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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 alpha = anglePoints3d(varargin)
%ANGLEPOINTS3D Compute angle between three 3D points.
%
% ALPHA = anglePoints3d(P1, P2)
% Computes angle (P1, O, P2), in radians, between 0 and PI.
%
% ALPHA = anglePoints3d(P1, P2, P3)
% Computes angle (P1, P2, P3), in radians, between 0 and PI.
%
% ALPHA = anglePoints3d(PTS)
% PTS is a 3x3 or 2x3 array containing coordinate of points.
%
% Example
% rad2deg(anglePoints3d([0 0 1],[1 1 0]))
%
% See also
% points3d, angles3d
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
p2 = [0 0 0];
if length(varargin) == 1
pts = varargin{1};
if size(pts, 1)==2
p1 = pts(1,:);
p0 = [0 0 0];
p2 = pts(2,:);
else
p1 = pts(1,:);
p0 = pts(2,:);
p2 = pts(3,:);
end
elseif length(varargin) == 2
p1 = varargin{1};
p0 = [0 0 0];
p2 = varargin{2};
elseif length(varargin) == 3
p1 = varargin{1};
p0 = varargin{2};
p2 = varargin{3};
end
% ensure all data have same size
n1 = size(p1, 1);
n2 = size(p2, 1);
n0 = size(p0, 1);
if n1 ~= n0
if n1 == 1
p1 = repmat(p1, [n0 1]);
n1 = n0;
elseif n0==1
p0 = repmat(p0, [n1 1]);
else
error('Arguments P1 and P0 must have the same size');
end
end
if n1 ~= n2
if n1 == 1
p1 = repmat(p1, [n2 1]);
elseif n2 == 1
p2 = repmat(p2, [n1 1]);
else
error('Arguments P1 and P2 must have the same size');
end
end
% normalized vectors
p1 = normalizeVector3d(p1 - p0);
p2 = normalizeVector3d(p2 - p0);
% compute angle
alpha = acos(dot(p1, p2, 2));
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