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.
|Publication status||Published - 2008|
|Event||ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08 - Singapore, Singapore|
Duration: 10 Dec 2008 → 13 Dec 2008
|Conference||ACM SIGGRAPH ASIA 2008 Courses, SIGGRAPH Asia'08|
|Period||10/12/08 → 13/12/08|