CUHK electronic theses & dissertations collection

In this thesis we present a general framework of geometric partial differential equations from the viewpoint of geometric energy functional. The proposed geometric functional involves the Gaussian curvature, the mean curvature and the squared norms of their gradients. The geometric partial differential equations are given as the Euler-Lagrangian Equations of the geometric energy functionals by using the calculus of variation method. As a special example, we focus on Gaussian curvature related geometric energy functionals and the corresponding partial differential equations. We present three numerical methods to solve the resulting geometric partial differential equations: the direct discretization method, the finite element method and the level set method. We test these numerical schemes with a large class of geometric models. Potential applications of our proposed geometric partial differential equations include mesh optimization, surface smoothing, surface blending, surface restoration and physical simulation. Finally, we point out some possible directions of future work including singular analysis of the derived geometric partial differential equations and numerical error estimates of our numerical schemes.Yan, Yinhui."September 2008."Adviser: Kwong Chung Piney.Source: Dissertation Abstracts International, Volume: 73-01, Section: B, page: .Thesis (Ph.D.)--Chinese University of Hong Kong, 2009.Includes bibliographical references (leaves 121-134).Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web