3D Mesh Model Representation Based on Conformal Geometric Algebra and Its Similarity Assessment Application

摘要

Put forward a kind of based on conformal geometric algebra (CGA) vector structure 3D mesh model representation method. In this method, the 3D mesh model with different dimensions is mapped to the corresponding basic element (blade) in geometric algebra, which unifies the representation of multidimensional data without losing the geometric structure. Geometric and topological calculations are also handled in a clear and coordinate free manner. Under CGA framework, the basic geometric, spatial and metric relations are formed by inner and outer operators. A CGA-based 3D mesh model representation method is designed to evaluate the similarity of 3D mesh models. Experiments show that our method surpasses the most advanced similarity evaluation algorithm for 3D mesh models. Under the unified space structure of the method for analysis and application of 3D mesh model provides effective tools.