Abstract: 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).