Rasmus Tamstorf

Interactive collision detection between deformable models using chromatic decomposition

We present a novel algorithm for accurately detecting all contacts, including self-collisions, between deformable models. We precompute a chromatic decomposition of a mesh into non-adjacent primitives using graph coloring algorithms. The chromatic decomposition enables us to check for collisions between non-adjacent primitives using a linear-time culling algorithm. As a result, we achieve higher culling efficiency and significantly reduce the number of false positives. We use our algorithm to check for collisions among complex deformable models consisting of tens of thousands of triangles for cloth modeling and medical simulation. Our algorithm accurately computes all contacts at interactive rates. We observed up to an order of magnitude speedup over prior methods.

Efficient elasticity for character skinning with contact and collisions

We present a new algorithm for near-interactive simulation of skeleton driven, high resolution elasticity models. Our methodology is used for soft tissue deformation in character animation. The algorithm is based on a novel discretization of corotational elasticity over a hexahedral lattice. Within this framework we enforce positive definiteness of the stiffness matrix to allow efficient quasistatics and dynamics. In addition, we present a multigrid method that converges with very high efficiency. Our design targets performance through parallelism using a fully vectorized and branch-free SVD algorithm as well as a stable one-point quadrature scheme. Since body collisions, self collisions and soft-constraints are necessary for real-world examples, we present a simple framework for enforcing them. The whole approach is demonstrated in an end-to-end production-level character skinning system.

Fast collision detection for deformable models using representative-triangles

We present a new approach to accelerate collision detection for deformable models. Our formulation applies to all triangulated models and significantly reduces the number of elementary tests between features of the mesh, i.e., vertices, edges and faces. We introduce the notion of Representative-Triangles, standard geometric triangles augmented with mesh feature information and use this representation to achieve better collision query performance. The resulting approach can be combined with bounding volume hierarchies and works well for both inter-object and self-collision detection. We demonstrate the benefit of Representative-Triangles on continuous collision detection for cloth simulation and N-body collision scenarios. We observe up to a one-order of magnitude reduction in feature-pair tests and up to a 5X improvement in query time.

Implicit Contact Handling for Deformable Objects

We present an algorithm for robust and efficient contact handling of deformable objects. By being aware of the internal dynamics of the colliding objects, our algorithm provides smooth rolling and sliding, stable stacking, robust impact handling, and seamless coupling of heterogeneous objects, all in a unified manner. We achieve dynamicsawareness through a constrained dynamics formulation with implicit complementarity constraints, and we present two major contributions that enable an efficient solution of the constrained dynamics problem: a time stepping algorithm that robustly ensures non‐penetration and progressively refines the formulation of constrained dynamics, and a new solver for large mixed linear complementarity problems, based on iterative constraint anticipation. We show the application of our algorithm in challenging scenarios such as multi‐layered cloth moving at high velocities, or colliding deformable solids simulated with large time steps.

Robust treatment of simultaneous collisions

Robust treatment of complex collisions is a challenging problem in cloth simulation. Some state of the art methods resolve collisions iteratively, invoking a fail-safe when a bound on iteration count is exceeded. The best-known fail-safe rigidifies the contact region, causing simulation artifacts. We present a fail-safe that cancels impact but not sliding motion, considerably reducing artificial dissipation. We equip the proposed fail-safe with an approximation of Coulomb friction, allowing finer control of sliding dissipation.

An artist friendly hair shading system

Rendering hair in motion pictures is an important and challenging task. Despite much research on physically based hair rendering, it is currently difficult to benefit from this work because physically based shading models do not offer artist friendly controls. As a consequence much production work so far has used ad hoc shaders that are easier to control, but often lack the richness seen in real hair. We show that physically based shading models fail to provide intuitive artist controls and we introduce a novel approach for creating an art-directable hair shading model from existing physically based models. Through an informal user study we show that this system is easier to use compared to existing systems. Our shader has been integrated into the production pipeline at the Walt Disney Animation Studios and is being used in the production of the upcoming animated feature film Tangled.

Motorcycle graphs: canonical quad mesh partitioning

We describe algorithms for canonically partitioning semi‐regular quadrilateral meshes into structured submeshes, using an adaptation of the geometric motorcycle graph of Eppstein and Erickson to quad meshes. Our partitions may be used to efficiently find isomorphisms between quad meshes. In addition, they may be used as a highly compressed representation of the original mesh. These partitions can be constructed in sublinear time from a list of the extraordinary vertices in a mesh. We also study the problem of further reducing the number of submeshes in our partitions—we prove that optimizing this number is NP‐hard, but it can be efficiently approximated.

Reflections on simultaneous impact

Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.

Speculative parallel asynchronous contact mechanics

We extend the Asynchronous Contact Mechanics algorithm [Harmon et al. 2009] and improve its performance by two orders of magnitude, using only optimizations that do not compromise ACMs three guarantees of safety, progress, and correctness. The key to this speedup is replacing ACMs timid, forward-looking mechanism for detecting collisions---locating and rescheduling separating plane kinetic data structures---with an optimistic speculative method inspired by Mirtichs rigid body Time Warp algorithm [2000]. Time warp allows us to perform collision detection over a window of time containing many of ACMs asynchronous trajectory changes; in this way we cull away large intervals as being collision free. Moreover, by replacing force processing intermingled with KDS rescheduling by windows of pure processing followed by collision detection, we transform an algorithm that is very difficult to parallelize into one that is embarrassingly parallel.

Adaptive nonlinearity for collisions in complex rod assemblies

We develop an algorithm for the efficient and stable simulation of large-scale elastic rod assemblies. We observe that the time-integration step is severely restricted by a strong nonlinearity in the response of stretching modes to transversal impact, the degree of this nonlinearity varying greatly with the shape of the rod. Building on these observations, we propose a collision response algorithm that adapts its degree of nonlinearity. We illustrate the advantages of the resulting algorithm by analyzing simulations involving elastic rod assemblies of varying density and scale, with up to 1.7 million individual contacts per time step.