A computational algebraic topology model for the deformation of curves

Abstract

A new method for the deformation of curves is presented. It is based upon a decomposition of the linear elasticity problem into basic physical laws. Unlike other methods which solve the partial differential equation arising from the physical laws by numerical techniques, we encode the basic laws using computational algebraic topology. Conservative laws use exact global values while constitutive allow to make wise assumptions using some knowledge about the problem and the domain. The deformations computed with our approach have a physical interpretation. Furthermore, our algorithm performs with either 2D or 3D problems. We finally present an application of the model in updating road databases and results validating our approach.