Sanan, Patrick David (2014) Geometric elasticity for graphics, simulation, and computation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechTHESIS:12052013-121547860
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)|
|Defense Date:||27 November 2013|
|Default Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Patrick Sanan|
|Deposited On:||27 Jan 2014 20:23|
|Last Modified:||14 Apr 2015 15:52|
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