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A Variational Approach to Eulerian Geometry Processing of Surfaces and Foliations


Mullen, Patrick Gary (2007) A Variational Approach to Eulerian Geometry Processing of Surfaces and Foliations. Master's thesis, California Institute of Technology. doi:10.7907/Q51A-W257.


We present a purely Eulerian framework for geometry processing of surfaces and foliations. Contrary to current Eulerian methods used in graphics, we use conservative methods and a variational interpretation, offering a unified framework for routine surface operations such as smoothing, offsetting, and animation. Computations are performed on a fixed volumetric grid without recourse to Lagrangian techniques such as triangle meshes, particles, or path tracing. At the core of our approach is the use of the Coarea Formula to express area integrals over isosurfaces as volume integrals. This enables the simultaneous processing of multiple isosurfaces, while a single interface can be treated as the special case of a dense foliation. We show that our method is a powerful alternative to conventional geometric representations in delicate cases such as the handling of high-genus surfaces, weighted offsetting, foliation smoothing of medical datasets, and incompressible fluid animation.

Item Type:Thesis (Master's thesis)
Subject Keywords:digital geometry processing; fluids; foliations; gradient flows; mean curvature flow
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:
  • Unknown, Unknown
Defense Date:21 May 2007
Record Number:CaltechETD:etd-05212007-160139
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1920
Deposited By: Imported from ETD-db
Deposited On:23 May 2007
Last Modified:05 Feb 2020 20:37

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PDF (MasterThesis.pdf) - Final Version
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