Parameterization For Meshes And Its Application In Texture Rendering

Texture rendering is an important component of realistic computer graphics. 3D meshes' texture rendering usually needs parameterize 3D meshes to 2D space and then map them to texture space. As an important part of 3D meshes' texture rendering, parameterizations of 3D meshes are also the fundament of the further processing of 3D meshes' geometry and topology information.Parameterizations for 3D meshes can be classified into two parts: planar parameterizations and spherical parameterizations. Planar parame- terizations will flatten the meshes and then parameterize them. Methods include: combination parameterization, minimal energy method, mesh pa- rameterization with virtual boundary, multi-resolution analysis, MIPS, subdivision methods. Spherical parameterization will map the meshes to sphere and then parameterize them. Methods include: spherical paramete- rizations based on relaxation, conformal spherical parameterizations, pro- gressive spherical parameterization. The time complexity of spherical parameterization is high and the mapping between sphere and planar will bring some new distortion. Planar parameterization is simple and stable, so it has been widely applied.This thesis summarizes the methods of parameterizations for meshes, and gives some introductions for planar parameterization and spherical parameterization. It gives the mathematics theories of planar convex parameterization. And based on it, this thesis compares algorithms of optimizing the parameterization according to the parameterization result. This thesis introduce a new optimization algorithm. It first finds all the crowded area, and them optimize them. The experiment result supports that this algorithm could decrease the distortion of parameterization. And this thesis compare this algorithm's time complexity with others'.This thesis also describes the framework of 3D meshes'texture rendering . It discusses the parameterization for meshes with borders, and the hidden algorithm in the 3D meshes'texture rendering. Also this thesis introduce the mapping algorithm between to triangles. With the parameterization algorithm and 3D meshes'texture rendering framework introduced by this thesis, the experiment results are presented.At last the thesis discuss the future work of parameterizations for 3D meshes.