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## Copyright (C) 2024 David Legland
## All rights reserved.
##
## Redistribution and use in source and binary forms, with or without
## modification, are permitted provided that the following conditions are met:
##
## 1 Redistributions of source code must retain the above copyright notice,
## this list of conditions and the following disclaimer.
## 2 Redistributions in binary form must reproduce the above copyright
## notice, this list of conditions and the following disclaimer in the
## documentation and/or other materials provided with the distribution.
##
## THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS ''AS IS''
## AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
## IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
## ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE FOR
## ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
## DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
## SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
## CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
## OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
## OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
##
## The views and conclusions contained in the software and documentation are
## those of the authors and should not be interpreted as representing official
## policies, either expressed or implied, of the copyright holders.
function varargout = randomAngle3d(varargin)
%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@inrae.fr
% Created: 2005-02-18
% Copyright 2005-2023 INRA - Cepia Software platform
N = 1;
if ~isempty(varargin)
N = varargin{1};
end
phi = 2*pi*rand(N, 1);
theta = asin(2*rand(N, 1)-1) + pi/2;
if nargout<2
var = [theta phi];
varargout{1} = var;
else
varargout{1} = theta;
varargout{2} = phi;
end
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