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.

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.

We built an anatomically accurate model of facial musculature, passive tissue and underlying skeletal structure using volumetric data acquired from a living male subject. The tissues are endowed with a highly nonlinear constitutive model including controllable anisotropic muscle activations based on fiber directions. Detailed models of this sort can be difficult to animate requiring complex coordinated stimulation of the underlying musculature. We propose a solution to this problem automatically determining muscle activations that track a sparse set of surface landmarks, e.g. acquired from motion capture marker data. Since the resulting animation is obtained via a three dimensional nonlinear finite element method, we obtain visually plausible and anatomically correct deformations with spatial and temporal coherence that provides robustness against outliers in the motion capture data. Moreover, the obtained muscle activations can be used in a robust simulation framework including contact and collision of the face with external objects.

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.

Though motion planning has been studied extensively for rigid and articulated robots, motion planning for deformable objects is an area that has received far less attention. In this paper we present a framework for planning paths in completely deformable, elastic environments. In particular we apply a deformable model to the robot and obstacles in the environment and we present a kinodynamic planning algorithm suited for this type of deformable motion planning. The planning algorithm is based on the Rapidly-Exploring Random Tree (rrt) path planning algorithm. To the best of our knowledge, this is the first work that plans paths in totally deformable environments. Figure 1: Barriers Environment. Both the robot (the cube) and the obstacles (the plate barriers) in this environment are deformable. This image sequence is shown from left to right and from top to bottom. 1

We present a novel approach to handle collisions of deformable objects represented by tetrahedral meshes. The scheme combines the physical correctness of constraint methods with the efficiency of penalty approaches. For a set of collided points, a collision-free state is computed that is governed by the elasticities and impulses of the collided objects. In contrast to existing constraint methods we show how to decouple the resulting system of equations in order to avoid iterative solvers. By considering the time step of the numerical integration scheme, the contact force can be analytically computed for each collided point in order to achieve the collision-free state. Since predicted information on positions, impulses, and penetration depths of the subsequent time step is considered, a collision-free state is maintained at each simulation step which is in contrast to existing penalty methods. Further, our approach does not require a user-defined stiffness constant. Our scheme can handle various underlying deformable models and numerical integration schemes. To illustrate its versatility, we have performed experiments with linear and non-linear finite element methods.

We introduce a new collision response scheme that handles collisions between deformable objects with triangulated surfaces. Based on internal forces and penetration depth information, the approach computes the contact surface of interpenetrating objects. In particular, we address discontinuity problems that arise in discrete-time simulations with coarse surface representations. The approach is independent of the actual deformation model and the applied collision detection algorithm, and in contrast to penalty-based collision response schemes, the method does not require any user-defined parameters. We compare the contact surface method to a penalty-based collision response scheme to illustrate the conceptual advantages of the proposed technique. 1

We present a new image-based method to process contacts between objects bounded by triangular surfaces. Unlike previous methods, it relies on image-based volume minimization, which eliminates complex geometrical computations and robustly handles deep intersections. The surfaces are rasterized in three orthogonal directions, and intersections are detected based on pixel depth and normal orientation. Per-pixel contact forces are computed and accumulated at the vertices. We show how to compute pressure forces which serve to minimize the intersection volume, as well as friction forces. No geometrical precomputation is required, which makes the method efficient for both deformable and rigid objects. We demonstrate it on rigid, skinned, and particle-based physical models with detailed surfaces in contacts at interactive frame rates. 1.

Abstract — We present an efficient algorithm to compute the generalized penetration depth (PD g) between rigid models. Given two overlapping objects, our algorithm attempts to compute the minimal translational and rotational motion that separates the two objects. We formulate the PD g computation based on modeldependent distance metrics using displacement vectors. As a result, our formulation is independent of the choice of inertial and body-fixed reference frames, as well as specific representation of the configuration space. Furthermore, we show that the optimum answer lies on the boundary of the contact space and pose the computation as a constrained optimization problem. We use global approaches to find an initial guess and present efficient techniques to compute a local approximation of the contact space for iterative refinement. We highlight the performance of our algorithm on many complex models. I.

Abstract: Meshless deformation based on shape matching is a new technique for simulating deformable objects without requiring mesh connectivity information. The approach focuses on speed, ease of use and stability at the expense of physical accuracy. In this paper we introduce improvements to the technique that increase physical realism and make it more suitable for use in interactive real-time environments such as games and virtual surgery applications. We also present intuitive real-time interaction techniques for picking, pushing and cutting objects simulated using meshless deformation based on shape matching. For deformable collision detection and response, we present a new method for surface meshes based on previous volumetric methods. 1