Chapter 2 - Mesh Simplification

Abstract

The purpose of this chapter is to provide an overview of various mesh simplification algorithms. It describes mesh simplification as an optimization process under fidelity-based or triangle-budget-based constraints, to be achieved by the application of local and global mesh simplification operators. A mesh in 3D graphics has two components: the mesh geometry, represented by the vertices, and the mesh connectivity, represented by the edges or faces that connect the vertices. The mesh connectivity encodes the topology of the mesh, that is, the number of holes, tunnels, and cavities in that mesh. Simplification of the mesh geometry may or may not result in simplification of the mesh topology. Algorithms for mesh simplification deal almost exclusively with triangle meshes. If a mesh is composed of non-triangulated polygons, one will need to triangulate them in a preprocessing step. Many triangulation algorithms exist such as Seidel's incremental randomized algorithm to triangulate a non-self-intersecting polygon with n vertices in time. Local operators simplify the geometry and connectivity in a local region of the mesh, reducing the number of polygons, while global operators operate over much larger regions and help simplify the mesh topology. This chapter also addresses the desirability of topology simplification for different applications. It provides a range of mesh simplification operators available. The chapter closes with a discussion on various optimization frameworks in which these operators are chosen and applied to the mesh.