Mesh Optimization

We present a method for solving the following problem: Given a set of data points scattered in three dimensions and an initial triangular mesh M0 , produce a mesh M , of the same topological type as M0 , that fits the data well and has a small number of vertices. Our approach is to minimize an energy function that explicitly models the competing desires of conciseness of representation and fidelity to the data. We show that mesh optimization can be effectively used in at least two applications: surface reconstruction from unorganized points, and mesh simplification (the reduction of the number of vertices in an initially dense mesh of triangles). CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling. Additional Keywords: Geometric Modeling, Surface Fitting, Three-Dimensional Shape Recovery, Range Data Analysis, Model Simplification. 1 Introduction The mesh optimization problem considered in this paper can be roughly stated as fo..