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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 = sphericalAngle(p1, p2, p3)
%SPHERICALANGLE Compute angle between points on the sphere.
%
% ALPHA = sphericalAngle(P1, P2, P3)
% Computes angle (P1, P2, P3), i.e. the angle, measured at point P2,
% between the direction (P2, P1) and the direction (P2, P3).
% The result is given in radians, between 0 and 2*PI.
%
% Points are given either as [x y z] (there will be normalized to lie on
% the unit sphere), or as [phi theta], with phi being the longitude in [0
% 2*PI] and theta being the elevation on horizontal [-pi/2 pi/2].
%
%
% NOTE:
% this is an 'oriented' version of the angle computation, that is, the
% result of sphericalAngle(P1, P2, P3) equals
% 2*pi-sphericalAngle(P3,P2,P1). To have the more classical relation
% (with results given betwen 0 and PI), it suffices to take the minimum
% of angle and 2*pi-angle.
%
% Examples
% % Use inputs as cartesian coordinates
% p1 = [0 1 0];
% p2 = [1 0 0];
% p3 = [0 0 1];
% alpha = sphericalAngle(p1, p2, p3)
% alpha =
% 1.5708
%
% % Use inputs as spherical coordinates
% sph1 = [.1 0];
% sph2 = [0 0];
% sph3 = [0 .1];
% alphas = sphericalAngle(sph1, sph2, sph3)
% alphas =
% 1.5708
%
%
% See also
% geom3d, angles3d, spheres, sph2cart
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% test if points are given as matlab spherical coordinates
if size(p1, 2) == 2
[x, y, z] = sph2cart(p1(:,1), p1(:,2), ones(size(p1,1), 1));
p1 = [x y z];
[x, y, z] = sph2cart(p2(:,1), p2(:,2), ones(size(p2,1), 1));
p2 = [x y z];
[x, y, z] = sph2cart(p3(:,1), p3(:,2), ones(size(p3,1), 1));
p3 = [x y z];
end
% normalize points
p1 = normalizeVector3d(p1);
p2 = normalizeVector3d(p2);
p3 = normalizeVector3d(p3);
% create the plane tangent to the unit sphere and containing central point
plane = createPlane(p2, p2);
% project the two other points on the plane
pp1 = planePosition(projPointOnPlane(p1, plane), plane);
pp3 = planePosition(projPointOnPlane(p3, plane), plane);
% compute angle on the tangent plane
pp2 = zeros(max(size(pp1, 1), size(pp3,1)), 2);
alpha = angle3Points(pp1, pp2, pp3);
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