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Modeling arbitrarily large deformations of surfaces smoothly embedded inthree-dimensional space is challenging. The difficulties come from two aspects:the existing geometry processing or forward simulation methods penalize thedifference between the current status and the rest configuration to maintainthe initial shape, which will lead to sharp spikes or wiggles for largedeformations; the co-dimensional nature of the problem makes it morecomplicated because the deformed surface has to locally satisfy compatibilityconditions on fundamental forms to guarantee a feasible solution exists. Toaddress these two challenges, we propose a rotation-strain method to modify thefundamental forms in a compatible way, and model the large deformation ofsurface meshes smoothly using plasticity. The user prescribes the positions ofa few vertices, and our method finds a smooth strain and rotation field underwhich the surface meets the target positions. We demonstrate several exampleswhereby triangle meshes are smoothly deformed to large strains while meetinguser constraints.

A Rotation-Strain Method to Model Surfaces using Plasticity