generateMinkowskiPartition

 generate a unified partition from Minkowski decomposition

 THIS IS NO USER FUNCTION

• closeCone compute the closure of the given cone
• decomposeMinkowskiHrep decompose the given polytope into Minkowski summands
• openCone remove the prior closure of the cone
• scaleToClose scale input matrix of hC-vectors to the closing condition of the cone
• convertVrepToHrep convert a V-representation into a H-representation

• obtainDec generates a decomposition for a fixed set of facet normals

0001 function partitionData = generateMinkowskiPartition(dec, hC, zerotol)
0002 % generate a unified partition from Minkowski decomposition
0003 %
0004 % THIS IS NO USER FUNCTION
0005 
0006 % The elk-library: convex geometry applied to crystallization modeling.
0007 %   Copyright (C) 2013 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 %% initialize acuumulating array structure
0023 partitionData.flagResult = [];
0024 partitionData.hrep = [];
0025 partitionData.seMatrix = [];
0026     
0027 % quit if no input is given; decomposeCone uses this call to initialize
0028 %   the accumulating array
0029 if ~exist('dec', 'var')
0030     partitionData(:) = [];
0031     return
0032 end
0033 
0034 %% perform Minkowski decomposition
0035 seMatrix = decomposeMinkowskiHrep(struct(...
0036     'A', dec.A, 'h', dec.mappingReducedToFull * hC), ...
0037     'constraint', dec.constraintMatrix, ...
0038     'zerotol', zerotol, ...
0039     'result', 'indecomposable', ...
0040     'matrix', 1);
0041 
0042 %% project to reduced space
0043 seMatrix = (dec.mappingFullToReduced * seMatrix')';
0044 
0045 %% valid or not
0046 % if full-dimensional, that is a partition! otherwise, we generate a
0047 % new hC
0048 if rank(seMatrix) == dec.nC
0049     % accept partition
0050     partitionData.flagResult = 1;
0051     partitionData.seMatrix = scaleToClose(seMatrix, dec);
0052     partitionData.hrep = openCone(convertVrepToHrep(closeCone(struct('V', ...
0053         partitionData.seMatrix ))));
0054       
0055 else
0056     % strange, retry with new hC
0057     partitionData.flagResult = 0;
0058     
0059 end
0060 
0061 end