Type
ThesisAuthors
Sun, Xiang
Advisors
Pottmann, Helmut
Committee members
Kasimov, Aslan R.
Mitra, Niloy J.

Date
2012-06Embargo End Date
2014-12-31Permanent link to this record
http://hdl.handle.net/10754/273092
Metadata
Show full item recordAccess Restrictions
At the time of archiving, the student author of this thesis opted to temporarily restrict access to it. The full text of this thesis became available to the public after the expiration of the embargo on 2014-12-31.Abstract
This thesis presents an overview of some approaches to compute Gaussian and mean curvature on discrete surfaces and discusses discrete minimal surfaces. The variety of applications of differential geometry in visualization and shape design leads to great interest in studying discrete surfaces. With the rich smooth surface theory in hand, one would hope that this elegant theory can still be applied to the discrete counter part. Such a generalization, however, is not always successful. While discrete surfaces have the advantage of being finite dimensional, thus easier to treat, their geometric properties such as curvatures are not well defined in the classical sense. Furthermore, the powerful calculus tool can hardly be applied. The methods in this thesis, including angular defect formula, cotangent formula, parallel meshes, relative geometry etc. are approaches based on offset meshes or generalized offset meshes. As an important application, we discuss discrete minimal surfaces and discrete Koenigs meshes.Citation
Sun, X. (2012). Discrete Curvatures and Discrete Minimal Surfaces. KAUST Research Repository. https://doi.org/10.25781/KAUST-TX818ae974a485f413a2113503eed53cd6c53
10.25781/KAUST-TX818