Optimization is an appealing way to compute the motion of an animated character because it allows the user to specify the desired motion in a sparse, intuitive way. The difficulty of solving this problem for complex characters such as humans is due in part to the high dimensionality of the search space. The dimensionality is an artifact of the problem representation because most dynamic human behaviors are intrinsically low dimensional with, for example, legs and arms operating in a coordinated way. We describe a method that exploits this observation to create an optimization problem that is easier to solve. Our method utilizes an existing motion capture database to find a low-dimensional space that captures the properties of the desired behavior. We show that when the optimization problem is solved within this low-dimensional subspace, a sparse sketch can be used as an initial guess and full physics constraints can be enabled. We demonstrate the power of our approach with examples of forward, vertical, and turning jumps; with running and walking; and with several acrobatic flips.

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.

Abstract We extend approaches for skinning characters to the general setting of skinning deformable mesh animations. We provide an automatic algorithm for generating progressive skinning approximations, that is particularly efficient for pseudo-articulated motions. Our contributions include the use of nonparametric mean shift clustering of high-dimensional mesh rotation sequences to automatically identify statistically relevant bones, and robust least squares methods to determine bone transformations, bone-vertex influence sets, and vertex weight values. We use a low-rank data reduction model defined in the undeformed mesh configuration to provide progressive convergence with a fixed number of bones. We show that the resulting skinned animations enable efficient hardware rendering, rest pose editing, and deformable collision detection. Finally, we present numerous examples where skins were automatically generated using a single set of parameter values.

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.

The ability to position a small subset of mesh vertices and produce a meaningful overall deformation of the entire mesh is a fundamental task in mesh editing and animation. However, the class of meaningful deformations varies from mesh to mesh and depends on mesh kinematics, which prescribes valid mesh configurations, and a selection mechanism for choosing among them. Drawing an analogy to the traditional use of skeleton-based inverse kinematics for posing skeletons, we define mesh-based inverse kinematics as the problem of finding meaningful mesh deformations that meet specified vertex constraints. Our solution relies on example meshes to indicate the class of meaningful deformations. Each example is represented with a feature vector of deformation gradients that capture the affine transformations which individual triangles undergo relative to a reference pose. To pose a mesh, our algorithm efficiently searches among all meshes with specified vertex positions to find the one that is closest to some pose in a nonlinear span of the example feature vectors. Since the search is not restricted to the span of example shapes, this produces compelling deformations even when the constraints require poses that are different from those observed in the examples. Furthermore, because the span is formed by a nonlinear blend of the example feature vectors, the blending component of our system may also be used independently to pose meshes by specifying blending weights or to compute multi-way morph sequences.

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.

This paper introduces a new data representation and compression technique for precomputed radiance transfer (PRT). The light transfer functions and light sources are modeled with spherical radial basis functions (SRBFs). A SRBF is a rotation-invariant function that depends on the geodesic distance between two points on the unit sphere. Rotating functions in SRBF representation is as straightforward as rotating the centers of SRBFs. Moreover, highfrequency signals are handled by adjusting the bandwidth parameters of SRBFs. To exploit inter-vertex coherence, the light transfer functions are further classified iteratively into disjoint clusters, and tensor approximation is applied within each cluster. Compared with previous methods, the proposed approach enables real-time rendering with comparable quality under high-frequency lighting environments. The data storage is also more compact than previous all-frequency PRT algorithms. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Color, shading, shadowing, and texture; G.1.2 [Numerical Analysis]: Approximation—Special function approximations; E.4 [Coding and Information Theory]: Data compaction and compression

Figure 1: By modeling user behavior and not thresholding transitions, we create a high overall quality on-line motion generator suitable for directly controlled characters. Left, a screen capture. Middle, users control the character with a gamepad. Right, characters must respond immediately to user input, lest they run afoul of environmental hazards. In game environments, animated character motion must rapidly adapt to changes in player input – for example, if a directional signal from the player’s gamepad is not incorporated into the character’s trajectory immediately, the character may blithely run off a ledge. Traditional schemes for data-driven character animation lack the split-second reactivity required for this direct control; while they can be made to work, motion artifacts will result. We describe an on-line character animation controller that assembles a motion stream from short motion fragments, choosing each fragment based on current player input and the previous fragment. By adding a simple model of player behavior we are able to improve

Simulating sounds produced by realistic vibrating objects is challenging because sound radiation involves complex diffraction and interreflection effects that are very perceptible and important. These wave phenomena are well understood, but have been largely ignored in computer graphics due to the high cost and complexity of computing them at audio rates.

Previous methods for soft shadows numerically integrate over many light directions at each receiver point, testing blocker visibility in each direction. We introduce a method for real-time soft shadows in dynamic scenes illuminated by large, low-frequency light sources where such integration is impractical. Our method operates on vectors representing low-frequency visibility of blockers in the spherical harmonic basis. Blocking geometry is modeled as a set of spheres; relatively few spheres capture the low-frequency blocking effect of complicated geometry. At each receiver point, we compute the product of visibility vectors for these blocker spheres as seen from the point. Instead of computing an expensive SH product per blocker as in previous work, we perform inexpensive vector sums to accumulate the log of blocker visibility. SH exponentiation then yields the product visibility vector over all blockers. We show how the SH exponentiation required can be approximated accurately and efficiently for low-order SH, accelerating previous CPUbased methods by a factor of 10 or more, depending on blocker complexity, and allowing real-time GPU implementation.