Research On Compatible Triangulation And Remeshing

Compatible triangulation is a basic problem in computational geometry. It is used in many areas, such as computer graphics, animations, movie and modeling. Our research is focused on compatible triangulations of planar polygons and techniques for remeshing. The main idea of this thesis is:First we introduce compatible triangulations and get the experiment result on existed algorithms. Then we analyze the results to compare the number of Steiner (interior) points added to the polygons and the algorithm complexity. We also present a method to compute compatible triangulations of planar polygons with a very small number of Steiner vertices. It will cost less time compared with other algorithms.Being close to optimal in terms of the number of Steiner vertices, these compatible triangulations are usually not of high quality, i. e., do not have well-shaped triangles. We show how to increase the quality of these triangulations by adding Steiner vertices in a compatible manner, combining several techniques for remeshing and mesh smoothing. The total scheme results in high-quality compatible meshes with a small number of triangles. Then we present how to compatible triangulate two polygons by Parameterization and smooth approximation of surface. This will get good result in some conditions.