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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.
#-------------------------------------------------------------------------------
object PolyhedralComplex {
method construct(topaz::GeometricSimplicialComplex) {
my $complex=$_[1];
if (!defined ($complex->lookup("FACETS"))) {
return new PolyhedralComplex(POINTS=>(ones_vector()|$complex->COORDINATES),INPUT_POLYTOPES=>$complex->INPUT_FACES,INPUT_LINEALITY=>new Matrix(0,$complex->COORDINATES->cols+1));
}
return new PolyhedralComplex(VERTICES=>(ones_vector()|$complex->COORDINATES->minor($complex->VERTEX_INDICES,All)),MAXIMAL_POLYTOPES=>$complex->FACETS,LINEALITY_SPACE=>new Matrix(0,$complex->COORDINATES->cols+1));
}
rule FAR_VERTICES : VERTICES {
$this->FAR_VERTICES=polytope::far_points($this->VERTICES);
}
weight 1.10;
rule COMPLETE : {
$this->COMPLETE = false;
}
weight 0.10;
}
object topaz::HyperbolicSurface {
# @category Other
# Computes the GKZ dome of the //k//-th Delaunay trianglation up to a given //depth//.
# Note that //k// is also the index of the corresponding flip word in [[FLIP_WORDS]].
# Projection to the disc yields (a part of) the covering triangulation of the Klein disc.
# @param Int k index of the flip word
# @param Int depth
# @return fan::PolyhedralComplex<Rational>
# @example
# > $T = new Matrix<Int>([[0,0,6,5],[0,0,1,10],[0,0,8,2],[1,0,11,4],[1,0,7,3],[1,0,9,0]]);
# > $s = new HyperbolicSurface(DCEL=>$T, PENNER_COORDINATES=>[1,1,1,1,1,1], SPECIAL_POINT=>[1,0]);
# > $d = $s->gkz_dome(0,3);
# > $d->VISUAL;
#
user_method gkz_dome($$){
my $self = shift;
my $triang = shift;
my $depth = shift;
covering_triangulation($self, $triang, $depth);
}
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# indent-tabs-mode:nil
# End:
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