = sp(($xb - $k) / $ul); $le = sp(($ye - $xb + $k) / $ul); $xtex .= "\\put(".$xbu.",".$ybu."){\\line(1,1){".$le."}}\n"; } $np = ($p3 - $p2) / 4; if ($p3 > $p2) { $xpu = sp($xp / $ul); $ypu = sp($yp / $ul); $ip1u = sp($ip1 / $ul); $ip2u = sp($ip2 / $ul); $lpu = sp($lp / $ul - 0.1); $xtex .= "\\multiput(".$xpu.",".$ypu.")(".$ip1u.",".$ip2u; $xtex .= "){".$np."}{\\line(1,1){".$lpu."}}\n"; } for ($k = $p3; $k <= $p4; $k += 4) { $xbu = sp(($yb + $k) / $ul); $ybu = sp($yb / $ul); $leu = sp(($xe - $yb - $k) / $ul); $xtex .= "\\put(".$xbu.",".$ybu."){\\line(1,1){".$leu."}}\n"; } } } #________________________________________________________ # Quadratic Bezier curve sub qbez { my ($x1,$y1,$x2,$y2,$x3,$y3) = @_; my $xb = $x1; my $yb = $y1; my $len = 0.0; for ($t = 0.02; $t <= 1.0; $t += 0.02) { bound($xb,$yb); $s = 1.0 - $t; $xe = $s * ($s * $x1 + $t * $x2) + $t * ($s * $x2 + $t * $x3); $ye = $s * ($s * $y1 + $t * $y2) + $t * ($s * $y2 + $t * $y3); $len += sqrt(($xe - $xb)**2 + ($ye - $yb)**2); $xb = $xe; $yb = $ye; } bound($x3,$y3); $x1 = sp($x1); $y1 = sp($y1); $x2 = sp($x2); $y2 = sp($y2); $x3 = sp($x3); $y3 = sp($y3); if ($Qbezflag) { $le = int($pointf * $ul * $len); $xtex .= "\\Qbezier[".$le."](".$x1.",".$y1.")(".$x2.",".$y2; $xtex .= ")(".$x3.",".$y3.")\n"; } else { $xtex .= "\\qbezier(".$x1.",".$y1.")(".$x2.",".$y2; $xtex .= ")(".$x3.",".$y3.")\n"; } } #________________________________________________________ # Cubic Bezier curve sub cbez { my ($x1,$y1,$x2,$y2,$x3,$y3,$x4,$y4) = @_; my $xb = $x1; my $yb = $y1; for ($t = 0.02; $t <= 1.0; $t += 0.02) { bound($xb,$yb); $s = 1.0 - $t; $u1 = $s * $x1 + $t * $x2; $v1 = $s * $y1 + $t * $y2; $u2 = $s * $x2 + $t * $x3; $v2 = $s * $y2 + $t * $y3; $u3 = $s * $x3 + $t * $x4; $v3 = $s * $y3 + $t * $y4; $xe = $s * ($s * $u1 + $t * $u2) + $t * ($s * $u2 + $t * $u3); $ye = $s * ($s * $v1 + $t * $v2) + $t * ($s * $v2 + $t * $v3); $xb = $xe; $yb = $ye; } bound($x4,$y4); $x1 = sp($x1); $y1 = sp($y1); $x2 = sp($x2); $y2 = sp($y2); $x3 = sp($x3); $y3 = sp($y3); $x4 = sp($x4); $y4 = sp($y4); $xtex .= "\\cbezier(".$x1.",".$y1.")(".$x2.",".$y2.")(".$x3.",".$y3.")(".$x4.",".$y4.")\n"; } #________________________________________________________ # Short arcs sub arc { my ($col,$xm,$ym,$r,$al,$be) = @_; $al1 = $al * $Pi / 180; $be1 = $be * $Pi / 180; $dx1 = $r * cos($al1); $dy1 = $r * sin($al1); $dx4 = $r * cos($be1); $dy4 = $r * sin($be1); $x1 = $xm + $dx1; $y1 = $ym + $dy1; $x4 = $xm + $dx4; $y4 = $ym + $dy4; bound($x1,$y1); bound($x4,$y4); $gal = 90 * int($al / 90); $gbe = 90 * int($be / 90); if ($gal != $gbe) { if ($gbe == 0) { $gx1 = $r; $gy1 = 0; } elsif ($gbe == 90) { $gx1 = 0; $gy1 = $r; } elsif ($gbe == 180) { $gx1 = (-1) * $r; $gy1 = 0; } elsif ($gbe == 270) { $gx1 = 0; $gy1 = (-1) * $r; } bound($xm + $gx1,$ym + $gy1); } $aux = 4 * (2 * $r - sqrt(($dx1 + $dx4)**2 + ($dy1 + $dy4)**2)) / 3; $lam = $aux / sqrt(($dx1 - $dx4)**2 + ($dy1 - $dy4)**2); $x1u = sp($x1); $y1u = sp($y1); $x4u = sp($x4); $y4u = sp($y4); if ($col eq $darkgreen) { $d1 = abs($al1 - $be1); if ($d1 > $Pi) {$d1 = 2 * $Pi - $d1} $le = int($pointf * $d1 * $r * $ul); $xmu = sp($xm); $ymu = sp($ym); $xtex .= "\\cArcs[".$le."](".$xmu.",".$ymu.")(".$x1u.",".$y1u, $xtex .= ")(".$x4u.",".$y4u.")\n"; } else { $x2u = sp($x1 - $lam * $dy1); $y2u = sp($y1 + $lam * $dx1); $x3u = sp($x4 + $lam * $dy4); $y3u = sp($y4 - $lam * $dx4); $xtex .= "\\cbezier(".$x1u.",".$y1u.")(".$x2u.",".$y2u.")(".$x3u.","; $xtex .= $y3u.")(".$x4u.",".$y4u.")\n"; } } #________________________________________________________ # Bounding box sub bound { my ($xn,$yn) = @_; if ($sflag) { $xmin = $xn; $xmax = $xn; $ymin = $yn; $ymax = $yn; $sflag = 0; } else { if ($xn < $xmin) {$xmin = $xn} elsif ($xmax < $xn) {$xmax = $xn} if ($yn < $ymin) {$ymin = $yn} elsif ($ymax < $yn) {$ymax = $yn} } } #________________________________________________________ # Sprintf sub sp { my $x = shift; return sprintf("%.3f",$x) + 0; } #________________________________________________________