"Behind every stack of books there is a flood of knowledge."
|Floraine Berthouzoz, Akash Garg, Danny M. Kaufman, Eitan Grinspun, and Maneesh Agrawala, Parsing Sewing Patterns into 3D Garment Models, to appear ACM Transactions on Graphics (SIGGRAPH 2013), July 2013.|
|Danny M. Kaufman and Dinesh K. Pai, Geometric Numerical Integration of Inequality Constrained Nonsmooth Hamiltonian Systems, SIAM Journal on Scientific Computing, 34(5), October 2012.
ABSTRACT: We consider the geometric numerical integration of Hamiltonian systems subject to both equality and “hard” inequality constraints. As in the standard geometric integration setting, we target long-term structure preservation. Additionally, however, we also consider invariant preservation over persistent, simultaneous, and/or frequent boundary interactions. Appropriately formulating geometric methods for these cases has long remained challenging due the inherent nonsmoothness and one-sided conditions that they impose. To resolve these issues we thus focus both on symplectic-momentum preserving behavior and the preservation of additional structures, unique to the inequality constrained setting. Toward these goals we introduce, for the first time, a fully nonsmooth, discrete Hamilton’s principle and obtain an associated framework for composing geometric numerical integration methods for inequality-equality–constrained systems. Applying this framework, we formulate a new family of geometric numerical integration methods that, by construction, preserve momentum and equality constraints and are observed to retain good long-term energy behavior. Along with these standard geometric properties, the derived methods also enforce multiple simultaneous inequality constraints, obtain smooth unilateral motion along constraint boundaries, and allow for both nonsmooth and smooth boundary approach and exit trajectories. Numerical experiments are presented to illustrate the behavior of these methods on difficult test examples where both smooth and nonsmooth active constraint modes persist with high frequency.
Supplemental material: Structure Preserving Integration of Inequality Constrained Dynamics, Oberwolfach Report No. 16/2011
|Breannan Smith, Danny M. Kaufman, Etienne Vouga, Rasmus Tamstorf, and Eitan Grinspun, Reflections on Simultaneous Impact, ACM Transactions on Graphics (SIGGRAPH 2012), 31(4), August 2012.
ABSTRACT: Resolving simultaneous impacts is an open and significant problem in collision response modeling. Existing algorithms in this domain fail to fulfill at least one of five physical desiderata. To address this we present a simple generalized impact model motivated by both the successes and pitfalls of two popular approaches: pair-wise propagation and linear complementarity models. Our algorithm is the first to satisfy all identified desiderata, including simultaneously guaranteeing symmetry preservation, kinetic energy conservation, and allowing break-away. Furthermore, we address the associated problem of inelastic collapse, proposing a complementary generalized restitution model that eliminates this source of nontermination. We then consider the application of our models to the synchronous time-integration of large-scale assemblies of impacting rigid bodies. To enable such simulations we formulate a consistent frictional impact model that continues to satisfy the desiderata. Finally, we validate our proposed algorithm by correctly capturing the observed characteristics of physical experiments including the phenomenon of extended patterns in vertically oscillated granular materials.
|Nobuyuki Umetani, Danny M. Kaufman, Takeo Igarashi, and Eitan Grinspun, Sensitive Couture for Interactive Garment Editing and Modeling, ACM Transactions on Graphics (SIGGRAPH 2011), 30(4), August 2011.
ABSTRACT: We present a novel interactive tool for garment design that enables, for the first time, interactive bidirectional editing between 2D patterns and 3D high-fidelity simulated draped forms. This provides a continuous, interactive, and natural design modality in which 2D and 3D representations are simultaneously visible and seamlessly maintain correspondence. Artists can now interactively edit 2D pattern designs and immediately obtain stable accurate feedback online, thus enabling rapid prototyping and an intuitive understanding of complex drape form.
|Danny M. Kaufman, Coupled Principles For Computational Frictional Contact Mechanics, 2009, Dissertation.
ABSTRACT: Methods for simulating frictional contact response are in high demand in robotics, graphics, biomechanics, structural engineering, and many other fields where the accurate modeling of interactions between solids are required. While techniques for accurately simulating structures and continua have advanced rapidly, methods for simulating contact between solids have lagged behind. This thesis considers the difficulties encountered in designing robust, accurate, and efficient computational methods for simulating frictional contact dynamics. We focus on understanding the fundamental sources of difficulty in frictional contact modeling, elucidating existing structures that can be leveraged to minimize them, and designing robust, accurate and efficient algorithms to simulate challenging frictional contact problems. In this thesis a Coupled Principles formulation of discrete, time-continuous frictional contact is developed. This is then applied as the basis for deriving novel, time-discrete, variational integrators that pose the discrete frictional contact problem as a system of coupled minimizations. Solutions to these resulting systems are given by points that are simultaneously optimal for both minimizations and avoid some known issues present in existing variational integration approaches for frictional contact. We then consider a specific two-step variant of these variational schemes that generalizes the popular Stewart-Trinkle model for frictional contact simulation. This is taken as a starting point for investigating encountered sources of difficulties found in solving numerical problems posed by these models. We show that many existing algorithms, that have generally been presumed suitable for solving the resulting contact-related numerical optimization problems, fail entirely for many important examples of frictional contact, and then address these limitations with our Staggered Projections algorithm. Applying a fixed-point scheme, derived from the Coupled Principles Formulation, we show that Staggered Projections efficiently obtains accurate solutions to the optimizations problems for many frictional contact problems that were previously impractical to solve. Finally, we also offer convergence analysis of the Staggered Projections algorithm, as well as simulations and instrumented examples that capture frictional contact behaviors for both rigid and large deformation models.
|Danny M. Kaufman, Shinjiro Sueda, Doug L. James, and Dinesh K. Pai, Staggered Projections for Frictional Contact in Multibody Systems, ACM Transactions on Graphics (SIGGRAPH Asia 2008), 27(5), December 2008, pp. 164:1-164:11.
|Danny M. Kaufman, Shinjiro Sueda, and Dinesh K. Pai, Contact Trees: Adaptive Contact Sampling for Robust Dynamics, Technical Sketches, SIGGRAPH 2007.
|Danny M. Kaufman and Dinesh K. Pai, Randomized Quadratic Programming with Applications to Rigid Body Contact, Technical Report, UBC, 2006.
|Danny M. Kaufman, Timothy Edmunds and Dinesh K. Pai, Fast Frictional Dynamics for Rigid Bodies, ACM Transactions on Graphics (SIGGRAPH 2005), 24(3), August 2005, pp. 946-956.
|Danny M. Kaufman and Dinesh K. Pai, Rapid Collision Dynamics for Multiple Contacts with Friction, in Multi-Point Physical Interaction with Real and Virtual Objects, Springer Tracts on Advanced Robotics,18, Springer-Verlag, 2005, pp. 3-19.
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