MATLAB: How to find a (set of) mapping between two polygons

Question

Provided that there are two set of points in a plane, we can find two minimum convex polygons containing these points. Two polygons may have the same or different amount of vertices, we assume polygon A has N vertices and polygon B has M vertices, how can we find a set of mappings M that containing all feasible mapping m(i) satisfying m(i)*A ∈ B, where A is a 2*N matrix and B is 2*M and m(i) is 2*2 mapping matrix?

If m(i) is diagonal matrix then we can find a intersection of all mappings map every vertex of A inside B, but if m(i) is full-element matrix, how to find a solution?

Thank you all.

Answer 1

You cannot take a 2*2 matrix and to a matrix multiplication of it on the left hand side of a 2*N matrix and end up with a 2*M matrix. Simple rules of matrix algebra tell you that you will get a 2*N matrix, not a 2*M matrix.

I'm also confused as to why you give an index to the matrix m, as in "m(i)*A". Normally when you specify an index, you get one scalar element of m (unless m is a cell array which it's not). So I assume you meant m*A where * is the matrix multiplication operator.