Multiresolution Modeling and Interactive Deformation of Large 3D Meshes

Due to their simplicity triangle meshes are often used to represent geometric surfaces. Their main drawback is the large number of triangles that are required to represent a smooth surface. This problem has been addressed by a large number of mesh simplification algorithms which reduce the number of triangles and approximate the initial mesh. Hierarchical triangle mesh representations provide access to a triangle mesh at a desired resolution, without omitting any information. In this paper we demonstrate how a hierarchical structure of a mesh can be derived for arbitrary meshes to enable intuitive and efficient modifications without restrictions on the underlying connectivity. We combine mesh reduction algorithms and constrained energy minimization to decompose the given mesh into several frequency bands and focus on a stabilizing technique to encode the geometric difference between the levels.