Physically based deformable models have been widely embraced by the Computer Graphics community. Many problems outlined in a previous survey by Gibson and Mirtich [GM97] have been addressed, thereby making these models interesting and useful for both offline and real-time applications, such as motion pictures and video games. In this paper, we present the most significant contributions of the past decade, which produce such impressive and perceivably realistic animations and simulations: finite element/difference/volume methods, mass-spring systems, meshfree methods, coupled particle systems and reduced deformable models based on modal analysis. For completeness, we also make a connection to the simulation of other continua, such as fluids, gases and melting objects. Since time integration is inherent to all simulated phenomena, the general notion of time discretization is treated separately, while specifics are left to the respective models. Finally, we discuss areas of application, such as elastoplastic deformation and fracture, cloth and hair animation, virtual surgery simulation, interactive entertainment and fluid/smoke animation, and also suggest areas for future research.

In this paper, we propose a stable and efficient algorithm for animating mass-spring systems. An integration scheme derived from implicit integration allows us to obtain interactive realistic animation of any mass-spring network. We alleviate the need to solve a linear system through the use of a predictor-corrector approach: We first compute a rapid approximation of the implicit integration, then we correct this estimate in a post-step process to preserve momentum. Combined with an inverse kinematics process to implement collisions and other constraints, this method provides a simple, stable and tunable model for deformable objects suitable for virtual reality. An implementation in a VR environment demonstrates this approach. 1

The linear strain measures that are commonly used in real-time animations of deformable objects yield fast and stable simulations. However, they are not suitable for large deformations. Recently, more realistic results have been achieved in computer graphics by using Green's non-linear strain tensor, but the non-linearity makes the simulation more costly and introduces numerical problems.

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 geome-try. We exploit the fact that model reduction on large deforma-tion 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 simula-tion of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geomet-ric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interac-tive sketching technique. Mass-scaled principal component analy-sis (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.

We present a method for modeling and animating a wide spectrum of volumetric objects, with material properties anywhere in the range from stiff elastic to highly plastic. Both the volume and the surface representation are point based, which allows arbitrarily large deviations form the original shape. In contrast to previous point based elasticity in computer graphics, our physical model is derived from continuum mechanics, which allows the specification of common material properties such as Young's Modulus and Poisson's Ratio. In each step

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, 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 study the problem of recovering the 3D shape, reflectance, and non-rigid motion of a dynamic 3D scene. Because these properties are completely unknown, our approach uses multiple views to build a piecewisecontinuous geometric and radiometric representation of the scene's trace in space-time. Basic primitive of this representation is the dynamic surfel, which (1) encodes the instantaneous local shape, reflectance, and motion of a small region in the scene, and (2) enables accurate prediction of the region's dynamic appearance under known illumination conditions. We show that complete surfel-based reconstructions can be created by repeatedly applying an algorithm called Surfel Sampling that combines sampling and parameter estimation to fit a single surfel to a small, bounded region of space-time. Experimental results with the Phong reflectance model and complex real scenes (clothing, skin, shiny objects) illustrate our method's ability to explain pixels and pixel variations in terms of their physical causes--- shape, reflectance, motion, illumination, and visibility.

In this paper we introduce a discrete shell model describing the behavior of thin flexible structures whose rest configuration is nonflat. Previously such models required complex continuum mechanics formulations and correspondingly expensive algorithms. We show that a straightforward shell model can be derived in the discrete setting of triangle meshes and implemented through a simple modification to standard cloth simulation algorithms. The resulting technique convincingly simulates a variety of thin shell models ranging from cloth to thin metal like materials. We show the importance of non-flat rest configurations with a number of examples and demonstrate the quality of our results by comparing a simulation of a falling hat with real video footage.

We propose three different physical models based on linear elasticity theory and finite- elements modeling that are well-suited for surgery simulation. The first model combines pre- computed deformations to deform in real-time large size meshes but does not allow any topo- logical changes to the mesh. The second model is similar to the spring-mass models where volumetric deformations and cutting operations can be simulated on small size meshes in real- time. Finally, we have developpeal a third method combining the previous two solutions into a hybrid model thus allowing the simulation of deformations and cutting on complex anatomical structures.

In this paper we describe how to simulate geometrically complex, interactive, physically-based, volumetric, dynamic deformation models with negligible main CPU costs. This is achieved using a Dynamic Response Texture, or DyRT, that can be mapped onto any conventional animation as an optional rendering stage using commodity graphics hardware. The DyRT simulation process employs precomputed modal vibration models excited by rigid body motions. We present several examples, with an emphasis on bone-based character animation for interactive applications.