First, this is 3d problem.
I have two circle type line (closed), these line shape don't need to be Perfect Circle. They don't need to be in one plane.
Based on the lines, we can get a surface and the domain which line will be the boundary.
Let say line A will give domain A, line B will give domain B.
Now there are many points, they are in domain A. I want to find the corresponding points in domain B.
The corresponding points means:
The domain A deformed (it may involves enlarging, shrinking, translation, rotation and reflection) to domain B. The points will also move with the deformation, and the final position in domain B is what I want.
The problem is I don't have mapping function, only I have the boundary. Also, based on my few conditions, I don't need the position after deformation accurately. At least the relative position of the points should be correct. That is suppose point b is between point a and point c, then after deformation, the point b is still between point a and point c
I am now trying to write a python program to solve this problem. But I am puzzled with the first step whether there is some formula or mathematics expressions for this question.
Thank you very much.