Chapter 5: Simple and efficient implementation of discrete plates and shells

Max Wardetzky, Miklós Bergou, Akash Garg, David Harmon, Denis Zorin, Eitan Grinspun

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Efficient computation of curvature-based energies is important for practical implementations of geometric modeling and physical simulation applications. Building on a simple geometric observation, we propose a hinge-based bending model that is simple to implement, efficient to compute, and offers a great number of effectivematerial parameters. Our formulation builds on two mathematical observations: (a) the bending energy of a thin flexible plate (resp. shell) can be expressed as a quadratic (resp. cubic) polynomial of surface positions provided that the surface does not stretch; (b) a general class of anisotropic materials-those that are orthotropic-is captured by appropriate choice of a single stiffness per hinge. We provide two approaches for deriving our isometric bending model (IBM): a purely geometric view and a derivation based on finite elements. By offering a highly efficient treatment of force Jacobians, our model impacts the speed of a general range of surface animation applications, from isotropic cloth and thin plates, over orthotropic fracturing of thin shells, to Willmore-type surface fairing.

Original languageEnglish (US)
Title of host publicationACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08
DOIs
StatePublished - 2008
EventACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08 - Singapore, Singapore
Duration: Dec 10 2008Dec 13 2008

Other

OtherACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08
CountrySingapore
CitySingapore
Period12/10/0812/13/08

Fingerprint

Hinges
Animation
Stiffness
Polynomials

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Human-Computer Interaction
  • Media Technology

Cite this

Wardetzky, M., Bergou, M., Garg, A., Harmon, D., Zorin, D., & Grinspun, E. (2008). Chapter 5: Simple and efficient implementation of discrete plates and shells. In ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08 [13] https://doi.org/10.1145/1508044.1508057

Chapter 5 : Simple and efficient implementation of discrete plates and shells. / Wardetzky, Max; Bergou, Miklós; Garg, Akash; Harmon, David; Zorin, Denis; Grinspun, Eitan.

ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08. 2008. 13.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Wardetzky, M, Bergou, M, Garg, A, Harmon, D, Zorin, D & Grinspun, E 2008, Chapter 5: Simple and efficient implementation of discrete plates and shells. in ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08., 13, ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08, Singapore, Singapore, 12/10/08. https://doi.org/10.1145/1508044.1508057
Wardetzky M, Bergou M, Garg A, Harmon D, Zorin D, Grinspun E. Chapter 5: Simple and efficient implementation of discrete plates and shells. In ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08. 2008. 13 https://doi.org/10.1145/1508044.1508057
Wardetzky, Max ; Bergou, Miklós ; Garg, Akash ; Harmon, David ; Zorin, Denis ; Grinspun, Eitan. / Chapter 5 : Simple and efficient implementation of discrete plates and shells. ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08. 2008.
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