Mesh Parameterization Methods And Compression Applications, The Geometric Information

The property of computer graphics is that the three dimensional geometry data sets are widely used for various purposes. In the most common form, the 3D dimensional data sets are represented as triangle meshes, i.e. collections of polygons with their associated properties . The triangle mesh is divided into two parts: the first part is termed topology information, which refers to the connectivity of the vertices in the mesh; the second part is termed as geometry information, which refers to the vertex locations and other attributes including color, normal, texture coordinates etc. The parametrization of triangle mesh is the basis of doing with these topology information and geometry information of triangle meshes. The parametrization of triangle mesh plays increasingly important roles in many fields including computer graphics, computer aided geometry design and digital geometry processing etc.First,we deeply discuss all of parameterization algorithms in term of the extent of parametrization and detailly compare various algorithms on theoretical base, time and space complexity, applied environments and numerical implementations. Second,by incorporating local parameterization into the progressive mesh representation, we provide a robust and fast global spherical parameterization algorithm for arbitrary 2-manifold meshes. The algorithm generates a spherical parameterization for each level mesh of the PM after a single run. At last, by generalizing our spherical parameterization algorithm and adaptive sampling scheme to the planar case, we can adopt image compression algorithms to compress geometric signals.After introducing some backgrounds and the state of art of triangle mesh and the parametrization of triangle mesh in Chapter 1 , we describe the two key algorithms of parametrization: planar parameterization and base mesh parameterization in Chapter 2. In Chapter 3, we describe spherical parameterization algorithm. Chapter 4 introduces our geometric signal compression algorithm based on planar parameterization. Finally, we conclude this dissertation .