A fully geometric approach for developable cloth deformation simulation

We present a new method for simulation of inextensible cloth subjected to a conservative force (e.g., the gravity) and collision-free constraint. Traditional algorithms for cloth simulation are all physically-based in which cloth is treated as an elastic material with some stiffness coefficient(s). These algorithms break down ultimately if one tries to set this stiffness coefficient to infinite which corresponds to inextensible cloth. The crux of the method is an algorithm for interpolating a given set of arbitrary points or space curves by a smooth developable mesh surface. We formulate this interpolation problem as a mesh deformation process that transforms an initial developable mesh surface, e.g., a planar figure, to a final mesh surface that interpolates the given points (called anchor points). During the deformation process, all the triangle elements in the intermediate meshes are kept isometric to their initial shapes, while the potential energy due to the conservative force is reduced gradually. The collision problem is resolved by introducing dynamic anchor points owing to the collision during the deformation. Notwithstanding its simplicity, the proposed method has shown some promising efficacy for simulation of inextensible cloth.