Matching free-form surfaces

Abstract

In this work, the matching problem between two free-form parametric surfaces, S 0(u, v) and S 1(u, v) , has been considered in the context of a first stage of the metamorphosis process, which is defined as gradual and continuous transformation of one key shape into another. A method is presented to approximate the two reparametrization functions, r(u, v) and t(u, v), via a discrete sampled set of N 2 grid samples on the surfaces. The N 2 samples on the source surface are matched against the N 2 samples on the target surface, employing a resemblance metric between their Gauss fields as a criterion. The method preserves the connectivity of the two key surfaces as well. Thus, the resulting reparameterization functions, interpolating the discrete solution must be diffeomorphism. The algorithm works with simple open surfaces, i.e. the surfaces that are homeomorphic to a disk.