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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 circle = intersectPlaneSphere(plane, sphere)
%INTERSECTPLANESPHERE Return intersection circle between a plane and a sphere.
%
% CIRC = intersectPlaneSphere(PLANE, SPHERE)
% Returns the circle which is the intersection of the given plane
% and sphere.
% PLANE : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2]
% SPHERE : [XS YS ZS RS]
% 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.
%
% See also
% planes3d, spheres, circles3d, intersectLinePlane, intersectLineSphere
% ------
% Author: David Legland
% E-mail: david.legland@inrae.fr
% Created: 2005-02-18
% Copyright 2005-2023 INRA - TPV URPOI - BIA IMASTE
% 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 = distancePoints3d(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];
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