Discrete Shells

How to read this

Category

Method: discrete differential geometry model for thin shells

Contributions

• A discrete shell model for thin flexible structures with a curved undeformed configuration, with nonlinear membrane and flexural energies defined geometrically over triangle meshes
• A bending energy expressed as the squared difference of dihedral angles between deformed and undeformed states, measuring change in mean curvature and invariant under rigid motion
• An implementation requiring only a small change to a standard cloth simulator, with materials ranging from paper to metal

Context

Builds on Baraff and Witkin's Large Steps in Cloth Simulation and the discrete-differential-geometry tradition, recasting thin-shell bending as a geometric hinge-angle energy.Builds on: Large Steps in Cloth Simulation

Correctness

Demonstrated across paper-to-metal materials including a real-versus-simulated falling-hat comparison and creased paper; reader caveat is that the model assumes a triangle-mesh hinge formulation, so behavior depends on mesh resolution and on energy parameters, and plasticity is handled in the demonstrated cases rather than a general elastoplastic theory.

Clarity

Accessible for a DDG paper; a first pass conveys the dihedral-angle bending idea, a second pass is needed for the energy derivation.

How to read it

Focus on the hinge-angle bending energy and its rigid-motion invariance, plus the curved rest-state assumption; a second pass on the energy formulation pays off if you implement or modify a shell solver.