Inverse Elastic Cloth Design with Contact and Friction

Physically based cloth modeling is classically achieved through a trial and error process. The rest (undeformed) configuration of the cloth, often represented as a 2D pattern assembly, is edited geometrically and adjusted iteratively depending on the feedback provided by a static cloth simulator, which predicts the deformed 3D shape under gravity and contacts. Matching a reference 3D shape while keeping the time of the modeling process reasonable is thus difficult , unless the user possesses advanced skills in real cloth tailoring. In contrast, in this paper we investigate a new, inverse strategy for modeling realistic cloth intuitively. Our goal is to take as input a target (deformed) 3D shape, and to interpret this configuration automatically as a stable equilibrium of a cloth simulator, by retrieving the unknown rest shape. In the presence of gravity and frictional contact, such an inverse problem formulates as an ill-posed nonlinear system subject to nonsmooth constraints. To select and compute a plausible solution, we design an iterative two-step solving process. In a first step, contacts are reduced to frictionless bilateral constraints, and starting from an as-flat-as possible pose, a unique rest pose is retrieved using the adjoint method on a regularized energy. The second step modifies this rest pose so as to project bilateral forces onto the admissible Coulomb friction cone, for each contact. We show that our method converges well in most cases towards a plausible rest configuration, and demonstrate practical inversion results on various cloth geometries modeled by an artist