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


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
StatePublished - 2008
EventACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08 - Singapore, Singapore
Duration: Dec 10 2008Dec 13 2008


OtherACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08

ASJC Scopus subject areas

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


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