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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 theta = circle3dPosition(point, circle)
%CIRCLE3DPOSITION Return the angular position of a point on a 3D circle.
%
% POS = circle3dPosition(POINT, CIRCLE)
% Returns angular position of point on the circle, in degrees, between 0
% and 360.
% with POINT: [xp yp zp]
% and CIRCLE: [X0 Y0 Z0 R THETA PHI] or [X0 Y0 Z0 R THETA PHI PSI]
% (THETA being the colatitude, and PHI the azimut)
%
% See also
% circles3d, circle3dOrigin, circle3dPoint
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-21
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% get center and radius
xc = circle(:,1);
yc = circle(:,2);
zc = circle(:,3);
% get angle of normal
theta = circle(:,5);
phi = circle(:,6);
% find origin of the circle
ori = circle3dOrigin(circle);
% normal vector of the supporting plane (cartesian coords)
vn = sph2cart2d([theta phi]);
% create plane containing the circle
plane = createPlane([xc yc zc], vn);
% find position of point on the circle plane
pp0 = planePosition(ori, plane);
pp = planePosition(point, plane);
% compute angles in the planes
theta0 = mod(atan2(pp0(:,2), pp0(:,1)) + 2*pi, 2*pi);
theta = mod(atan2(pp(:,2), pp(:,1)) + 2*pi - theta0, 2*pi);
% convert to degrees
theta = theta * 180 / pi;
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