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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::TVD;
# cutoff factor for visualizing a tropical Voronoi diagram
custom $cutoff=new Rational(20);
# Voronoi diagram with respect to the tropical metric in the tropical projective torus.
# Its combinatorics is controlled by a [[POLYTROPE_PARTITION]].
# See P. Criado, M. Joswig, P. Santos: Tropical bisectors and Voronoi diagrams, arXiv:1906.10950
#
# @example The following computes a tropical Voronoi diagram of three [[SITES]] in the tropical 3-torus.
# > $T= new VoronoiDiagram(SITES=>[[-4,-4,0,0],[-3,0,2,0],[-2,-5,-2,0]]);
# > print $T->POLYTROPE_PARTITION->size();
# | 134
declare object VoronoiDiagram {
file_suffix tvd
# The sites of the tropical Voronoi diagram.
property SITES : Matrix<Rational>;
# Number of sites of the diagram.
property N_SITES : Int;
rule N_SITES : SITES {
$this->N_SITES= $this->SITES->rows;
}
# Number of dimensions of the diagram. One less than the number of coordinates.
property AMBIENT_DIM : Int;
rule AMBIENT_DIM : SITES {
$this->AMBIENT_DIM= $this->SITES->cols-1;
}
# Representation of the tropical Voronoi diagram.
# Each such polyhedron is a domain in which the distance to the set of sites $S$ is a minimum of linear functions.
# This list of regions is represented as an array of pairs of matrices.
# The first matrix in each pair represents the region itself (a polytrope) as a shortest path matrix.
# The second matrix (the labels) gives the index of the site $s\in S$ with maximum $s_j-s_i$ such that the cone $\{x:x_i-s_i<= x_k-s_k <= x_j-s_j \forall k\in [d+1]\}$ intersects this cell (or $-1$ if no such index exists).
# Then, in this region, $dist(x,S)$ is a minimum of the linear functions $(x_j-s_j)-(x_i-s_i)$ for each $s$ labelled with $(i,j)$.
# @example Here is one polytrope cell.
# > $T= new VoronoiDiagram(SITES=>[[-4,-4,0,0],[-3,0,2,0],[-2,-5,-2,0]]);
# > print $T->POLYTROPE_PARTITION->[0];
# | <0 inf inf inf
# | -4 0 2 0
# | -5 inf 0 inf
# | -4 inf inf 0
# | >
# | <-1 1 -1 -1
# | -1 -1 -1 -1
# | -1 -1 -1 -1
# | -1 -1 -1 -1
# | >
property POLYTROPE_PARTITION : Array<Pair<Matrix<Rational>, Matrix<Int>>>;
rule POLYTROPE_PARTITION : SITES {
compute_polytrope_partition($this);
}
user_method VISUAL : AMBIENT_DIM, SITES, POLYTROPE_PARTITION {
my $this= shift;
my @result = visualizable_cells($this->SITES, $this->AMBIENT_DIM, $this->POLYTROPE_PARTITION, $Visual::TVD::cutoff);
compose(map {$_->VISUAL} @result);
}
}
# Local Variables:
# mode: perl
# cperl-indent-level: 3
# indent-tabs-mode:nil
# End:
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