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|
use POSIX qw(floor log10);
application 'polytope';
sub normal2color($$) {
my ($facets,$i) = @_;
my @facets = @{$facets};
my $normal = $facets[$i];
my ($a,$r,$g,$b) = split(/\s+/,$normal);
no integer;
my $norm = sqrt($r*$r+$g*$g+$b*$b);
map { $_ = floor(255*$_/$norm) } ($r,$g,$b);
return join(" ",($r,$g,$b));
}
#
# @param compose 0 cut
# 1 cut + polytope
# 2 all cuts + polytope
# 3 color the cut differently
#
#
die "usage: polymake --script cuts <polytope with LP> <n_cuts> <compose>\n" unless($#ARGV == 2);
my $poly=ref($ARGV[0]) ? $ARGV[0] : load($ARGV[0]);
die "defined for objects of type Polytope<Scalar> only" unless ref($poly) =~ m/^Polymake::polytope::Polytope__/;
die "defined for polytopes of dimension 3 and 4 only" unless($poly->DIM == 3 || $poly->DIM == 4);
shift @ARGV;
my ($n_cuts,$compose) = @ARGV;
my $n_digits = floor(log10($n_cuts));
no integer;
my ($min,$max) = ($poly->LP->MINIMAL_VALUE,$poly->LP->MAXIMAL_VALUE);
my $step = ($max-$min)/$n_cuts;
my @normal = split(/\s+/,$poly->LP->LINEAR_OBJECTIVE);
my @cuts = ();
my %cut_params = (FacetColor => "25 25 255",
EdgeThickness => ".3",
VertexThickness => ".5",
VertexColor => "255 127 0",
VertexStyle => "hidden"
);
my %visual_params = (FacetStyle => "hidden",
EdgeThickness => ".4",
VertexThickness => ".6",
VertexColor=> "red"
);
for(my $i = 0; $i <= $n_cuts; ++$i) {
print ".";
print "\n" if(($i+1) % 20 == 0);
no integer;
$normal[0] = $min + $i*$step;
my $cut = new Polytope<Rational>("cut at height $normal[0]");
my $equation = join(" ",@normal)."\n";
if($compose == 3) {
$cut->INEQUALITIES = [$equation, @{$poly->FACETS}];
} else {
$cut->INEQUALITIES = \@{$poly->FACETS};
$cut->EQUATIONS = $equation;
}
$cut->commit;
if($poly->DIM == 4 && $cut->DIM == 3) {
my $cut3D = projection($cut,[1,2,3]);
$cut3D->name = "cut at height $normal[0] in 3D";
my $filename = $poly->name;
$filename =~ s/(.*)\..*$/$1/;
$filename .= ".".("0"x($n_digits-floor(log10($i)))).$i.".pov";
my %cut_params = ( FacetColor => "25 25 255",
EdgeThickness => ".3",
VertexThickness => ".5",
VertexColor => "255 127 0"
);
povray(static($cut3D->VISUAL(\%cut_params))) if $cut3D->DIM == 3;
# povray(static($cut3D->VISUAL(FacetColor => sub {my $i = shift; return normal2color($cut3D->FACETS,$i);})),File=>"$filename") unless $cut3D->DIM != 3;
} elsif($poly->DIM == 3) {
my $filename = $poly->name;
$filename =~ s/(.*)\..*$/$1/;
$filename .= ".".("0"x($n_digits-floor(log10($i)))).$i.".pov";
if($compose == 1) {
compose($poly->VISUAL(\%visual_params),static($cut->VISUAL(\%cut_params))) unless $cut->DIM < 2;
} elsif ($compose == 0) {
compose(static($cut->VISUAL(\%cut_params))) unless $cut->DIM < 2;
} elsif ($compose == 2) {
push @cuts,$cut->VISUAL(\%cut_params) unless $cut->DIM < 2;
} elsif ($compose == 3) {
my @facet0 = (${$cut->FACETS}[0] =~ m/\d+/g);
my %facet0;
map { $facet0{$_} = 1 } @facet0;
my %cut_params = (
EdgeThickness => ".3",
VertexThickness => ".5",
);
compose(static($cut->VISUAL(\%cut_params,
VertexColor => sub {
my $index = shift;
if($facet0{$index} == 1) {
return "255 0 0";
} else {
return "255 127 0";}
},
FacetColor => sub {
my $index = shift;
if($index == 0) {
return "255 127 0";
} else {
return "0 0 255";}
},
))) unless $cut->DIM < 2;
}
}
}
print "\n";
if($compose == 2) {
my $filename = $poly->name;
$filename =~ s/(.*)\..*$/$1/;
compose($poly->VISUAL(\%visual_params),@cuts);
}
# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
|
