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.

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.

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.

This paper presents a framework for the skeleton-driven animation of elastically deformable characters. A character is embedded in a coarse volumetric control lattice, which provides the structure needed to apply the finite element method. To incorporate skeletal controls, we introduce line constraints along the bones of simple skeletons. The bones are made to coincide with edges of the control lattice, which enables us to apply the constraints efficiently using algebraic methods. To accelerate computation, we associate regions of the volumetric mesh with particular bones and perform locally linearized simulations, which are blended at each time step. We define a hierarchical basis on the control lattice, so for detailed interactions the simulation can adapt the level of detail. We demonstrate the ability to animate complex models using simple skeletons and coarse volumetric meshes in a manner that simulates secondary motions at interactive rates.

dynamics by driving the scene with parameterized interactions representative of runtime usage. (b) Model reduction on observed dynamic deformations yields a low-rank approximation to the system’s parameterized impulse response functions. (c) Deformed state geometries are then sampled and used to precompute and coparameterize a radiance transfer model for deformable objects. (d) The final simulation responds plausibly to interactions similar to those precomputed, includes complex collision and global illumination effects, and runs in real time. We present an approach for precomputing data-driven models of interactive physically based deformable scenes. The method permits real-time hardware synthesis of nonlinear deformation dynamics, including self-contact and global illumination effects, and supports real-time user interaction. We use data-driven tabulation of the system’s deterministic state space dynamics, and model reduction to build efficient low-rank parameterizations of the deformed shapes. To support runtime interaction, we also tabulate impulse response functions for a palette of external excitations. Although our approach simulates particular systems under very particular interaction conditions, it has several advantages. First, parameterizing all possible scene deformations enables us to precompute novel reduced coparameterizations of global scene illumination for lowfrequency lighting conditions. Second, because the deformation dynamics are precomputed and parameterized as a whole, collisions are resolved within the scene during precomputation so that runtime self-collision handling is implicit. Optionally, the data-driven models can be synthesized on programmable graphics hardware, leaving only the low-dimensional state space dynamics and appearance data models to be computed by the main CPU.

We propose a virtual node algorithm that allows material to separate along arbitrary (possibly branched) piecewise linear paths through a mesh. The material within an element is fragmented by creating several replicas of the element and assigning a portion of real material to each replica. This results in elements that contain both real material and empty regions. The missing material is contained in another copy (or copies) of this element. Our new virtual node algorithm automatically determines the number of replicas and the assignment of material to each. Moreover, it provides the degrees of freedom required to simulate the partially or fully fragmented material in a fashion consistent with the embedded geometry. This approach enables efficient simulation of complex geometry with a simple mesh, i.e. the geometry need not align itself with element boundaries. It also alleviates many shortcomings of traditional Lagrangian simulation techniques for meshes with changing topology. For example, slivers do not require small CFL time step restrictions since they are embedded in well shaped larger elements. To enable robust simulation of embedded geometry, we propose new algorithms for handling rigid body and self collisions. In addition, we present several mechanisms for influencing and controlling fracture with grain boundaries, prescoring, etc. We illustrate our method for both volumetric and thin-shell simulations.

In this paper, we present a versatile and robust model for geometrically complex deformable solids. Our approach can be applied to deformable tetrahedral meshes and to deformable triangle meshes. The model considers elastic and plastic deformation. It handles a large variety of material properties ranging from stiff to fluid-like behavior. Due to the computational efficiency of our approach, complex environments consisting of up to several thousand primitives can be simulated at interactive speed.

We present a novel framework for dynamic simulation of elastically deformable solids. Our approach combines classical finite element methodology with subdivision wavelets to meet the needs of computer graphics applications. We represent deformations using a wavelet basis constructed from volumetric Catmull-Clark subdivision. Catmull-Clark subdivision solids allow the domain of deformation to be tailored to objects of arbitrary topology. The domain of deformation can correspond to the interior of a subdivision surface or can enclose an arbitrary surface mesh. Within the wavelet framework we develop the equations of motion for elastic deformations in the presence of external forces and constraints. We solve the resulting differential equations using an implicit method, which lends stability. Our framework allows trade-off between speed and accuracy. For interactive applications, we accelerate the simulation by adaptively refining the wavelet basis while avoiding visual "popping" artifacts. Off-line simulations can employ a fine basis for higher accuracy at the cost of more computation time. By exploiting the properties of smooth subdivision we can compute less expensive solutions using a trilinear basis yet produce a smooth result that meets the constraints.

the geometry into frequency space by computing the Manifold Harmonic Transform (MHT). C: Apply the frequency space filter on the transformed geometry. D: Transform back into geometric space by computing the inverse MHT. We present a new method to convert the geometry of a mesh into frequency space. The eigenfunctions of the Laplace-Beltrami operator are used to define Fourier-like function basis and transform. Since this generalizes the classical Spherical Harmonics to arbitrary manifolds, the basis functions will be called Manifold Harmonics. It is well known that the eigenvectors of the discrete Laplacian define such a function basis. However, important theoretical and practical problems hinder us from using this idea directly. From the theoretical point of view, the combinatorial graph Laplacian does not take the geometry into account. The discrete Laplacian (cotan weights) does not have this limitation, but its eigenvectors are not orthogonal. From the practical point of view, computing even just a few eigenvectors is currently impossible for meshes with more than a few thousand vertices. In this paper, we address both issues. On the theoretical side, we show how the FEM (Finite Element Modeling) formulation defines a function basis which is both geometry-aware and orthogonal. On the practical side, we propose a band-by-band spectrum computation algorithm and an out-of-core implementation that can compute thousands of eigenvectors for meshes with up to a million vertices. Finally, we demonstrate some applications of our method to interactive convolution geometry filtering and interactive shading design.