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 reducedcoordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation 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 simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (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 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 reducedcoordinate deformable models for objects with complex geometry. We exploit the fact that model reduction on large deformation 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 simulation of nonlinear dynamics using fast implicit Newmark subspace integrators, with subspace integration costs independent of geometric complexity. We present two useful approaches for generating low-dimensional subspace bases: modal derivatives and an interactive sketching technique. Mass-scaled principal component analysis (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.

No abstract

We propose an efficient scheme for evaluating nonlinear subspace forces (and Jacobians) associated with subspace deformations. The core problem we address is efficient integration of the subspace force density over the 3D spatial domain. Similar to Gaussian quadrature schemes that efficiently integrate functions that lie in particular polynomial subspaces, we propose cubature schemes (multi-dimensional quadrature) optimized for efficient integration of force densities associated with particular subspace deformations, particular materials, and particular geometric domains. We support generic subspace deformation kinematics, and nonlinear hyperelastic materials. For an r-dimensional deformation subspace with O(r) cubature points, our method is able to evaluate subspace forces at O(r2) cost. We also describe composite cubature rules for runtime error estimation. Results are provided for various subspace deformation models, several hyperelastic materials (St.Venant-Kirchhoff, Mooney-Rivlin, Arruda-Boyce), and multimodal (graphics, haptics, sound) applications. We show dramatically better efficiency than traditional Monte Carlo integration. CR Categories: I.6.8 [Simulation and Modeling]: Types of Simulation—Animation, I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling—Physically based modeling G.1.4 [Mathematics of Computing]: Numerical Analysis—Quadrature and Numerical Differentiation

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.

Figure 1: Yarn-level cloth: Three knitting patterns relaxed to rest in our simulator. Each starts from a flat input configuration like at left; they differ only in their interlocking patterns. Characteristic shapes and textures of each knit emerge from our yarn-level physical model. AbstractKnitted fabric is widely used in clothing because of its unique and stretchy behavior, which is fundamentally different from the behavior of woven cloth. The properties of knits come from the nonlinear, three-dimensional kinematics of long, inter-looping yarns, and despite significant advances in cloth animation we still do not know how to simulate knitted fabric faithfully. Existing cloth simulators mainly adopt elastic-sheet mechanical models inspired by woven materials, focusing less on the model itself than on important simulation challenges such as efficiency, stability, and robustness. We define a new computational model for knits in terms of the motion of yarns, rather than the motion of a sheet. Each yarn is modeled as an inextensible, yet otherwise flexible, B-spline tube. To simulate complex knitted garments, we propose an implicit-explicit integrator, with yarn inextensibility constraints imposed using efficient projections. Friction among yarns is approximated using rigid-body velocity filters, and key yarn-yarn interactions are mediated by stiff penalty forces. Our results show that this simple model predicts the key mechanical properties of different knits, as demonstrated by qualitative comparisons to observed deformations of actual samples in the laboratory, and that the simulator can scale up to substantial animations with complex dynamic motion.

Abstract-Real-time evaluation of distributed contact forces between rigid or deformable 3D objects is a key ingredient of 6-DoF force-feedback rendering. Unfortunately, at very high temporal rates, there is often insufficient time to resolve contact between geometrically complex objects. We propose a spatially and temporally adaptive approach to approximate distributed contact forces under hard real-time constraints. Our method is CPU-based and supports contact between rigid or reduced deformable models with complex geometry. We propose a contact model that uses a point-based representation for one object and a signed-distance field for the other. This model is related to the Voxmap-PointShell (VPS) method, but gives continuous contact forces and torques, enabling stable rendering of stiff penalty-based distributed contacts. We demonstrate that stable haptic interactions can be achieved by point-sampling offset surfaces to input "polygon soup" geometry using particle repulsion. We introduce a multiresolution nested pointshell construction that permits level-of-detail contact forces and enables graceful degradation of contact in close-proximity scenarios. Parametrically deformed distance fields are proposed for contact between reduced deformable objects. We present several examples of 6-DoF haptic rendering of geometrically complex rigid and deformable objects in distributed contact at real-time kilohertz rates.