randomAngle3d

RANDOMANGLE3D Return a 3D angle uniformly distributed on unit sphere.

   usage
   [THETA PHI] = randomAngle3d
   Generate an angle unformly distributed on the surface of the unit
   sphere.

   "Mathematical" convention is used: theta is the colatitude (angle with
   vertical axis, 0 for north pole, +pi for south pole, pi/2 for points at
   equator) with z=0. 
   phi is the same as matlab cart2sph: angle from Ox axis, counted
   positively counter-clockwise.

   [THETA PHI] = randomAngle3d(N)
   generates N random angles (N is a scalar). The result is a N-by-2
   array.

   Example:
     % Draw some points on the surface of a sphere
     figure;
     drawSphere; hold on;
     drawPoint3d(pts, '.');
     axis equal;

   See also:
   angles3d, sph2cart2, cart2sph2

 ------
 Author: David Legland
 e-mail: david.legland@grignon.inra.fr
 created the 18/02/2005.
 Copyright INRA - Cepia Software platform

0001 function varargout = randomAngle3d(varargin)
0002 %RANDOMANGLE3D Return a 3D angle uniformly distributed on unit sphere.
0003 %
0004 %   usage
0005 %   [THETA PHI] = randomAngle3d
0006 %   Generate an angle unformly distributed on the surface of the unit
0007 %   sphere.
0008 %
0009 %   "Mathematical" convention is used: theta is the colatitude (angle with
0010 %   vertical axis, 0 for north pole, +pi for south pole, pi/2 for points at
0011 %   equator) with z=0.
0012 %   phi is the same as matlab cart2sph: angle from Ox axis, counted
0013 %   positively counter-clockwise.
0014 %
0015 %   [THETA PHI] = randomAngle3d(N)
0016 %   generates N random angles (N is a scalar). The result is a N-by-2
0017 %   array.
0018 %
0019 %   Example:
0020 %     % Draw some points on the surface of a sphere
0021 %     figure;
0022 %     drawSphere; hold on;
0023 %     drawPoint3d(pts, '.');
0024 %     axis equal;
0025 %
0026 %   See also:
0027 %   angles3d, sph2cart2, cart2sph2
0028 %
0029 % ------
0030 % Author: David Legland
0031 % e-mail: david.legland@grignon.inra.fr
0032 % created the 18/02/2005.
0033 % Copyright INRA - Cepia Software platform
0034 
0035 %   HISTORY
0036 %   2007-01-04 change angle order, update doc
0037 %   2011-06-27 fix bug in input parsing, add doc
0038 
0039 
0040 N = 1;
0041 if ~isempty(varargin)
0042     N = varargin{1};
0043 end
0044 
0045 phi = 2*pi*rand(N, 1);
0046 theta = asin(2*rand(N, 1)-1) + pi/2;
0047 
0048 if nargout<2
0049     var = [theta phi];
0050     varargout{1} = var;
0051 else
0052     varargout{1} = theta;
0053     varargout{2} = phi;
0054 end