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Discrete Differential Operators for Computer Graphics


Meyer, Mark (2004) Discrete Differential Operators for Computer Graphics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/M3NP-4G18.


This thesis presents a family of discrete differential operators. Since these operators are derived taking into account the continuous notions of differential geometry, they possess many similar properties. This family consists of first- and second-order properties, both geometric and parametric. These operators are then analyzed and their practical use is tested in several example applications.

First, the operators are used in a smoothing application. Due to the properties of the operators, the resulting smoothing algorithm is general, efficient and robust to sampling problems. The smoothing can be applied to many different inputs ranging from images to surfaces to volume data.

Second, a surface remeshing technique using the operators is presented. Given the operators, we present an algorithm that resamples a surface mesh according to several geometric criteria (integrated curvature, directional curvature, geometric distortion). The resulting algorithm is efficient, general and user-tunable.

Next, a surface mesh parameterization technique is presented. Using geometric invariants associated with the discrete operators, we present an efficient, tunable parameterization algorithm that is robust to sampling irregularities in the input model. Using the properties of the differential operators allows us to make a parameterization algorithm that relies only on geometric information and not the original parameterization of the input model.

Finally, we conclude and present future work including physical simulation and sampling theory.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:curvature; parameterization; remeshing; smoothing
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Barr, Alan H.
Thesis Committee:
  • Barr, Alan H. (chair)
  • Desbrun, Mathieu
  • Schroeder, Peter
  • Perona, Pietro
Defense Date:26 May 2004
Record Number:CaltechETD:etd-05282004-085345
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:2186
Deposited By: Imported from ETD-db
Deposited On:28 May 2004
Last Modified:03 Feb 2021 23:46

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