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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.
#-------------------------------------------------------------------------------
CREDIT qhull
The Quickhull algorithm for convex hulls.
Copyright by The Geometry Center, University of Minnesota
http://www.qhull.org/
# path to the qhull executable
custom $qhull;
CONFIGURE {
find_program($qhull, "qhull");
}
object Polytope<Float> {
# @category Convex hull computation
# Use the [[wiki:external_software#qhull]] program for convex hull computation.
label qhull
sub run_qhull_primal {
my ($points) = @_;
my $input = new TempTextFile;
print $input "begin\n", $points->rows, " ", $points->cols, " real\n", dense($points), "end\n";
open my $output, "$qhull Fd n i <$input |"
or die "can't start $qhull: $!\n";
local $_ = <$output>; # dimension
my ($d)= /(\d+)/;
$_ = <$output>; # number of facets
my ($n)= /(\d+)/;
my $FACETS = new Matrix<Float>($n, $d); --$d;
# toggle the signs and move the facet offset in the first position
for (my $i = 0; $i < $n; ++$i) {
defined($_ = <$output>) or die "premature end of input\n";
my $f = new Vector<Float>($_);
@{$FACETS->[$i]} = (-$f->[$d], @{ -($f->slice(sequence(0,$d))) });
}
$_ = <$output>;
/(\d+)/ && $1 == $n or die "inconsistency in qhull output\n";
my @VIF; $#VIF = $n-1;
for (my $i = 0; $i < $n; ++$i) {
defined($_ = <$output>) or die "premature end of input\n";
chomp;
$VIF[$i] = "{$_}";
}
($n, $FACETS, \@VIF);
}
rule qhull.convex_hull.primal, qhull.convex_hull: FACETS, N_FACETS, VERTICES_IN_FACETS : VERTICES {
my ($n, $FACETS, $VIF)=run_qhull_primal($this->VERTICES);
$this->FACETS=$FACETS;
$this->N_FACETS=$n;
$this->VERTICES_IN_FACETS=$VIF;
}
precondition : BOUNDED;
precondition : FULL_DIM;
weight 4.10;
incurs FacetPerm;
# @notest
rule qhull.convex_hull.primal, qhull.convex_hull: FACETS, N_FACETS, POINTS_IN_FACETS : POINTS {
my ($n, $FACETS, $VIF) = run_qhull_primal($this->POINTS);
$this->FACETS = $FACETS;
$this->N_FACETS = $n;
$this->POINTS_IN_FACETS = $VIF;
}
precondition : BOUNDED;
precondition : FULL_DIM;
weight 4.10;
incurs FacetPerm;
sub run_qhull_dual {
my ($rip, $ineqs)=@_;
my $input = new TempTextFile;
print $input $rip->dim-1, " 1\n" , dense(dehomogenize($rip)),
"\nbegin\n", $ineqs->rows, " ", $ineqs->cols, " real\n", dense($ineqs), "end\n";
#Fp = vertex coordinates
#FN = vertices in inequalties/facets
#Fx = facet defining inequalities
open my $output, "$qhull Fd H Fp FN <$input |"
or die "can't start $qhull: $!\n";
local $_ = <$output>; # dimension
my ($d)= /(\d+)/;
$_ = <$output>; # number of vertices
my ($n) = /(\d+)/;
my $vertices = new Matrix<Float>($n,$d+1);
# read vertices
for (my $i = 0; $i < $n; ++$i) {
defined($_ = <$output>) or die "premature end of input\n";
my $v = new Vector<Float>($_);
@{$vertices->[$i]} = (1, @$v);
}
$_ = <$output>;
my ($m) = /(\d+)/;
my @vertices_in_ineqs;
$#vertices_in_ineqs = $m - 1;
for (my $i = 0; $i < $m; ++$i) {
defined($_ = <$output>) or die "premature end of input\n";
chomp;
my @vii = $_ =~ /(\d+)/g;
splice @vii, 0, 1;
$vertices_in_ineqs[$i]="{@vii}";
}
($n, $vertices, \@vertices_in_ineqs);
}
rule qhull.convex_hull.dual, qhull.convex_hull: VERTICES, N_VERTICES, VERTICES_IN_FACETS : FACETS, REL_INT_POINT {
my ($n, $vertices, $vif) = run_qhull_dual($this->REL_INT_POINT,$this->FACETS);
$this->VERTICES = $vertices;
$this->N_VERTICES = $n;
$this->VERTICES_IN_FACETS = $vif;
}
precondition : BOUNDED;
precondition : FULL_DIM;
weight 4.10;
incurs VertexPerm;
# @notest
rule qhull.convex_hull.dual, qhull.convex_hull: VERTICES, N_VERTICES, VERTICES_IN_INEQUALITIES : INEQUALITIES, REL_INT_POINT {
my ($n, $vertices, $vii) = run_qhull_dual($this->REL_INT_POINT,$this->INEQUALITIES);
$this->VERTICES = $vertices;
$this->N_VERTICES = $n;
$this->VERTICES_IN_INEQUALITIES = $vii;
}
precondition : BOUNDED;
precondition : FULL_DIM;
weight 4.10;
incurs VertexPerm;
}
# Local Variables:
# mode: perl
# cperl-indent-level:3
# End:
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