There is a sphere located in a point s with radius r. The Sphere is a perfect mirror. If i'm sitting in the point c, I want to cast a ray to the sphere such that I hit the point p after bouncing in the surface of the sphere. For this, I want to find the point x.
I've had some trouble formulating this problem.
How can I find x?
The point p is always visible (in the reflection) from c.
A formulation in 2D would be enough to begin with.
NOTE
The lines xc and xp do not have the same length. The line sx should be the bisector of the angle xcp.
I need to solve this problem analytically, can't use numeric methods to approximate the solution.
Best Answer
It seems that “Computing a Point of Reflection on a Sphere” was done by David Eberly and it needs to compute roots of a quartic polynomial.