How to project a point on to a sphere

Question

If i have a point (x,y,z) how to project it on to a sphere(x0,y0,z0,radius) (on its surface). My input will be the coordinates of point and sphere. The output should be the

Answer 1

Basically you want to construct a line going through the spheres centre and the point. Then you intersect this line with the sphere and you have your projection point.

In greater detail:

Let p be the point, s the sphere's centre and r the radius then x = s + r*(p-s)/(norm(p-s)) where x is the point you are looking for. The implementation is left to you.

I agree that the spherical coordinate approach will work as well but is computationally more demanding. In the above formula the only non-trivial operation is the square root for the norm.