Polygon reduction of 3D objects using Stokes' theorem

Surface over volume rendering can be useful for many applications. However, the tremendously large number of polygons composing the surface primitives should be reduced to a manageable size so as to utilize the capability of low cost hardware and software rendering engines, a standard Internet protocol and VRML format. In this paper, we propose a novel algorithm that deletes several vertices simultaneously by forming a closed arbitrary shaped boundary. The Stokes' theorem, used in electro-magnetic field analysis, was newly adapted to extract the arbitrary shaped boundary. The simultaneous deletion procedure provides a computational gain and increases the reduction ratio without sacrificing the topological distortion of the original mesh. Numerically synthesized polygonal objects and real CT data were tested to evaluate the performance of the new algorithm and to demonstrate the possibility of a medical rendering application. The new algorithm outperforms the conventional decimation algorithm in both computational and reduction efficiency.