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 focuses on these aspects and summarizes recent research in the area of deformable collision detection. Various approaches based on bounding volume hierarchies

Figure 1: The presented technique is stable under all circumstances and allows to simulate hundreds of deformable objects in real-time. AbstractWe 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 propose a novel formulation of the projection method for Smoothed Particle Hydrodynamics (SPH). We combine a symmetric SPH pressure force and an SPH discretization of the continuity equation to obtain a discretized form of the pressure Poisson equation (PPE). In contrast to previous projection schemes, our system does consider the actual computation of the pressure force. This incorporation improves the convergence rate of the solver. Furthermore, we propose to compute the density deviation based on velocities instead of positions as this formulation improves the robustness of the time-integration scheme. We show that our novel formulation outperforms previous projection schemes and state-of-the-art SPH methods. Large time steps and small density deviations of down to 0.01 percent can be handled in typical scenarios. The practical relevance of the approach is illustrated by scenarios with up to 40 million SPH particles.

We propose a momentum-conserving two-way coupling method of SPH fluids and arbitrary rigid objects based on hydrodynamic forces. Our approach samples the surface of rigid bodies with boundary particles that interact with the fluid, preventing deficiency issues and both spatial and temporal discontinuities. The problem of inhomogeneous boundary sampling is addressed by considering the relative contribution of a boundary particle to a physical quantity. This facilitates not only the initialization process but also allows the simulation of multiple dynamic objects. Thin structures consisting of only one layer or one line of boundary particles, and also non-manifold geometries can be handled without any additional treatment. We have integrated our approach into WCSPH and PCISPH, and demonstrate its stability and flexibility with several scenarios including multiphase flow.

The dynamic simulation of mechanical effects has a long history in computer graphics. The classical methods in this field discretize Newton's second law in a variety of Lagrangian or Eulerian ways, and formulate forces appropriate for each mechanical effect: joints for rigid bodies; stretching, shearing or bending for deformable bodies and pressure, or viscosity for fluids, to mention just a few. In the last years, the class of position-based methods has become popular in the graphics community. These kinds of methods are fast, stable and controllable which make them well-suited for use in interactive environments. Position-based methods are not as accurate as force-based methods in general but they provide visual plausibility. Therefore, the main application areas of these approaches are virtual reality, computer games and special effects in movies. This state-of-the-art report covers the large variety of position-based methods that were developed in the field of physically based simulation. We will introduce the concept of position-based dynamics, present dynamic simulation based on shape matching and discuss data-driven upsampling approaches. Furthermore, we will present several applications for these methods.