Interleaved Cloth Simulation

Implicit integration is a standard for stiff spring-based cloth simulation because of its stability. However constraints are useful to simulate various physical behaviors such as contact collisions or interaction with rigid bodies. Modified Conjugate Gradient (MCG) could support constraints as a part of implicit integration but constraints could not be added or removed during integration and they were limited to vertex nodes. Normally, a contact constraint has one or two frictional constraints and act inside of triangle or edge rather than vertex node. Also its inequality property makes it harder to be included in MCG. For this reason, constraints are typically applied after implicit integration as a separate step or replaced with springs. In this paper, we propose a novel method to interleave various constraints with stiff springs so that we can take advantages from both sides. Also our Jacobian-free and matrix-free implicit integration allows us to use various nonlinear forces such as pressure or none vertex-centered forces. Interleaving collision constraints into integration step can eliminate unpleasant local deformation.