ACM SIGGRAPH 1993 Proceedings, 19-26.
Traversing the space of triangle meshes to optimize model fidelity and conciseness.
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 M_0, produce a mesh M, of the same topological type as M_0, 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).
Hindsight: The technique demonstrates that general optimization can achieve surprisingly good results. This particular optimization searches over a broad space of both discrete and continuous variables to find a concise mesh accurately fitting a set of data points. A similar approach was used by Lindstrom and Turk in their Image-driven mesh optimization work. Mesh optimization is quite powerful for feature-sensitive remeshing, as it automatically migrates vertices onto sharp features (e.g. as used in multi-chart geometry images). For the application of mesh simplification, progressive meshes offer a more elegant solution.
ACM Copyright Notice
Copyright by the Association for Computing Machinery, Inc. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Publications Dept, ACM Inc., fax +1 (212) 869-0481, or email@example.com. The definitive version of this paper can be found at ACM's Digital Library http://www.acm.org/dl/.