This paper presents a robust, adaptive method for animating dynamic visco-elastic deformable objects that provides a guaranteed frame rate. Our approach uses a novel automatic space and time adaptive level of detail technique, in combination with a largedisplacement (Green) strain tensor formulation. The body is partitioned in a non-nested multiresolution hierarchy of tetrahedral meshes. The local resolution is determined by a quality condition that indicates where and when the resolution is too coarse. As the object moves and deforms, the sampling is refined to concentrate the computational load into the regions that deform the most. Our model consists of a continuous differential equation that is solved using a local explicit finite element method. We demonstrate that our adaptive Green strain tensor formulation suppresses unwanted artifacts in the dynamic behavior, compared to adaptive mass-spring and other adaptive approaches. In particular, damped elastic vibration modes are shown to be nearly unchanged for several levels of refinement. Results are presented in the context of a virtual reality system. The user interacts in real-time with the dynamic object through the control of a rigid tool, attached to a haptic device driven with forces derived from the method.

We present an interactive system that lets a user move and deform a two-dimensional shape without manually establishing a skeleton or freeform deformation (FFD) domain beforehand. The shape is represented by a triangle mesh and the user moves several vertices of the mesh as constrained handles. The system then computes the positions of the remaining free vertices by minimizing the distortion of each triangle. While physically based simulation or iterative refinement can also be used for this purpose, they tend to be slow. We present a two-step closed-form algorithm that achieves real-time interaction. The first step finds an appropriate rotation for each triangle and the second step adjusts its scale. The key idea is to use quadratic error metrics so that each minimization problem becomes a system of linear equations. After solving the simultaneous equations at the beginning of interaction, we can quickly find the positions of free vertices during interactive manipulation. Our approach successfully conveys a sense of rigidity of the shape, which is difficult in space-warp approaches. With a multiple-point input device, even beginners can easily move, rotate, and deform shapes at will.

In this paper we present a fast and robust approach for simulating elasto-plastic materials and fracture in real time. Our method extends the warped stiffness finite element approach for linear elasticity and combines it with a strain-state-based plasticity model. The internal principal stress components provided by the finite element computation are used to determine fracture locations and orientations. We also present a method to consistently animate and fracture a detailed surface mesh along with the underlying volumetric tetrahedral mesh. This multi-resolution strategy produces realistic animations of a wide spectrum of materials at interactive rates that have typically been simulated off-line thus far.

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.

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.

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

We present a technique which allows subtle nonlinear quasi-static deformations of articulated characters to be compactly approximated by data-dependent eigenbases which are optimized for real time rendering on commodity graphics hardware. The method extends the common Skeletal-Subspace Deformation (SSD) technique to provide efficient approximations of the complex deformation behaviours exhibited in simulated, measured, and artist-drawn characters. Instead of storing displacements for key poses (which may be numerous), we precompute principal components of the deformation influences for individual kinematic joints, and so construct error-optimal eigenbases describing each joint's deformation subspace. Pose-dependent deformations are then expressed in terms of these reduced eigenbases, allowing precomputed coefficients of the eigenbasis to be interpolated at run time. Vertex program hardware can then efficiently render nonlinear skin deformations using a small number of eigendisplacements stored in graphics hardware. We refer to the final resulting character skinning construct as the model's EigenSkin. Animation results are presented for a very large nonlinear finite element model of a human hand rendered in real time at minimal cost to the main CPU.

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.