A new representation of orientable 2-manifold polygonal surfaces for geometric modelling

INTRODUCTION Polygonal surface has become ubiquitous due to its efficient representation of highly detailed geomet- ric objects with arbitrary topological type. In real-world simulation and analysis, a 3D physical object is modelled as a closed subset in ú3 bounded by a connected, compact and orientable 2D manifold. For algorithmically describing orientable 2-manifold polygonal surfaces, the practical data structure should not only easily check manifold property and topo- logical consist…

A new representation of orientable 2-manifold polygonal surfaces for geometric modelling

Many graphics and computer-aided design applications require that the polygonal meshes used in geometric com- puting have the properties of not only 2-manifold but also are orientable. In this paper, by collecting previous work scattered in the topology and geometry literature, we rigorously present a theoretical basis for orientable polygonal surface representation from a modern point of view. Based on the presented basis, we propose a new combinatorial data structure that can guarantee the property of orientable 2-manifolds and is primal/dual efficient. Comparisons with other widely used data structures are also presented in terms of time and space efficiency.