MATLAB: How to get the coordinate of a point on Sphere
mathematics
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The solution requires the definition of a rotation matrix. There are several ways to use it. Matlab has the rotx, roty and rotz functions, but they only work with one rotation at time. My implementation (see attachment) works by defining the new coordinate system identified by the position of the new center P0, any point along the new z axis Pz, and any point along the new x axis Px. So the call is R = rotationMatrix(P0,Pz,Px); I understand that these few words can be complex to understand but if you need details, I can explain further. Now the code
clear variables, close all% points
P1 = [0 0 0]; P8 = [0 0 1]; P5 = [1 .5 2]; P6 = [2 2 3];% plot
h = figure; hold onplot3(P1(1),P1(2),P1(3),'o')plot3(P8(1),P8(2),P8(3),'o')plot3(P5(1),P5(2),P5(3),'o')plot3(P6(1),P6(2),P6(3),'o')axis equal, view([1 1 1])% center
C0 = (P1+P5)/2; % centerfigure(h), plot3(C0(1),C0(2),C0(3),'*')% radius
R = sqrt(sum((P5-P1).^2,2))/2;% circumpherence in local coordinates
nPt = 100;alpha = linspace(0,2*pi,nPt).';P = [R.*cos(alpha) R.*sin(alpha) zeros(nPt,1)];% direction orthogonal to circumpherence 1
v1 = cross(P8-P1,P5-P1);figure(h), quiver3(C0(1),C0(2),C0(3),v1(1),v1(2),v1(3))% rotation matrix
R1 = rotationMatrix(C0,C0+v1,P5);% circumpherence 1 rotate points
Pc1 = P*R1'+C0;plot3(Pc1(:,1),Pc1(:,2),Pc1(:,3),'-');% direction orthogonal to circumpherence 2
v2 = cross(P6-P1,P5-P1);figure(h), quiver3(C0(1),C0(2),C0(3),v2(1),v2(2),v2(3))% rotation matrixR2 = rotationMatrix(C0,C0+v2,P5);% circumpherence 2 rotate points
Pc2 = P*R2'+C0;plot3(Pc2(:,1),Pc2(:,2),Pc2(:,3),'-');Please check if I have provided everything you need, because I have many personal utility functions in matalb path
First get the radius of sphere....I hope center is (0,0,0). To get radius use:
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