Discrete models for geometric objects

Abstract

This lecture presents and discusses the use of discrete models for modeling geometric objects. Discrete models (voxel representations, octrees, KD-trees, interval solids or even point representations) are emerging as a flexible tool for geometric modeling. These algorithms exploit the trade-off between robustness and memory. The availability at low cost of large amounts of memory affords thus completely robust models. Discrete bands can be used for instance for reconstructing valid closed models from point clouds, and to obtain different kinds of smooth Boundary Representations. On the other hand, discrete representations are specially well suited for error-bounded geometry and topology simplification, being also useful for occlusion culling in the inspection and navigation of very large virtual environments. Basic tools for modeling, surface extraction and visualization, simplification and relaxation will be described, and a number of potential applications will be presented.