Here is problem. I have one torus defined in space by coordinates (x,y,z) and it can be rotated in any direction. You can imagine it as torus total free in space. Torus is defined by two radius (R,r) as well. This torus is ring torus. For example: location (10,10,10) rotation (20°,20°,20°) R=50, r=1
1) How to test is given point M(x,y) is inside that torus?
2) If I have another torus with same (R,r) and it has two points that belong to both torus how I can calculate x,y,z and rotation in space for the second torus? (I have all information for first torus and coordinates for two points)
3) This is a variation of the second question. If I have two tori with same (R,r) and x,y,z and rotations in space, how do I calculate intersection points (one or two points that is located on surface and belong to both torus - like on image). Of course if those points exist for given conditions.
The simplest answer is better. I need it for software.