Cubic shells

Hinge-based bending models are widely used in the physically-based animation of cloth, thin plates and shells. We propose a hinge-based model that is simpler to implement, more efficient to compute, and offers a greater number of effective material parameters than existing models. Our formulation builds on two mathematical observations: (a) the bending energy of curved flexible surfaces can be expressed as a cubic polynomial if 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. Our contribution impacts a general range of surface animation applications, from isotropic cloth and thin plates to orthotropic fracturing thin shells.