Manipulation of parametric surfaces through a simple deformation algorithm

Abstract

In this paper, we present a novel but simple physics based method to manipulate parametric surfaces. This method can deal with local deformations with an arbitrarily complicated boundary shape. We firstly map a deformation region of a 3D surface to a circle on a 2D parametric plane. Then we derive an approximate analytical solution of a set of fourth order partial differential equations subjected to sculpting forces and the boundary conditions of the circle. With the obtained solution, we show how to create a deformed surface and how sculpting forces and the shape control parameters affect the shape of a deformed surface. Finally, we provide some examples to demonstrate the applications of our proposed method in surface manipulation.