getRotationMatrix3d

 obtain rotation matrix based on angle and coordinate axis OR a vector

 Syntax: rot = getRotationMatrix3d(axis, angle)
   or    rot = getRotationMatrix3d('vector', v)

 The axis is 'x', 'y' or 'z' and the angle must be provided in radian.
   With the case 'vector', the the rotation matrix is calculated so that
   the normalized vector v matches the unit vector if the z-axis.

 See also: getRotationMatrix2d, getRotationMatrix4d, rotatePolytope

• getRotationMatrix3d obtain rotation matrix based on angle and coordinate axis OR a vector

• getRotationMatrix3d obtain rotation matrix based on angle and coordinate axis OR a vector
• rotateHrep3d rotates a polytope in H-representation by given axis and angle
• rotateVrep3d rotates a polytope in V-representation by given axis and angle

0001 function rot = getRotationMatrix3d(axis, a)
0002 % obtain rotation matrix based on angle and coordinate axis OR a vector
0003 %
0004 % Syntax: rot = getRotationMatrix3d(axis, angle)
0005 %   or    rot = getRotationMatrix3d('vector', v)
0006 %
0007 % The axis is 'x', 'y' or 'z' and the angle must be provided in radian.
0008 %   With the case 'vector', the the rotation matrix is calculated so that
0009 %   the normalized vector v matches the unit vector if the z-axis.
0010 %
0011 % See also: getRotationMatrix2d, getRotationMatrix4d, rotatePolytope
0012 
0013 % The elk-library: convex geometry applied to crystallization modeling.
0014 %   Copyright (C) 2012 Alexander Reinhold
0015 %
0016 % This program is free software: you can redistribute it and/or modify it
0017 %   under the terms of the GNU General Public License as published by the
0018 %   Free Software Foundation, either version 3 of the License, or (at your
0019 %   option) any later version.
0020 %
0021 % This program is distributed in the hope that it will be useful, but
0022 %   WITHOUT ANY WARRANTY; without even the implied warranty of
0023 %   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
0024 %   General Public License for more details.
0025 %
0026 % You should have received a copy of the GNU General Public License along
0027 %   with this program.  If not, see <http://www.gnu.org/licenses/>.
0028 
0029 switch lower(axis)
0030     case 'x'
0031         rot = [1       0       0;
0032                0       cos(a) -sin(a);
0033                0       sin(a)  cos(a)];
0034     case 'y'
0035         rot = [cos(a)  0       sin(a);
0036                0       1       0;
0037               -sin(a)  0       cos(a)];
0038     case 'z'
0039         rot = [cos(a) -sin(a)  0;
0040                sin(a)  cos(a)  0;
0041                0       0       1];
0042     case 'vector'
0043         % correct v to be a column vector
0044         if size(a, 1) == 1
0045             a = a';
0046         end
0047         
0048         % rotate vector so that it lies in xz-plane (eliminates y-direction)
0049         if a(2) ~=0
0050             anglez = acos(dot(a(1:2) / norm(a(1:2)), [1,0])) * ...
0051                 -sign(a(2));
0052             matrix_z = getRotationMatrix3d('z', anglez);
0053             a = matrix_z*a;
0054         else
0055             matrix_z = eye(3);
0056         end
0057         
0058         % rotate vector so that it lies in yz-plane (eliminates z-direction)
0059         % normal is then colinear with z-axis
0060         if a(1) ~= 0
0061             angley = acos(dot(a([1,3]) / norm(a([1,3])),[0,1])) * ...
0062                 -sign(a(1));
0063             matrix_y = getRotationMatrix3d('y', angley);
0064         else
0065             matrix_y = eye(3);
0066         end
0067         
0068         % assign rotation matrix
0069         rot = matrix_y*matrix_z;
0070         
0071     otherwise
0072         error(['Axis ''' axis ''' unknown, use ''x'', ''y'', ''z'' or ''vector''.'])
0073 end