computeMeanWidthHrep

 compute the mean width of a polytope in H-representation

 Syntax: meanWidth = computeMeanWidthHrep(hrep)

 computeMeanWidthHrep(.., zerotol) allows to set the tolerance for 
   underlying algorithms (determining flat polytopes; default in
   elkZerotol).

 See also: computeMeanWidthHrep, computeVolumeVrep, computeFacetAreaVrep,
   computeFeretVrep, obtainMeasureInfo

• computeEdgeSetVrep identify the edges of a V-representation
• computeFacetAreaHrep surface area or facet area of a H-polytope
• computeMeanWidthCore compute the mean width of a polytope given H-rep and V-rep
• computeMeanWidthVrep compute the mean width of a polytope in V-representation
• computeVolumeHrep compute the volume of a polytope in H-representation
• convertHrepToVrep convert the H-representation of a polytope into V-representation
• normalizeHrep normalize length of facet normals to 1
• reduceHrep reduce a H-representation to non-redundant support hyperplanes
• reduceVrepDimension project lower dimensional (flat) polytope into embedding space

• scaleToReal scale input matrix of hC-vectors to some real geometry

0001 function meanWidth = computeMeanWidthHrep(hrep, zerotol)
0002 % compute the mean width of a polytope in H-representation
0003 %
0004 % Syntax: meanWidth = computeMeanWidthHrep(hrep)
0005 %
0006 % computeMeanWidthHrep(.., zerotol) allows to set the tolerance for
0007 %   underlying algorithms (determining flat polytopes; default in
0008 %   elkZerotol).
0009 %
0010 % See also: computeMeanWidthHrep, computeVolumeVrep, computeFacetAreaVrep,
0011 %   computeFeretVrep, obtainMeasureInfo
0012 
0013 % The elk-library: convex geometry applied to crystallization modeling.
0014 %   Copyright (C) 2012 Alexander Reinhold
0015 %
0016 % This program is free software: you can redistribute it and/or modify it
0017 %   under the terms of the GNU General Public License as published by the
0018 %   Free Software Foundation, either version 3 of the License, or (at your
0019 %   option) any later version.
0020 %
0021 % This program is distributed in the hope that it will be useful, but
0022 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0023 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0024 %   General Public License for more details.
0025 %
0026 % You should have received a copy of the GNU General Public License along
0027 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0028 
0029 % default zerotol
0030 if ~exist('zerotol', 'var')
0031     zerotol = elkZerotol;
0032 end
0033 
0034 % check dimension
0035 if size(hrep.A, 2) > 3
0036     error('elk:polytope:inputError', ...
0037         'Only 1-, 2- or three dimensional polytopes can be handled');
0038 elseif size(hrep.A, 2) == 2
0039     meanWidth = computeFacetAreaHrep(hrep, [], zerotol) / pi;
0040     return
0041 elseif size(hrep.A, 2) == 1
0042     meanWidth = computeVolumeHrep(hrep, zerotol);
0043     return
0044 end
0045 
0046 % obtain edge-information
0047 hrep = normalizeHrep(reduceHrep(hrep));
0048 vrep = convertHrepToVrep(hrep, zerotol);
0049 vrepReduced = reduceVrepDimension(vrep, zerotol);
0050 if size(vrepReduced.V, 2) < size(vrep.V, 2)
0051     meanWidth = computeMeanWidthVrep(vrepReduced, zerotol);
0052     if size(vrep.V, 2) == 3 && size(vrepReduced.V, 2) == 1
0053         meanWidth = 0.5*meanWidth;
0054     elseif size(vrep.V, 2) == 3 && size(vrepReduced.V, 2) == 2
0055         meanWidth = 0.25*pi*meanWidth;
0056     end
0057 else
0058     edgeStruct = computeEdgeSetVrep(vrep, 'hrep', hrep, ...
0059         'zerotol', zerotol, 'output', 'full');
0060     % call mean width core algorithm
0061     meanWidth = computeMeanWidthCore(hrep, vrep, edgeStruct);
0062 end
0063