projectVrep3d

 project a V-polytope onto a plane defined by normal vector

 Syntax: vrep = projectVrep3d(vrep, normal)

 The projection set is returned in the reduced dimension so that vrep
   has only 2 columns.

 See also: computeSupportSetVrep

• reduceVrep reduce a V-representation to extreme points of convex hull
• rotatePolytope rotate a polytope of H- or V-representation

• computeProjectionAreaVrep projection area of a V-polytope

0001 function vrep = projectVrep3d(vrep, normal)
0002 % project a V-polytope onto a plane defined by normal vector
0003 %
0004 % Syntax: vrep = projectVrep3d(vrep, normal)
0005 %
0006 % The projection set is returned in the reduced dimension so that vrep
0007 %   has only 2 columns.
0008 %
0009 % See also: computeSupportSetVrep
0010 
0011 % The elk-library: convex geometry applied to crystallization modeling.
0012 %   Copyright (C) 2012 Alexander Reinhold
0013 %
0014 % This program is free software: you can redistribute it and/or modify it
0015 %   under the terms of the GNU General Public License as published by the
0016 %   Free Software Foundation, either version 3 of the License, or (at your
0017 %   option) any later version.
0018 %
0019 % This program is distributed in the hope that it will be useful, but
0020 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0021 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0022 %   General Public License for more details.
0023 %
0024 % You should have received a copy of the GNU General Public License along
0025 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0026 
0027 if size(vrep.V, 2) ~= 3 || length(normal) ~=3
0028     error('elk:polytope:wrongType', ...
0029         'projectVrep3d is for 3-dimensional polytopes only');
0030 end
0031 
0032 %% Rotate
0033 vrep = rotatePolytope(vrep, 'vector', normal);
0034 % so that we can project onto xy-plane
0035 vrep.V(:,end) = [];
0036 vrep = reduceVrep(vrep);
0037 
0038 end