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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.
#-------------------------------------------------------------------------------
use application "polytope";
# volume of a union of polytopes (in the same space); by inclusion-exclusion
sub vol_union(@) {
my $n = scalar(@_);
die "usage: vol_union(poly1,poly2,...)\n" unless $n>0;
my $total = 0;
my $sign = 1;
for (my $k=1; $k<=$n; ++$k) {
my $v = 0;
foreach my $subset (@{all_subsets_of_k(sequence(0, $n), $k)}) {
$v += intersection(@_[@$subset])->VOLUME;
}
$total += $sign * $v;
$sign = -$sign;
}
return $total;
}
# Local Variables:
# mode: perl
# c-basic-offset:3
# End:
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