Validity-Preserving Simplification of Very Complex Polyhedral Solids

In this paper we introduce the Discretized Polyhedra Simplification (DPS), a framework for polyhedra simplification using space decomposition models. The DPS is based on a new error measurement and provides a sound scheme for error-bounded, geometry and topology simplification while preserving the validity of the model. A method following this framework, Direct DPS, is presented and discussed. Direct DPS uses an octree for topology simplification and error control, and generates valid solid representations. Our method is also able to generate approximations which do not interpenetrate the original model, either being completely contained in the input solid or bounding it. Unlike most of the current methods, restricted to triangle meshes, our algorithm can deal and also produces faces with arbitrary complexity.