Implicit Surface Polygonization

The aim of implicit surface polygonization is to generate robust and curvature-related regular mesh. Since Bloomenthal's polygonization is robust enough, ue will use the mesh generated by Bloomenthal's polxgonizer as the initial mesh, then we adapt it to what we need. We present two polygonizers. One is fast polygonization of implicit surface, which can generate a regular mesh quickly. The other is re-polygonization of implicit surface, which can generate curvature-related regular mesh.The whole framework of the paper is organized as follows: In chapter one. we introduce background knowledge of implicit surface polygonization. analyze the existing algorithms, and present the innovative contribution of the paper. In chapter two. we present fast polygonization of implicit surface. We discuss in detail the two steps of this algorithm. This approach has two advantages. One is simplicity and high performance. The algorithm is simple to implement, and is much faster than Bloomenthal's polygonizer. The other is good mesh regularity. As mesh optimization is applied before subdivision step, this approach can generate uniform triangles with high quality mesh regularity. In chapter three, we present re-polygonization of implicit surface. This approach will generate a middle tessellation based on the initial mesh, removing the old vertices from the middle tessellation, and we can get a curvature-based regular mesh. Finally, we conclude this dissertation and discuss some directions for future work.