Self-organization of surface shapes

A problem in surface modeling and approximation is how to sample a surface into a set of significant points. It is desirable that the sampling is done in such a way that best preserves the original shape. A principle is that highly curved area should be sampled densely and vice versa. This paper presents a self-organization method for automated surface sampling in this principle. Given a scale shape function of local curvedness of the surface and a number of samples, the set of optimal locations of sample points is defined as the solution to a system of nonlinear equations. The solution can be found using a simple iterative algorithm involving no free parameters. The algorithm forms topology-preserving meshes from random initialisation. Mesh spacing vs. surface curvedness can be easily controlled by a single parameter in the shape function. Key locations can be prescribed by imposing additional boundary conditions. Experiments are presented with synthetic data.