Parameterization of Mesh Models: Theory, Implementation and Applications

http://portal.acm.org/Mesh parameterization has been a very active research topic for the last several years, since it appeared as a fundamental tool for a wide class of problems in Digital Geometry. Its applications include texture mapping, geometry processing, remeshing, pasting, morphing, compression and reconstruction to name but a few. Computing a parameterization of a mesh model means finding a set of 2d coordinates associated to each vertex of the mesh. These coordinates are defined by the solution of a linear system, or correspond to the minimizer of a (possibly non-linear) energy functional. We will first explain the basic concepts and theorems that transform the parameterization problem into a numerical problem, and review the most popular methods. We will then explain how to solve the numerical optimization problem in practice. The presentation will be illustrated by demonstrations and examples of applications in the industry. The source-code corresponding to the demos is available online, in the OpenNL library (http://www.loria.fr/~levy/software/). To conclude, we will review some on-going research about the parameterization of meshes with arbitrary genus, currently tackled by the Digital Geometry research community