Shin Yoshizawa

This thesis presents a set of new mesh processing methods which are based on computational dierential geometry techniques. The underlying idea of the methods consists of using proper discrete approximations of dierential surface properties. The methods developed in the thesis contribute to the areas of curvature feature detection, mesh parameterization, fair mesh gener-ation, mesh denoising, and free-form and variational mesh deformations. Comparisons of the developed methods with several state-of-the-art techniques and algorithms are done. The results of numerous numerical experiments demonstrate signicant advantages of the proposed methods over conventional techniques. Applications of the methods are discussed and demonstrated. The main contributions of the thesis are as follows: Similarity-based Mesh Denoising. A new, powerful, and high quality feature preserving mesh/soup denoising technique and a new scheme for comparing dierent mesh/soup smoothing methods are proposed. The technique is based on a similarity-weighted av-eraging procedure and a new and robust similarity measuring scheme. Fair Mesh Generation via Elastica. A new numerical scheme for generating fair meshes i