Algorithms for meshing smooth surfaces and their volumes

Abstract

Quality meshes of molecular models are essential to support computational tools for new drug discovery. However, it is still challenging to generate the meshes efficiently. This thesis developed and implemented efficient algorithms for triangulating the molecular skin surface and their bounded volumes with guaranteed quality. Two skin surface meshing algorithms were developed, namely, the adaptive sweeping skin meshing algorithm and the Delaunay skin meshing algorithm. The algorithms improve the efficiency of skin meshing dramatically. Moreover, the mesh quality and the homeomorphism between the triangulation and the surface are guaranteed as well. Based on the result of quality skin surface meshing, an algorithm for generating quality tetrahedral meshes of the volumes bounded by skin surfaces was presented. The implementation results provide evidence of the efficiency and quality guarantees of the algorithms. The skin meshes generated by the algorithms will serve as an essential component in the study of the molecular shape and functions.