/usr/share/octave/packages/geometry-1.7.0/geom3d/intersectPlaneSphere.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.
##
## 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
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## -*- texinfo -*-
## @deftypefn {Function File} {@var{circ} =} intersectPlaneSphere(@var{plane}, @var{sphere})
## Return intersection circle between a plane and a sphere
##
## Returns the circle which is the intersection of the given plane
## and sphere.
## @var{plane} : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
## @var{sphere} : [XS YS ZS RS]
## @var{circ} : [XC YC ZC RC THETA PHI PSI]
## [x0 y0 z0] is the origin of the plane, [dx1 dy1 dz1] and [dx2 dy2 dz2]
## are two direction vectors,
## [XS YS ZS] are coordinates of the sphere center, RS is the sphere
## radius,
## [XC YC ZC] are coordinates of the circle center, RC is the radius of
## the circle, [THETA PHI] is the normal of the plane containing the
## circle (THETA being the colatitude, and PHI the azimut), and PSI is a
## rotation angle around the normal (equal to zero in this function, but
## kept for compatibility with other functions). All angles are given in
## degrees.
##
## @seealso{planes3d, spheres, circles3d, intersectLinePlane, intersectLineSphere}
## @end deftypefn
function circle = intersectPlaneSphere(plane, sphere)
# number of inputs of each type
Ns = size(sphere, 1);
Np = size(plane, 1);
# unify data dimension
if Ns ~= Np
if Ns == 1
sphere = sphere(ones(Np, 1), :);
elseif Np == 1
plane = plane(ones(Ns, 1), :);
else
error('data should have same length, or one data should have length 1');
end
end
# center of the spheres
center = sphere(:,1:3);
# radius of spheres
if size(sphere, 2) == 4
Rs = sphere(:,4);
else
# assume default radius equal to 1
Rs = ones(size(sphere, 1), 1);
end
# projection of sphere center on plane -> gives circle center
circle0 = projPointOnPlane(center, plane);
# radius of circles
d = distancePoints (center, circle0);
Rc = sqrt(Rs.*Rs - d.*d);
# normal of planes = normal of circles
nor = planeNormal(plane);
# convert to angles
[theta phi] = cart2sph2(nor(:,1), nor(:,2), nor(:,3));
psi = zeros(Np, 1);
# create structure for circle
k = 180 / pi;
circle = [circle0 Rc [theta phi psi]*k];
endfunction
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