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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.
#-------------------------------------------------------------------------------
package Visual::PointConfiguration;
use Polymake::Struct (
[ '@ISA' => 'Container' ],
[ '$PointConfiguration' => '#%' ],
);
# where to keep the view transformation matrix etc.
method representative { $_[0]->PointConfiguration }
method basis_solid { $_[0]->elements->[0] }
# Visualize the [[TRIANGULATION]] of a point configuration
# @param Array<Set<Int>> t facets of the triangulation
# @options %Visual::Polygons::decorations
# @return Visual::PointConfiguration
user_method TRIANGULATION(; $=$_[0]->PointConfiguration->TRIANGULATION->FACETS, %Visual::Polygons::decorations) {
my ($self, $TR, $decor)=@_;
my $d=$self->PointConfiguration->VECTOR_AMBIENT_DIM-1;
if ($d > 3) {
die "don't know how to visualize the triangulation of a $d-d configuration\n";
}
my $skeleton=$self->basis_solid;
$skeleton->VertexStyle="hidden";
$skeleton->FacetStyle="hidden";
my $labels= delete $decor->{VertexLabels};
if ($labels ne "hidden") {
$labels=$skeleton->VertexLabels;
} else {
undef $labels;
}
my $Points=$skeleton->Vertices;
my $Signs=triang_sign($TR, $self->PointConfiguration->POINTS);
$self->Name="Triangulation of ".$self->PointConfiguration->name;
push @{$self->elements}, [ $self->PointConfiguration->CONVEX_HULL->VisualSimplices($TR,$Points,$Signs,$labels,$decor) ];
visualize($self);
}
# Visualize a [[POLYTOPAL_SUBDIVISION]] of a point configuration.
# @param Int index Index of the subdivision to visualize
# @options %Visual::Polygons::decorations
# @options %geometric_options
# @return Visual::PointConfiguration
user_method POLYTOPAL_SUBDIVISION(;$=0,%Visual::Polygons::decorations, %geometric_options) {
my ($self, $index, $decor, $geom)=@_;
my $d=$self->PointConfiguration->VECTOR_AMBIENT_DIM-1;
if ($d > 3) {
die "don't know how to visualize the polytopal subdivision of a $d-d configuration\n";
}
$self->Name="Polytopal subdivision of ".$self->PointConfiguration->name;
my $pc=$self->PointConfiguration->POINTS;
my $psd=$self->PointConfiguration->POLYTOPAL_SUBDIVISION->[$index]->MAXIMAL_CELLS;
my @faces=();
my $skeleton=$self->basis_solid;
# $skeleton->EdgeStyle="hidden";
if ( $d == 3 ) {
$skeleton->FacetStyle="hidden";
foreach (@{$psd}) {
my $p=new polytope::Polytope<Rational>(POINTS=>$pc->minor($_,All));
my $P=new Visual::Polygons( Vertices => Visual::transform_float(dehomogenize(convert_to<Float>($p->VERTICES)),$geom->{Transformation},$geom->{Offset}),
Facets => $p->VIF_CYCLIC_NORMAL,
VertexLabels => "hidden",
FacetNeighbors => $p->NEIGHBOR_FACETS_CYCLIC_NORMAL,
Closed => 1,
NEdges => $p->N_EDGES,
$decor
);
push @faces, new Visual::Polytope(Polytope=>$p,$P);
}
} else {
foreach (@{$psd}) {
my $p=new polytope::Polytope<Rational>(POINTS=>$pc->minor($_,All));
my $P=new Visual::Polygon(Vertices => Visual::transform_float(dehomogenize(convert_to<Float>($p->VERTICES)),$geom->{Transformation},$geom->{Offset}),
VertexLabels => "hidden",
Facet => $p->VIF_CYCLIC_NORMAL->[0],
NEdges => $p->N_EDGES,
$decor
);
push @{faces}, new Visual::Polytope(Polytope=>$p,$P);
}
}
compose($self,@faces);
}
package Visual::Color;
# Color for the non-vertices.
custom $non_vertices="255 255 0";
# @topic objects/Visual::PointConfiguration
# @category Visualization
# Visualization of the point configuration.
object PointConfiguration {
# @category Visualization
# Visualize the [[POINTS]] of a point configuration.
# @options %Visual::Polygons::decorations
# @options %geometric_options
# @return Visual::Object
user_method VISUAL_POINTS(%Visual::Polygons::decorations, %geometric_options) : POINTS, NON_VERTICES, N_POINTS {
my ($this, $decor, $geom)=@_;
my @colors = map { exists $this->NON_VERTICES->{$_} ? $Visual::Color::non_vertices : $Visual::Color::vertices } @{range(0,$this->N_POINTS-1)};
visualize( new Visual::PointSet(Name => $this->name,
Points => Visual::transform_float(dehomogenize(convert_to<Float>($this->POINTS)),$geom->{Transformation},$geom->{Offset}),
PointLabels =>$this->lookup("LABELS"),
PointColor => \@colors,
$decor
));
}
# @category Visualization
# Visualize a point configuration.
# @options %Visual::Polygons::decorations
# @options %geometric_options
# @return Visual::PointConfiguration
user_method VISUAL(%Visual::Polygons::decorations, %geometric_options) : POINTS, NON_VERTICES, N_POINTS, PIF_CYCLIC_NORMAL {
my ($this, $decor, $geom)=@_;
my @colors = map { exists $this->NON_VERTICES->{$_} ? $Visual::Color::non_vertices : $Visual::Color::vertices } @{range(0,$this->N_POINTS-1)};
my $P= $this->VECTOR_DIM==3
? new Visual::Polygon( Name => $this->name,
Points => Visual::transform_float(dehomogenize(convert_to<Float>($this->POINTS)),$geom->{Transformation},$geom->{Offset}),
PointLabels =>$this->lookup("POINT_LABELS") ,
PointColor => \@colors,
Facet => $this->PIF_CYCLIC_NORMAL->[0],
FacetTransparency => 0.5,
NEdges => $this->CONVEX_HULL->N_EDGES,
$decor
)
: new Visual::Polygons( Name => $this->name,
Points => Visual::transform_float(dehomogenize(convert_to<Float>($this->POINTS)),$geom->{Transformation},$geom->{Offset}),
PointLabels => $this->lookup("POINT_LABELS"),
PointColor => \@colors,
Facets => $this->PIF_CYCLIC_NORMAL,
FacetNeighbors => $this->CONVEX_HULL->NEIGHBOR_FACETS_CYCLIC_NORMAL,
FacetNormals => Visual::transform_float_facets(convert_to<Float>($this->CONVEX_HULL->FACETS),$geom->{Transformation},$geom->{Offset}),
FacetLabels => $this->CONVEX_HULL->lookup("FACET_LABELS") || "hidden",
FacetTransparency => 0.5,
Closed => 1,
NEdges => $this->CONVEX_HULL->N_EDGES,
$decor
);
visualize( new Visual::PointConfiguration(Name => $this->name, PointConfiguration => $this, $P));
}
precondition : VECTOR_DIM { $this->VECTOR_DIM>=3 }
precondition : VECTOR_AMBIENT_DIM { $this->VECTOR_AMBIENT_DIM<=4 }
precondition : BOUNDED;
# @hide
user_method VISUAL(%Visual::Polygons::decorations, %geometric_options) : POINTS, GRAPH.ADJACENCY {
my ($this, $decor, $geom)=@_;
my $pc=$this->VISUAL_POINTS(Name=>'points', $decor, $geom);
my $G=$this->GRAPH->VISUAL(Name=>$this->name, Coord=>Visual::transform_float(dehomogenize(convert_to<Float>($this->POINTS)),$geom->{Transformation},$geom->{Offset}), $decor);
visualize( new Visual::PointConfiguration(Name => $this->name, PointConfiguration => $this, $G, $pc) );
}
precondition : VECTOR_DIM { $this->VECTOR_DIM==2 }
precondition : VECTOR_AMBIENT_DIM { $this->VECTOR_AMBIENT_DIM<=4 }
precondition : BOUNDED;
}
package Visual::VectorConfiguration;
use Polymake::Struct (
[ '@ISA' => 'Container' ],
[ '$VectorConfiguration' => '#%' ],
);
object VectorConfiguration {
# @category Visualization
# Visualize a vector configuration.
# @options %Visual::Polygons::decorations
# @options %geometric_options_linear
# @return Visual::PointConfiguration
user_method VISUAL(%Visual::Polygons::decorations, %geometric_options_linear) : VECTORS, N_VECTORS {
my ($this, $decor, $geom)=@_;
visualize( new Visual::PointSet(Name => $this->name,
Points => Visual::transform_float(convert_to<Float>($this->VECTORS),$geom->{Transformation}),
PointLabels =>$this->lookup("LABELS"),
$decor
));
}
precondition : VECTOR_AMBIENT_DIM { $this->VECTOR_AMBIENT_DIM<=3 }
}
# Local Variables:
# mode: perl
# cperl-indent-level:4
# indent-tabs-mode:nil
# End:
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