addValidityCone

 data to identify valid hC-vectors

 THIS FUNCTION IS NO USER FUNCTION.

• closeCone compute the closure of the given cone
• computeExtremeRaysFromCone compute extreme rays of a cone
• scaleToClose scale input matrix of hC-vectors to the closing condition of the cone
• scaleToReal scale input matrix of hC-vectors to some real geometry
• computeVolumeHrep compute the volume of a polytope in H-representation
• normalizeHrep normalize length of facet normals to 1

• obtainDec generates a decomposition for a fixed set of facet normals
• projectCompleteDec project a complete proper representation
• projectIncompleteDec project a complete proper representation

0001 function dec = addValidityCone(dec, validityConeNormalMatrix, zerotol)
0002 % data to identify valid hC-vectors
0003 %
0004 % THIS FUNCTION IS NO USER FUNCTION.
0005 
0006 % The elk-library: convex geometry applied to crystallization modeling.
0007 %   Copyright (C) 2012 Alexander Reinhold
0008 %
0009 % This program is free software: you can redistribute it and/or modify it
0010 %   under the terms of the GNU General Public License as published by the
0011 %   Free Software Foundation, either version 3 of the License, or (at your
0012 %   option) any later version.
0013 %
0014 % This program is distributed in the hope that it will be useful, but
0015 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0016 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0017 %   General Public License for more details.
0018 %
0019 % You should have received a copy of the GNU General Public License along
0020 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0021 
0022 %% generate validityCone (irredundant H-rep)
0023 % we only need unique rows
0024 validityConeNormalMatrix = unique(validityConeNormalMatrix, 'rows');
0025 % hrep data
0026 %! DEV: reduceHrep did not work out for one case, it reduced 4D A matrix to
0027 %    only 3 rows even though when computing the extreme rays from the full
0028 %    matrix, it results in 4 properly spanning rays.
0029 %  Hence, the reduce step is ignored which should not do much harm in
0030 %  applications.
0031 dec.validityCone =  struct('A', validityConeNormalMatrix, ...
0032            'h', zeros(size(validityConeNormalMatrix, 1), 1)...
0033            );
0034 % dec.validityCone = reduceHrep(dec.validityCone);
0035 dec.validityCone = normalizeHrep(dec.validityCone);
0036 
0037 % vrep data (rays)
0038 rayMatrix = computeExtremeRaysFromCone(dec.validityCone.A, zerotol);
0039 
0040 if isempty(rayMatrix)
0041     %% empty validity cone
0042     % this happens only in the context of projectDec, where it is expected
0043     %   to initialize the following variables with proper sizes.
0044     dec.se = zeros(0, dec.nC);
0045     dec.nS = 0;
0046     dec.validityCone.seIndexVector = [];
0047     dec.centerRay = zeros(1, dec.nC);
0048     dec.seScaledToClose = dec.se;
0049     dec.validityCone.volume = 0;
0050     
0051 else
0052     % enter more SE data
0053     dec.se = scaleToReal(rayMatrix, dec, zerotol);
0054     dec.nS = size(rayMatrix, 1);
0055     dec.validityCone.seIndexVector = 1:dec.nS;
0056     
0057     % center ray
0058     dec.centerRay = mean(dec.se, 1)';
0059     dec.centerRay = dec.centerRay / norm(dec.centerRay, 2);
0060     % calculate SEs as they actually close the validity cone
0061     dec.seScaledToClose = scaleToClose(rayMatrix, dec);
0062     
0063     % volume computation is based on V-representation so we use the structuring
0064     %   elements and the origin as generating points.
0065     dec.validityCone.volume = computeVolumeHrep(closeCone(dec.validityCone, ...
0066         dec.centerRay));
0067 end