Details

Autor(en) / Beteiligte

• Sanan, Patrick

Titel

Geometric Elasticity for Graphics, Simulation, and Computation

Ort / Verlag

ProQuest Dissertations Publishing

Erscheinungsjahr

2014

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• 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.