Implicit untangling

We propose a robust method for untangling an arbitrary number of cloth layers, possibly exhibiting deep interpenetrations, to a collision-free state, ready for animation. Our method relies on an intermediate, implicit representation to solve the problem: the user selects a few garments stored in a library together with their implicit approximations, and places them over a mannequin while specifying the desired order between layers. The intersecting implicit surfaces are then combined using a new family of N-ary composition operators, specially designed for untangling layers. Garment meshes are finally projected to the deformed implicit surfaces in linear time, while best preserving triangles and avoiding loss of details. Each of the untangling operators computes the target surface for a given garment in a single step, while accounting for the order between cloth layers and their individual thicknesses. As a group, they guarantee an intersection-free output configuration. Moreover, a weight can be associated with each layer to tune their relative influence during untangling, such as leather being less deformed than cloth. Results for each layer then reflect the combined effect of the other layers, enabling us to output a plausible configuration in contact regions. As our results show, our method can be used to generate plausible, new static shapes of garments when underwear has been added, as well as collision-free configurations enabling a user to safely launch animations of arbitrarily complex layered clothing.