convertHrepToVrepByCddlib

 convert the H-representation of a polytope into V-representation

 Syntax: vrep = convertHrepToVrep(hrep, zerotol, infinityBoxSize)

 The input should already be scaled by calling function.
 
 Consider that cddlib applies an additional zerotol that is stored in the 
   function zerotolCddlib during initialization of this library 
   (buildCddlib).

 THIS FUNCTION IS NO USER FUNCTION.

• callCddLib ==========================================================================
• stretchHrep stretch the polytope in arbitrary representation along axes
• stretchVrep stretch the polytope in arbitrary representation along axes

• convertHrepToVrep convert the H-representation of a polytope into V-representation

0001 function vrep = convertHrepToVrepByCddlib(hrep, maxTrial)
0002 % convert the H-representation of a polytope into V-representation
0003 %
0004 % Syntax: vrep = convertHrepToVrep(hrep, zerotol, infinityBoxSize)
0005 %
0006 % The input should already be scaled by calling function.
0007 %
0008 % Consider that cddlib applies an additional zerotol that is stored in the
0009 %   function zerotolCddlib during initialization of this library
0010 %   (buildCddlib).
0011 %
0012 % THIS FUNCTION IS NO USER FUNCTION.
0013 
0014 % The elk-library: convex geometry applied to crystallization modeling.
0015 %   Copyright (C) 2012 Alexander Reinhold
0016 %
0017 % This program is free software: you can redistribute it and/or modify it
0018 %   under the terms of the GNU General Public License as published by the
0019 %   Free Software Foundation, either version 3 of the License, or (at your
0020 %   option) any later version.
0021 %
0022 % This program is distributed in the hope that it will be useful, but
0023 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0024 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0025 %   General Public License for more details.
0026 %
0027 % You should have received a copy of the GNU General Public License along
0028 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0029 
0030 %% conversion
0031 % the try/catch environment and while-loop is connected to a currently
0032 %   "strange" numerical behavior of cddlib. It seems to be sensitive to
0033 %   slight adjustments of the input (e.g. scaling).
0034 callCddLibLoop = 1;
0035 extraScalingVector = [1 (0.1 + linspace(0, 0.8, maxTrial-1))];
0036 thisExtraScaling = extraScalingVector(1);
0037 hrepExtraScaled = hrep;
0038 while callCddLibLoop
0039     try
0040         resCddlib = callCddLib('extreme', ...
0041             struct('A', hrepExtraScaled.A, 'B', hrepExtraScaled.h));
0042         callCddLibLoop = 0;
0043     catch dumpError
0044         callCddLibLoop = callCddLibLoop + 1;
0045         if callCddLibLoop > maxTrial
0046           % we don't want to rethrow the error message that would be:
0047           %   "CDD returned an error, see above(!) for details", instead we
0048           %   use:
0049           error('elk:polytope:conversion', ['cddlib (MEX-interface) ' ...
0050                 'returned an error']);
0051         end
0052         thisExtraScaling = extraScalingVector(callCddLibLoop);
0053         hrepExtraScaled = stretchHrep(hrep, thisExtraScaling);
0054     end
0055 end
0056 % strip everything except field V
0057 vrepExtraScaled = struct('V', resCddlib.V);
0058 
0059 % failure if there are rays (unbounded polytope)
0060 if ~isempty(resCddlib.R)
0061     vrep = [];
0062 else
0063     if thisExtraScaling ~= 1
0064         vrep = stretchVrep(vrep, 1/thisExtraScaling);
0065     else
0066         vrep = vrepExtraScaled;
0067     end
0068 end