computeProjectionAreaHrep

 projection area of a H-polytope

 Syntax: area = computeProjectionAreaHrep(hrep, dirMatrix)

 This function calculates a vector of projection areas for all directions
   in dirMatrix that contains one direction in each row.

 computeProjectionAreaHrep(..., zerotol) allows to set the tolerance for 
   underlying algorithms (determining flat polytopes; default in
   elkZerotol).

 See also: computeProjectionAreaVrep, computeVolumeHrep,
   computeFacetAreaHrep, computeFeretHrep, computeSupportValueHrep

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

0001 function area = computeProjectionAreaHrep(hrep, dirMatrix, zerotol)
0002 % projection area of a H-polytope
0003 %
0004 % Syntax: area = computeProjectionAreaHrep(hrep, 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 % computeProjectionAreaHrep(..., zerotol) allows to set the tolerance for
0010 %   underlying algorithms (determining flat polytopes; default in
0011 %   elkZerotol).
0012 %
0013 % See also: computeProjectionAreaVrep, computeVolumeHrep,
0014 %   computeFacetAreaHrep, computeFeretHrep, computeSupportValueHrep
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 %% Calculating area
0039 % fall back to computeProjectionAreaVrep
0040 vrep = convertHrepToVrep(hrep, zerotol);
0041 if ~isempty(vrep.V)
0042     area = computeProjectionAreaVrep(vrep, dirMatrix, zerotol);
0043 else
0044     area = 0;
0045 end