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Geometric Discretization through Primal-Dual Meshes


Ferrari de Goes, Fernando (2014) Geometric Discretization through Primal-Dual Meshes. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/32CA-7376.


This thesis introduces new tools for geometric discretization in computer graphics and computational physics. Our work builds upon the duality between weighted triangulations and power diagrams to provide concise, yet expressive discretization of manifolds and differential operators. Our exposition begins with a review of the construction of power diagrams, followed by novel optimization procedures to fully control the local volume and spatial distribution of power cells. Based on this power diagram framework, we develop a new family of discrete differential operators, an effective stippling algorithm, as well as a new fluid solver for Lagrangian particles. We then turn our attention to applications in geometry processing. We show that orthogonal primal-dual meshes augment the notion of local metric in non-flat discrete surfaces. In particular, we introduce a reduced set of coordinates for the construction of orthogonal primal-dual structures of arbitrary topology, and provide alternative metric characterizations through convex optimizations. We finally leverage these novel theoretical contributions to generate well-centered primal-dual meshes, sphere packing on surfaces, and self-supporting triangulations.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:geometric discretization, discrete differential geometry, power diagrams, triangulations, meshing
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Computer Science
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Desbrun, Mathieu
Thesis Committee:
  • Desbrun, Mathieu (chair)
  • Schroeder, Peter
  • Owhadi, Houman
  • Alliez, Pierre
Defense Date:29 April 2014
Funding AgencyGrant Number
GooglePhD Fellowship
Record Number:CaltechTHESIS:05222014-134831171
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8258
Deposited By: Fernando Ferrari De Goes
Deposited On:29 May 2014 21:19
Last Modified:06 Nov 2019 18:15

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