We present a new approach for simulating deformable objects. The underlying model is geometrically motivated. It handles pointbased objects and does not need connectivity information. The approach does not require any pre-processing, is simple to compute, and provides unconditionally stable dynamic simulations. The main idea of our deformable model is to replace energies by geometric constraints and forces by distances of current positions to goal positions. These goal positions are determined via a generalized shape matching of an undeformed rest state with the current deformed state of the point cloud. Since points are always drawn towards well-defined locations, the overshooting problem of explicit integration schemes is eliminated. The versatility of the approach in terms of object representations that can be handled, the efficiency in terms of memory and computational complexity, and the unconditional stability of the dynamic simulation make the approach particularly interesting for games.

We extend approaches for skinning characters to the general setting of skinning deformable mesh animations. We provide an automatic algorithm for generating progressive skinning approximations, that is particularly efficient for pseudo-articulated motions. Our contributions include the use of nonparametric mean shift clustering of high-dimensional mesh rotation sequences to automatically identify statistically relevant bones, and robust least squares methods to determine bone transformations, bone-vertex influence sets, and vertex weight values. We use a low-rank data reduction model defined in the undeformed mesh configuration to provide progressive convergence with a fixed number of bones. We show that the resulting skinned animations enable efficient hardware rendering, rest pose editing, and deformable collision detection. Finally, we present numerous examples where skins were automatically generated using a single set of parameter values.

Interactive environments for dynamically deforming objects play an important role in surgery simulation and entertainment technology. These environments require fast deformable models and very efficient collision handling techniques. While collision detection for rigid bodies is well-investigated, collision detection for deformable objects introduces additional challenging problems. This paper focusses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies, distance fields, and spatial partitioning are discussed. Further, image-space techniques and stochastic methods are considered. Applications in cloth modeling and surgical simulation are presented.

In this paper, we present an approach for fast subspace integration of reduced-coordinate nonlinear deformable models that is suitable for interactive applications in computer graphics and haptics. Our approach exploits dimensional model reduction to build reduced-coordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation models with linear materials (as commonly used in graphics) result in internal force models that are simply cubic polynomials in reduced coordinates. Coefficients of these polynomials can be precomputed, for efficient runtime evaluation. This allows simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (mass-PCA) is suggested for dimensionality reduction. Finally, several examples are given from computer animation to illustrate high performance, including force-feedback haptic rendering of a complicated object undergoing large deformations.

Figure 1: Multiple deformable models simulation: This sequence shows the positions of the objects at three time instances in a simulation. The environment initially consists of 10 deforming objects represented using 5.5K triangles. As the simulation proceeds, the objects break into 25 sub-objects. Our algorithm is able to perform collision and separation distance computations, including self-collisions, among dynamically generated objects within 120 ms on a high-end PC. We present novel algorithms to perform collision and distance queries among multiple deformable models in dynamic environments. These include inter-object queries between different objects as well as intra-object queries. We describe a unified approach to compute these queries based on N-body distance computation and use properties of the 2 nd order discrete Voronoi diagram to perform N-body culling. Our algorithms involve no preprocessing and also work well on models with changing topologies. We can perform all proximity queries among complex deformable models consisting of thousands of triangles in a fraction of a second on a high-end PC. Moreover, our Voronoi-based culling algorithm can improve the performance of separation distance and penetration queries by an order of magnitude.

Abstract — We present an algorithm for path planning for a flexible robot in complex environments. Our algorithm computes a collision free path by taking into account geometric and physical constraints, including obstacle avoidance, non-penetration constraint, volume preservation, surface tension, and energy minimization. We describe a new algorithm for collision detection between a deformable robot and fixed obstacles using graphics processors. We also present techniques to efficiently handle complex deformable models composed of tens of thousands of polygons and obtain significant performance improvement over previous approaches. Moreover, we demonstrate a practical application of our algorithm in performing path planning of catheters in liver chemoembolization. I.

We present efficient data structures and caching schemes to accelerate ray-surface intersections for deforming point-sampled surfaces. By exploiting spatial and temporal coherence of the deformation during the animation, we are able to improve rendering performance by a factor of two to three compared to existing techniques. Starting from a tight bounding sphere hierarchy for the undeformed object, we use a lazy updating scheme to adapt the hierarchy to the deformed surface in each animation step. In addition, we achieve a significant speedup for ray-surface intersections by caching per-ray intersection points. We also present a technique for rendering sharp edges and corners in point-sampled models by introducing a novel surface clipping algorithm.

Figure 1: Staggered Projections resolves frictional contact between a wide range of rigid and deformable models at rates suitable for (a) interactive haptic simulations, as well as accurate animations that capture important frictional contact phenomena such as: (b) large-deformation frictional contact with reduced StVK models, (c) large-scale, frictional stacking and jamming of large numbers of objects without constraint drift, (d) and long term stable simulation of difficult, frictionally dependent structures. We present a new discrete velocity-level formulation of frictional contact dynamics that reduces to a pair of coupled projections and introduce a simple fixed-point property of this coupled system. This allows us to construct a novel algorithm for accurate frictional contact resolution based on a simple staggered sequence of projections. The algorithm accelerates performance using warm starts to leverage the potentially high temporal coherence between contact states and provides users with direct control over frictional accuracy. Applying this algorithm to rigid and deformable systems, we obtain robust and accurate simulations of frictional contact behavior not previously possible, at rates suitable for interactive haptic simulations, as well as large-scale animations. By construction, the proposed algorithm guarantees exact, velocity-level contact constraint enforcement and obtains long-term stable and robust integration. Examples are given to illustrate the performance, plausibility and accuracy of the obtained solutions.

We present a novel algorithm to selectively restructure bounding volume hierarchies (BVHs) for ray tracing dynamic scenes. We derive two new metrics to evaluate the culling efficiency and restructuring benefit of any BVH. Based on these metrics, we perform selective restructuring operations that efficiently reconstruct small portions of a BVH instead of the entire BVH. Our approach is general and applicable to complex and dynamic scenes, including topological changes. We use the selective restructuring algorithm to improve the performance of ray tracing dynamic scenes that consist of hundreds of thousands of triangles. In our benchmarks, we observe up to an order of magnitude improvement over prior BVH-based ray tracing algorithms.

We present a fast collision culling algorithm for performing interand intra-object collision detection among complex models using graphics hardware. Our algorithm is based on CULLIDE [8] and performs visibility queries on the GPUs to eliminate a subset of geometric primitives that are not in close proximity. We present an extension to CULLIDE to perform intra-object or selfcollisions between complex models. Furthermore, we describe a novel visibility-based classification scheme to compute potentiallycolliding and collision-free subsets of objects and primitives, which considerably improves the culling performance. We have implemented our algorithm on a PC with an NVIDIA GeForce FX 6800 Ultra graphics card and applied it to three complex simulations, each consisting of objects with tens of thousands of triangles. In practice, we are able to compute all the self-collisions for cloth simulation up to image-space precision at interactive rates.