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 INRA - TPV URPOI - BIA IMASTE created the 18/02/2005.
0001 function circle = intersectPlaneSphere(plane, sphere) 0002 %INTERSECTPLANESPHERE Return intersection circle between a plane and a sphere. 0003 % 0004 % CIRC = intersectPlaneSphere(PLANE, SPHERE) 0005 % Returns the circle which is the intersection of the given plane 0006 % and sphere. 0007 % PLANE : [x0 y0 z0 dx1 dy1 dz1 dx2 dy2 dz2] 0008 % SPHERE : [XS YS ZS RS] 0009 % CIRC : [XC YC ZC RC THETA PHI PSI] 0010 % [x0 y0 z0] is the origin of the plane, [dx1 dy1 dz1] and [dx2 dy2 dz2] 0011 % are two direction vectors, 0012 % [XS YS ZS] are coordinates of the sphere center, RS is the sphere 0013 % radius, 0014 % [XC YC ZC] are coordinates of the circle center, RC is the radius of 0015 % the circle, [THETA PHI] is the normal of the plane containing the 0016 % circle (THETA being the colatitude, and PHI the azimut), and PSI is a 0017 % rotation angle around the normal (equal to zero in this function, but 0018 % kept for compatibility with other functions). All angles are given in 0019 % degrees. 0020 % 0021 % See Also: 0022 % planes3d, spheres, circles3d, intersectLinePlane, intersectLineSphere 0023 % 0024 % --------- 0025 % author : David Legland 0026 % INRA - TPV URPOI - BIA IMASTE 0027 % created the 18/02/2005. 0028 % 0029 0030 % HISTORY 0031 % 27/06/2007: change output format of circle, add support for multiple 0032 % data 0033 % 2011-06-21 use degrees for angles 0034 0035 % number of inputs of each type 0036 Ns = size(sphere, 1); 0037 Np = size(plane, 1); 0038 0039 % unify data dimension 0040 if Ns ~= Np 0041 if Ns == 1 0042 sphere = sphere(ones(Np, 1), :); 0043 elseif Np == 1 0044 plane = plane(ones(Ns, 1), :); 0045 else 0046 error('data should have same length, or one data should have length 1'); 0047 end 0048 end 0049 % center of the spheres 0050 center = sphere(:,1:3); 0051 0052 % radius of spheres 0053 if size(sphere, 2) == 4 0054 Rs = sphere(:,4); 0055 else 0056 % assume default radius equal to 1 0057 Rs = ones(size(sphere, 1), 1); 0058 end 0059 0060 % projection of sphere center on plane -> gives circle center 0061 circle0 = projPointOnPlane(center, plane); 0062 0063 % radius of circles 0064 d = distancePoints3d(center, circle0); 0065 Rc = sqrt(Rs.*Rs - d.*d); 0066 0067 % normal of planes = normal of circles 0068 nor = planeNormal(plane); 0069 0070 % convert to angles 0071 [theta, phi] = cart2sph2(nor(:,1), nor(:,2), nor(:,3)); 0072 psi = zeros(Np, 1); 0073 0074 % create structure for circle 0075 k = 180 / pi; 0076 circle = [circle0 Rc [theta phi psi]*k];