/usr/share/octave/packages/geometry-1.7.0/geom3d/circle3dPosition.m is in octave-geometry 1.7.0-1build1.
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## Copyright (C) 2004-2011 INRA - CEPIA Nantes - MIAJ (Jouy-en-Josas)
## Copyright (C) 2012 Adapted to Octave by Juan Pablo Carbajal <carbajal@ifi.uzh.ch>
## All rights reserved.
##
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{pos} =} circle3dPosition(@var{point}, @var{circle})
## Return the angular position of a point on a 3D circle
##
## Returns angular position of point on the circle, in degrees, between 0
## and 360.
## with @var{point}: [xp yp zp]
## and @var{circle}: [X0 Y0 Z0 R THETA PHI] or [X0 Y0 Z0 R THETA PHI PSI]
## (THETA being the colatitude, and PHI the azimut)
##
## @seealso{circles3d, circle3dOrigin, circle3dPoint}
## @end deftypefn
function theta = circle3dPosition(point, circle)
# 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;
endfunction
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