projection area of a V-polytope Syntax: area = computeProjectionAreaVrep(vrep, dirMatrix) This function calculates a vector of projection areas for all directions in dirMatrix that contains one direction in each row. computeProjectionAreaVrep(..., zerotol) allows to set the tolerance for underlying algorithms (e.g. determining flat polytopes; default in elkZerotol). See also: computeProjectionAreaHrep, computeVolumeVrep, computeFacetAreaVrep, computeFeretVrep, computeSupportValueVrep
0001 function area = computeProjectionAreaVrep(vrep, dirMatrix, zerotol) 0002 % projection area of a V-polytope 0003 % 0004 % Syntax: area = computeProjectionAreaVrep(vrep, dirMatrix) 0005 % 0006 % This function calculates a vector of projection areas for all directions 0007 % in dirMatrix that contains one direction in each row. 0008 % 0009 % computeProjectionAreaVrep(..., zerotol) allows to set the tolerance for 0010 % underlying algorithms (e.g. determining flat polytopes; default in 0011 % elkZerotol). 0012 % 0013 % See also: computeProjectionAreaHrep, computeVolumeVrep, 0014 % computeFacetAreaVrep, computeFeretVrep, computeSupportValueVrep 0015 0016 % The elk-library: convex geometry applied to crystallization modeling. 0017 % Copyright (C) 2012 Alexander Reinhold 0018 % 0019 % This program is free software: you can redistribute it and/or modify it 0020 % under the terms of the GNU General Public License as published by the 0021 % Free Software Foundation, either version 3 of the License, or (at your 0022 % option) any later version. 0023 % 0024 % This program is distributed in the hope that it will be useful, but 0025 % WITHOUT ANY WARRANTY; without even the implied warranty of 0026 % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU 0027 % General Public License for more details. 0028 % 0029 % You should have received a copy of the GNU General Public License along 0030 % with this program. If not, see <http://www.gnu.org/licenses/>. 0031 0032 %% Input handling 0033 % default zerotol 0034 if ~exist('zerotol', 'var') 0035 zerotol = elkZerotol; 0036 end 0037 0038 % check dimension 0039 if size(vrep.V, 2) == 3 0040 % everything OK, that is the normal case 0041 elseif size(vrep.V, 2) == 2 0042 % we use the maximum and minimum projection onto the given line 0043 % normalize dir matrix 0044 dirMatrix = bsxfun(@times, ... 0045 1./sqrt(sum(dirMatrix.^2, 2)), ... 0046 dirMatrix); 0047 projectionLengthVector = dirMatrix * vrep.V'; 0048 area = max(projectionLengthVector, [], 2) - min(projectionLengthVector, [], 2); 0049 return 0050 elseif size(vrep.V, 2) == 1 0051 % this is trivial 0052 area = 0; 0053 return 0054 else 0055 error('elk:polytope:inputError', ... 0056 'Only three dimensional polytopes can be handled'); 0057 end 0058 0059 %% do for each facet 0060 area = zeros(1,size(dirMatrix, 1)); 0061 for iFacet = 1:size(dirMatrix, 1) 0062 % Get support set in direction 0063 projectedVrep = projectVrep3d(vrep, dirMatrix(iFacet, :)); 0064 % Calculate volume of support set (2-D Volume) 0065 area(iFacet) = computeVolumeVrep(projectedVrep, zerotol); 0066 end