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# Copyright (c) 1997-2024
# Ewgenij Gawrilow, Michael Joswig, and the polymake team
# Technische Universität Berlin, Germany
# https://polymake.org
#
# This program is free software; you can redistribute it and/or modify it
# under the terms of the GNU General Public License as published by the
# Free Software Foundation; either version 2, or (at your option) any
# later version: http://www.gnu.org/licenses/gpl.txt.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#-------------------------------------------------------------------------------
REQUIRE graph::graphviz.rules
sub getRadius_sq {
my $vec = $_[0];
my $vec_sliced=$vec->slice(sequence(1, $vec->dim-1)); # cut off homog. 1
my $rad_sq=0;
foreach my $entry (@$vec_sliced) {
$rad_sq+=$entry*$entry;
}
return $rad_sq;
}
sub listOfRadii {
my $lp_reps = $_[0];
my %radii = ();
my $rad=-1;
for (my $i=0; $i<$lp_reps->rows; ++$i) {
$rad=sprintf( getRadius_sq($lp_reps->[$i]) );
my @list=();
if(exists($radii{$rad})) {
my $list_ref=$radii{$rad};
@list=@$list_ref;
}
push(@list,$i);
$radii{$rad}=\@list;
}
my @array = ();
my $count = 0;
foreach(keys %radii) {
my $list_ref=$radii{$_};
my @nodes=@$list_ref;
$array[$count]=new Pair<Int, Set<Int>>($_, new Set<Int>(@nodes));
++$count;
}
return new Array < Pair< Int,Set<Int> > >(\@array);
}
sub visualizeNOPGraph_sub {
my ($Graph,$colors_ref,$filename,$radii)=@_;
my $my_tmp=new Tempfile;
my $my_tmp_tred="${my_tmp}_tred";
graphviz($Graph->VISUAL(NodeColor=>$colors_ref),File=>"$my_tmp");
my $command_txt1 = "tred $my_tmp.dot > $my_tmp_tred.dot;";
$command_txt1 .= " sed \'\$d\' $my_tmp_tred.dot > $filename.dot\;";
system($command_txt1);
open DOT_FILE, ">>$filename.dot"
or die "cannot open file: $!";
my @my_radii=map {$_->first} @$radii;
my @sorted_radii=sort{$a<=>$b} (@my_radii);
print DOT_FILE << ".";
ranksep=1;
nodesep=0.25;
node [shape=plaintext, fontsize=14];
edge [shape=plaintext, fontsize=14];
/* radii */
.
for (my $i=$radii->size-1;$i>0;--$i) {
my $r=$sorted_radii[$i];
print DOT_FILE '"r^2='.$r.'"';
print DOT_FILE ' -> ';
}
print DOT_FILE '"r^2='.$sorted_radii[0].'";'."\n";
foreach ( @$radii ) {
print DOT_FILE '{'."\n rank = same\;\n";
my $r=$_->first;
print DOT_FILE '"r^2='.$r.'";';
foreach my $index(@{$_->second}) {
print DOT_FILE '"n'.$index.'"; '
}
print DOT_FILE "\n".'};'."\n";
}
print DOT_FILE "\n\n".'}'; # closing bracket was removed by sed
close DOT_FILE;
my $command_txt2 = "$Graphviz::dot -Tps -o$filename.ps $filename.dot; $Postscript::viewer $filename.ps \&";
system($command_txt2);
}
object_specialization Polytope::PointOrbit {
# @category Symmetry
# Visualizes the NOP-graph of an orbit polytope.
# Requires 'graphviz' and a Postscript viewer.
# Produces a file which is to be processed with
# the program 'dot' from the graphviz package.
# If 'dot' is installed, the NOP-graph is visualized
# by the Postscript viewer.
# @param String filename the filename for the 'dot' file
user_method VISUAL_NOP_GRAPH ($) : GROUP.COORDINATE_ACTION.NOP_GRAPH , GROUP.COORDINATE_ACTION.REPRESENTATIVE_CERTIFIERS , GROUP.COORDINATE_ACTION.CP_INDICES {
my ($orb, $filename) = @_;
my @colors = map {$orb->GROUP->COORDINATE_ACTION->CP_INDICES->contains($_) ? $Visual::Color::CorePointColor : $Visual::Color::NonCorePointColor} 0..$orb->GROUP->COORDINATE_ACTION->N_REPRESENTATIVE_CERTIFIERS-1;
my $radii = listOfRadii($orb->GROUP->COORDINATE_ACTION->REPRESENTATIVE_CERTIFIERS);
visualizeNOPGraph_sub($orb->GROUP->COORDINATE_ACTION->NOP_GRAPH,\@colors,$filename,$radii);
}
# @category Symmetry
# Visualizes all (nested) orbit polytopes contained in
# //orb// in one picture.
# @param ARRAY colors_ref the reference to an array of colors
# @param ARRAY trans_ref the reference to an array of transparency values
user_method VISUAL_NOP ($,$) : GROUP.COORDINATE_ACTION.NOP_GRAPH , GROUP.COORDINATE_ACTION.REPRESENTATIVE_CERTIFIERS , GROUP.COORDINATE_ACTION.CP_INDICES {
my ($orb, $colors_ref, $trans_ref) = @_;
my $N_reps = $orb->GROUP->COORDINATE_ACTION->N_REPRESENTATIVE_CERTIFIERS;
my @polys = ();
my @polys_degen = ();
if ($orb->AMBIENT_DIM > 4) {
die "visualizeNestedOPs: Cannot visualize orbit polytopes of dimension greater than 4!";
} else {
for (my $i = 0; $i < $N_reps; ++$i) {
my $p = new Polytope("GROUP.COORDINATE_ACTION.POINTS_GENERATORS"=>[$orb->GROUP->COORDINATE_ACTION->REPRESENTATIVE_CERTIFIERS->[$i]],"GROUP.COORDINATE_ACTION.GENERATORS"=>$orb->GROUP->COORDINATE_ACTION->GENERATORS);
if ($orb->AMBIENT_DIM == 4) {
my $proj = ortho_project($p);
if ($proj->DIM == 3) {
push(@polys,$proj);
} else {
push(@polys_degen,$proj);
}
} else {
if ($p->DIM == 3) {
push(@polys,$p);
} else {
push(@polys_degen,$p);
}
}
}
}
my @colors = @{$colors_ref};
if (scalar(@colors) < $N_reps) {
print "\nWarning: Number of specified colors is too small! Added default color 'red'.\n";
while (scalar(@colors) < $N_reps) {
push(@colors,"red");
}
}
my @trans = @{$trans_ref};
if (scalar(@trans) < $N_reps) {
print "\nWarning: Number of specified transparency values is too small! Added default transparency value '0.2'\n.";
while (scalar(@trans) < $N_reps) {
push(@trans,0.2);
}
}
compose((map{$polys[$_]->VISUAL(FacetTransparency=>$trans[$_],
FacetColor=>$colors[$_],
EdgeColor=>$colors[$_],
EdgeThickness=>2,
VertexThickness=>0.6,
VertexLabels=>[],
VertexColor=>$colors[$_]
)}0..$#polys),
(map{$polys_degen[$_]->VISUAL(
VertexThickness=>1,
VertexLabels=>[],
VertexColor=>$colors[$_+scalar(@polys)]
)}0..$#polys_degen)
);
}
}
# Local Variables:
# mode: perl
# c-basic-offset:4
# End:
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