rotatePolytope

 rotate a polytope of H- or V-representation

 Syntax: poly = rotatePolytope(poly, ...)

 This function is for 2- and 3-dimensional polytopes only.

 The arguments are provided in option/value pairs that are:
   'center' uses the given fixed point for rotation. Default: [] (origin
              of coordinate system)
   ''       an empty option name can be used for 2-dimensional rotations
              and is followed by the angle in radian.
   'x',     3-dimensional polytopes are rotated around these axes with the
   'y', 'z'   angle given in radian.
   'vector' for 3-dimensional polytopes a vector can be provided and the
              polytope is rotated so that this vector would match the
              z-axis afterwards.

 You can append as many rotation operations, as you like.

 Example (3D): rotatePolytope(poly, 'x', pi/4, 'center', [1 0 0], ...
                 'y', pi/4, 'center', [0 0 1], 'z', pi/4)

 Example (2D): rotatePolytope(poly, '', pi/4, 'center', [1 1], '', pi/4)

 See also: rotateHrep2d, rotateVrep2d, rotateHrep3d, rotateVrep3d,
   movePolytope, stretchPolytope

• identifyPolytope returns basic information on the geometric object
• rotateHrep2d rotates a polytope in H-representation by given axis and angle
• rotateHrep3d rotates a polytope in H-representation by given axis and angle
• rotateVrep2d rotates a polytope in V-representation by given axis and angle
• rotateVrep3d rotates a polytope in V-representation by given axis and angle

• projectVrep3d project a V-polytope onto a plane defined by normal vector

0001 function poly = rotatePolytope(poly, varargin)
0002 % rotate a polytope of H- or V-representation
0003 %
0004 % Syntax: poly = rotatePolytope(poly, ...)
0005 %
0006 % This function is for 2- and 3-dimensional polytopes only.
0007 %
0008 % The arguments are provided in option/value pairs that are:
0009 %   'center' uses the given fixed point for rotation. Default: [] (origin
0010 %              of coordinate system)
0011 %   ''       an empty option name can be used for 2-dimensional rotations
0012 %              and is followed by the angle in radian.
0013 %   'x',     3-dimensional polytopes are rotated around these axes with the
0014 %   'y', 'z'   angle given in radian.
0015 %   'vector' for 3-dimensional polytopes a vector can be provided and the
0016 %              polytope is rotated so that this vector would match the
0017 %              z-axis afterwards.
0018 %
0019 % You can append as many rotation operations, as you like.
0020 %
0021 % Example (3D): rotatePolytope(poly, 'x', pi/4, 'center', [1 0 0], ...
0022 %                 'y', pi/4, 'center', [0 0 1], 'z', pi/4)
0023 %
0024 % Example (2D): rotatePolytope(poly, '', pi/4, 'center', [1 1], '', pi/4)
0025 %
0026 % See also: rotateHrep2d, rotateVrep2d, rotateHrep3d, rotateVrep3d,
0027 %   movePolytope, stretchPolytope
0028 
0029 % The elk-library: convex geometry applied to crystallization modeling.
0030 %   Copyright (C) 2012 Alexander Reinhold
0031 %
0032 % This program is free software: you can redistribute it and/or modify it
0033 %   under the terms of the GNU General Public License as published by the
0034 %   Free Software Foundation, either version 3 of the License, or (at your
0035 %   option) any later version.
0036 %
0037 % This program is distributed in the hope that it will be useful, but
0038 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0039 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0040 %   General Public License for more details.
0041 %
0042 % You should have received a copy of the GNU General Public License along
0043 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0044 
0045 infoP = identifyPolytope(poly);
0046 
0047 %% evaluate operations subsequently
0048 x0 = [];
0049 for iArg = 1:2:(nargin-1)
0050     if strcmpi(varargin{iArg}, 'center')
0051         x0 = varargin{iArg+1};
0052         continue;
0053     end
0054     
0055     switch infoP.dim
0056         case 2
0057             switch infoP.rep
0058                 case 'Vrep'
0059                     poly = rotateVrep2d(poly, varargin{iArg+1}, x0);
0060                 case 'Hrep'
0061                     poly = rotateHrep2d(poly, varargin{iArg+1}, x0);
0062             end
0063         case 3
0064             switch infoP.rep
0065                 case 'Vrep'
0066                     poly = rotateVrep3d(poly, varargin{iArg}, varargin{iArg+1}, x0);
0067                 case 'Hrep'
0068                     poly = rotateHrep3d(poly, varargin{iArg}, varargin{iArg+1}, x0);
0069             end
0070         otherwise
0071             error('elk:polytope:wrongType', ...
0072                 'This function is only supported for 2- or 3-dimesnional polytopes');
0073     end
0074 end
0075 
0076 end