convert a V-representation into a H-representation Syntax: hrep = convertVrepToHrep(vrep) or hrep = convertVrepToHrep(vrep, zerotol, flatness) The parameter zerotol applies for scaleVrep only (default is elkZerotol). Consider that cddlib applies an additional zerotol that is stored in the function zerotolCddlib during initialization of this library (buildCddlib). The parameter flatness is only applied if the dimension of the object is smaller than the dimension it is embedded in (e.g. a 2D object in 3D space). The flatness is applied by adding [flatness/2] to all facet distances for which the corresponding hyperplane fully contains the polytope. There are two underlying methods to perform this conversion. The direct approach uses triangulation (convhulln). An alternative approach is to utilize duality and use convertHrepToVrep with the underlying double-description method (cddlib). The default is choosen by speed and reliability. The alternative is used if this approach fails. convert(.., prefereCddlib) gives the possibility to change the default standard algorithm to be used. Default: 0 See also: convertPolytope, convertHrepToVrep, scaleVrep
0001 function hrep = convertVrepToHrep(vrep, zerotol, flatness, useCddlib) 0002 % convert a V-representation into a H-representation 0003 % 0004 % Syntax: hrep = convertVrepToHrep(vrep) 0005 % or hrep = convertVrepToHrep(vrep, zerotol, flatness) 0006 % 0007 % The parameter zerotol applies for scaleVrep only (default is elkZerotol). 0008 % 0009 % Consider that cddlib applies an additional zerotol that is stored in the 0010 % function zerotolCddlib during initialization of this library 0011 % (buildCddlib). 0012 % 0013 % The parameter flatness is only applied if the dimension of the object is 0014 % smaller than the dimension it is embedded in (e.g. a 2D object in 3D 0015 % space). The flatness is applied by adding [flatness/2] to all facet 0016 % distances for which the corresponding hyperplane fully contains the 0017 % polytope. 0018 % 0019 % There are two underlying methods to perform this conversion. The direct 0020 % approach uses triangulation (convhulln). An alternative approach is to 0021 % utilize duality and use convertHrepToVrep with the underlying 0022 % double-description method (cddlib). The default is choosen by 0023 % speed and reliability. The alternative is used if this approach fails. 0024 % 0025 % convert(.., prefereCddlib) gives the possibility to change the default 0026 % standard algorithm to be used. Default: 0 0027 % 0028 % See also: convertPolytope, convertHrepToVrep, scaleVrep 0029 0030 % The elk-library: convex geometry applied to crystallization modeling. 0031 % Copyright (C) 2012 Alexander Reinhold 0032 % 0033 % This program is free software: you can redistribute it and/or modify it 0034 % under the terms of the GNU General Public License as published by the 0035 % Free Software Foundation, either version 3 of the License, or (at your 0036 % option) any later version. 0037 % 0038 % This program is distributed in the hope that it will be useful, but 0039 % WITHOUT ANY WARRANTY; without even the implied warranty of 0040 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0041 % General Public License for more details. 0042 % 0043 % You should have received a copy of the GNU General Public License along 0044 % with this program. If not, see <http://www.gnu.org/licenses/>. 0045 0046 %% Input handling 0047 if ~exist('zerotol', 'var') || isempty(zerotol) 0048 zerotol = elkZerotol; 0049 end 0050 if ~exist('flatness', 'var') || isempty(flatness) 0051 flatness = 0; 0052 end 0053 if ~exist('useCddlib', 'var') || isempty(useCddlib) 0054 useCddlib = 0; 0055 end 0056 if isempty(vrep.V) 0057 hrep.A = vrep.V; 0058 hrep.h = []; 0059 return 0060 end 0061 vrepDim = size(vrep.V, 2); 0062 0063 %% Reduce dimension if flat 0064 [vrepReduced, reduceTrafo, reduceOffset] = reduceVrepDimension(vrep, zerotol); 0065 reducedDim = size(vrepReduced.V, 2); 0066 0067 %% Scale polytope 0068 [vrepScaled, scale, scaleOffset] = scaleVrep(vrepReduced, zerotol); 0069 0070 % outer conversion structure 0071 useAlternative = 0; 0072 while useCddlib > -1 0073 try 0074 if ~useCddlib 0075 %% direct approach (convhulln) 0076 hrep = convertVrepToHrepByConvhulln(vrepScaled, zerotol); 0077 else 0078 %% dual approach (cddlib) 0079 % map to dual polytope in H-representation 0080 dualHrep = computeDualPolytope(vrepScaled); 0081 0082 % convert to dual Vrep 0083 dualVrep = convertHrepToVrep(dualHrep, zerotol, inf, 1); 0084 0085 % convert back to normal Hrep 0086 hrep = computeDualPolytope(dualVrep); 0087 end 0088 % assign to exit loop: 0089 useCddlib = -1; 0090 catch thisError 0091 if ~useAlternative 0092 warning('elk:conversion:method', thisError.message); 0093 warning('elk:conversion:method', ... 0094 'Using alternative approach to convert polytope.'); 0095 useAlternative = 1; 0096 useCddlib = ~useCddlib; 0097 else 0098 % safe input polytope 0099 if exist('log_convertVrepToHrep.mat', 'file') 0100 load log_convertVrepToHrep.mat 0101 logVrep{end+1} = vrep; 0102 else 0103 logVrep{1} = vrep; 0104 end 0105 save log_convertVrepToHrep.mat logVrep 0106 warning('elk:polytope:method', ... 0107 ['Given vrep cannot be converted to hrep (usually cddlib). ' ... 0108 'Polytope stored in: ' cd filesep 'log_convertVrepToHrep.mat']); 0109 rethrow(thisError); 0110 end 0111 end 0112 end 0113 0114 %% Revert scaling 0115 hrep = stretchHrep(hrep, scale, zeros(length(scale), 1)); 0116 hrep = moveHrep(hrep, scaleOffset); 0117 0118 %% Project back to original dimension 0119 if reducedDim < vrepDim 0120 hrep = liftHrepDimension(hrep, reduceTrafo, reduceOffset, flatness); 0121 end 0122 0123 %% apply flatness 0124 % flatFacetIndexList = (1:(2*(vrepDim-reducedDim))) + size(hrep.A, 1); 0125 % hrep.h(flatFacetIndexList) = hrep.h(flatFacetIndexList) + flatness/2; 0126 0127 %% Normalize 0128 hrep = normalizeHrep(hrep); 0129