Simulating Cloth Using Bilinear Elements

The most widely used cloth simulation algorithms within the computer graphics community are defined exclusively for triangle meshes. However, assets used in production are often made up of non-planar quadrilaterals. Dividing these elements into triangles and then mapping the displacements back to the original mesh results in faceting and tent-like artifacts when quadrilaterals are rendered as bilinear patches. We propose a method to simulate cloth dynamics on quadrilateral meshes directly, drawing on the well studied Koiter thin sheet model [Koiter 1960] to define consistent elastic energies for linear and bilinear elements. The algorithm elides the need for artifact-prone geometric mapping, and has computation times similar to its fully triangular counterpart.