I have two surfaces, neither of which has an analytic expression. As an illustration, see the image below.
The outer surface has a series of points on it, derived from a meshing software. I need to map these points to the other surface in such a way that as many of the mesh characteristics (angle between points in particular) is preserved as possible. Think of shrink wrapping the outer surface onto the inner surface. The actual surfaces are "nice" in that they are smooth, no sharp edges and no discontinuities, and the boundaries are always circular.
My thoughts... Start with the boundaries - there is one opening on each surface. Map the points on the outer surface boundary to the inner surface boundary such that the distance between each pair of points is shrunk by the ratio of boundary arc lengths. Then for the rest of the points my idea is to shrink the distances between points by the square root of the ratio of the areas of the surfaces to try to end up with shape preserved triangles. Of course this will not lead to the correct solution because the surfaces have different local curvature. Does anyone know how to account for the local curvature? Numerical methods are expected.
Thanks!