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).

Highly detailed geometric models are rapidly becoming common-place in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.

Many applications in computer graphics require complex, highly detailed models. However, the level of detail actually necessary may vary considerably. To control processing time, it is often desirable to use approximations in place of excessively detailed models. We have developed a surface simplification algorithm which can rapidly produce high quality approximations of polygonal models. The algorithm uses iterative contractions of vertex pairs to simplify models and maintains surface error approximations using quadric matrices. By contracting arbitrary vertex pairs (not just edges), our algorithm is able to join unconnected regions of models. This can facilitate much better approximations, both visually and with respect to geometric error. In order to allow topological joining, our system also supports non-manifold surface models.