Intersection between a line and a sphere

Question

I\'m trying to find the point of intersection between a sphere and a line but honestly, I don\'t have any idea of how to do so. Could anyone help me on this one ?

Answer 1

Here's a more concise formulation using inner products, less than 100 LOCs, and no external links. Also, the question was asked for a line, not a line segment.

Assume that the sphere is centered at C with radius r. The line is described by P+l*D where D*D=1. P and C are points, D is a vector, l is a number.

We set PC = P-C, pd = PC*D and s = pd*pd - PC*PC + r*r. If s < 0 there are no solutions, if s == 0 there is just one, otherwise there are two. For the solutions we set l = -pd +- sqrt(s), then plug into P+l*D.