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Geometric Elasticity for Graphics, Simulation, and Computation


Sanan, Patrick David (2014) Geometric Elasticity for Graphics, Simulation, and Computation. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/DF7X-F354.


We develop new algorithms which combine the rigorous theory of mathematical elasticity with the geometric underpinnings and computational attractiveness of modern tools in geometry processing. We develop a simple elastic energy based on the Biot strain measure, which improves on state-of-the-art methods in geometry processing. We use this energy within a constrained optimization problem to, for the first time, provide surface parameterization tools which guarantee injectivity and bounded distortion, are user-directable, and which scale to large meshes. With the help of some new generalizations in the computation of matrix functions and their derivative, we extend our methods to a large class of hyperelastic stored energy functions quadratic in piecewise analytic strain measures, including the Hencky (logarithmic) strain, opening up a wide range of possibilities for robust and efficient nonlinear elastic simulation and geometry processing by elastic analogy.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Geometry Processing, Elasticity, Matrix Functions, Surface Parameterization, Shape Interpolation
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied And Computational Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Schroeder, Peter
Thesis Committee:
  • Schroeder, Peter (chair)
  • Desbrun, Mathieu
  • Bruno, Oscar P.
  • Owhadi, Houman
Defense Date:27 November 2013
Record Number:CaltechTHESIS:12052013-121547860
Persistent URL:
Related URLs:
URLURL TypeDescription adapted for ch.2
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8039
Deposited By: Patrick Sanan
Deposited On:27 Jan 2014 20:23
Last Modified:04 Oct 2019 00:03

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