1## Copyright (C) 2021 David Legland
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27
28function theta = circle3dPosition(point, circle)
29%CIRCLE3DPOSITION Return the angular position of a point on a 3D circle.
30%
31%   POS = circle3dPosition(POINT, CIRCLE)
32%   Returns angular position of point on the circle, in degrees, between 0
33%   and 360.
34%   with POINT: [xp yp zp]
35%   and CIRCLE: [X0 Y0 Z0 R THETA PHI] or [X0 Y0 Z0 R THETA PHI PSI]
36%   (THETA being the colatitude, and PHI the azimut)
37%
38%   See also:
39%   circles3d, circle3dOrigin, circle3dPoint
40%
41%   ---------
42%   author : David Legland
43%   INRA - TPV URPOI - BIA IMASTE
44%   created the 21/02/2005
45%
46
47%   HISTORY
48%   27/06/2007: change 3D angle convention
49%   2011-06-21 use degrees for angles
50
51
52% get center and radius
53xc = circle(:,1);
54yc = circle(:,2);
55zc = circle(:,3);
56
57% get angle of normal
58theta   = circle(:,5);
59phi     = circle(:,6);
60
61% find origin of the circle
62ori     = circle3dOrigin(circle);
63
64% normal vector of the supporting plane (cartesian coords)
65vn      = sph2cart2d([theta phi]);
66
67% create plane containing the circle
68plane   = createPlane([xc yc zc], vn);
69
70% find position of point on the circle plane
71pp0     = planePosition(ori,    plane);
72pp      = planePosition(point,  plane);
73
74% compute angles in the planes
75theta0  = mod(atan2(pp0(:,2), pp0(:,1)) + 2*pi, 2*pi);
76theta   = mod(atan2(pp(:,2), pp(:,1)) + 2*pi - theta0, 2*pi);
77
78% convert to degrees
79theta = theta * 180 / pi;
80