A Caltech Library Service

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.


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:14 Apr 2015 15:52

Thesis Files

PDF - Final Version
See Usage Policy.


Repository Staff Only: item control page