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278
Large steps in cloth simulation
 SIGGRAPH 98 Conference Proceedings
, 1998
"... The bottleneck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particle ..."
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Cited by 576 (5 self)
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The bottleneck in most cloth simulation systems is that time steps must be small to avoid numerical instability. This paper describes a cloth simulation system that can stably take large time steps. The simulation system couples a new technique for enforcing constraints on individual cloth particles with an implicit integration method. The simulator models cloth as a triangular mesh, with internal cloth forces derived using a simple continuum formulation that supports modeling operations such as local anisotropic stretch or compression; a unified treatment of damping forces is included as well. The implicit integration method generates a large, unbanded sparse linear system at each time step which is solved using a modified conjugate gradient method that simultaneously enforces particles ’ constraints. The constraints are always maintained exactly, independent of the number of conjugate gradient iterations, which is typically small. The resulting simulation system is significantly faster than previous accounts of cloth simulation systems in the literature. Keywords—Cloth, simulation, constraints, implicit integration, physicallybased modeling. 1
Robust treatment of collisions, contact and friction for cloth animation
 ACM Transactions on Graphics
, 2002
"... We present an algorithm to efficiently and robustly process collisions, contact and friction in cloth simulation. It works with any technique for simulating the internal dynamics of the cloth, and allows true modeling of cloth thickness. We also show how our simulation data can be postprocessed wit ..."
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Cited by 300 (28 self)
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We present an algorithm to efficiently and robustly process collisions, contact and friction in cloth simulation. It works with any technique for simulating the internal dynamics of the cloth, and allows true modeling of cloth thickness. We also show how our simulation data can be postprocessed with a collisionaware subdivision scheme to produce smooth and interference free data for rendering.
Efficient collision detection using bounding volume hierarchies of kdops
 IEEE Transactions on Visualization and Computer Graphics
, 1998
"... Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment ..."
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Cited by 290 (4 self)
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Abstract—Collision detection is of paramount importance for many applications in computer graphics and visualization. Typically, the input to a collision detection algorithm is a large number of geometric objects comprising an environment, together with a set of objects moving within the environment. In addition to determining accurately the contacts that occur between pairs of objects, one needs also to do so at realtime rates. Applications such as haptic forcefeedback can require over 1,000 collision queries per second. In this paper, we develop and analyze a method, based on boundingvolume hierarchies, for efficient collision detection for objects moving within highly complex environments. Our choice of bounding volume is to use a “discrete orientation polytope” (“kdop”), a convex polytope whose facets are determined by halfspaces whose outward normals come from a small fixed set of k orientations. We compare a variety of methods for constructing hierarchies (“BVtrees”) of bounding kdops. Further, we propose algorithms for maintaining an effective BVtree of kdops for moving objects, as they rotate, and for performing fast collision detection using BVtrees of the moving objects and of the environment. Our algorithms have been implemented and tested. We provide experimental evidence showing that our approach yields substantially faster collision detection than previous methods. Index Terms—Collision detection, intersection searching, bounding volume hierarchies, discrete orientation polytopes, bounding boxes, virtual reality, virtual environments. 1
Physically based motion transformation
 In Proceedings of ACM SIGGRAPH 99. Computer Graphics Proceedings
, 1999
"... We introduce a novel algorithm for transforming character animation sequences that preserves essential physical properties of the motion. By using the spacetime constraints dynamics formulation our algorithm maintains realism of the original motion sequence without sacrificing full user control of ..."
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Cited by 203 (6 self)
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We introduce a novel algorithm for transforming character animation sequences that preserves essential physical properties of the motion. By using the spacetime constraints dynamics formulation our algorithm maintains realism of the original motion sequence without sacrificing full user control of the editing process. In contrast to most physically based animation techniques that synthesize motion from scratch, we take the approach of motion transformation as the underlying paradigm for generating computer animations. In doing so, we combine the expressive richness of an input animation sequence with the controllability of spacetime optimization to create a wide range of realistic character animations. The spacetime dynamics formulation also allows editing of intuitive, highlevel motion concepts such as the time and placement of footprints, length and mass of various extremities, number of body joints and gravity. Our algorithm is well suited for the reuse of highlydetailed captured motion animations. In addition, we describe a new methodology for mapping a motion between characters with drastically different numbers of degrees of freedom. We use this method to reduce the complexity of the spacetime optimization problems. Furthermore, our approach provides a paradigm for controlling complex dynamic and kinematic systems with simpler ones.
Engineering and economic applications of complementarity problems
 SIAM REVIEW
, 1997
"... This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the c ..."
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Cited by 195 (24 self)
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This paper gives an extensive documentation of applications of finitedimensional nonlinear complementarity problems in engineering and equilibrium modeling. For most applications, we describe the problem briefly, state the defining equations of the model, and give functional expressions for the complementarity formulations. The goal of this documentation is threefold: (i) to summarize the essential applications of the nonlinear complementarity problem known to date, (ii) to provide a basis for the continued research on the nonlinear complementarity problem, and (iii) to supply a broad collection of realistic complementarity problems for use in algorithmic experimentation and other studies.
Six DegreeofFreedom Haptic Rendering Using Voxel Sampling
 Proc. ACM Siggraph, ACM
, 1999
"... A simple, fast, and approximate voxelbased approach to 6DOF haptic rendering is presented. It can reliably sustain a 1000 Hz haptic refresh rate without resorting to asynchronous physics and haptic rendering loops. It enables the manipulation of a modestly complex rigid object within an arbitraril ..."
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Cited by 174 (1 self)
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A simple, fast, and approximate voxelbased approach to 6DOF haptic rendering is presented. It can reliably sustain a 1000 Hz haptic refresh rate without resorting to asynchronous physics and haptic rendering loops. It enables the manipulation of a modestly complex rigid object within an arbitrarily complex environment of static rigid objects. It renders a shortrange force field surrounding the static objects, which repels the manipulated object and strives to maintain a voxelscale minimum separation distance that is known to preclude exact surface interpenetration. Force discontinuities arising from the use of a simple penalty force model are mitigated by a dynamic simulation based on virtual coupling. A generalization of octree improves voxel memory efficiency. In a preliminary implementation, a commercially available 6DOF haptic prototype device is driven at a constant 1000 Hz haptic refresh rate from one dedicated haptic processor, with a separate processor for graphics. This system yields stable and convincing force feedback for a wide range of user controlled motion inside a large, complex virtual environment, with very few surface interpenetration events. This level of performance appears suited to applications such as certain maintenance and assembly task simulations that can tolerate voxelscale minimum separation distances.
Lineartime dynamics using lagrange multipliers
 In SIGGRAPH 96 Conference Proceedings, Computer Graphics Proceedings, Annual Conference Series
, 1996
"... Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics ..."
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Cited by 139 (0 self)
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Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics applications because they bypass the difficult (and often intractable) problem of parameterizing a system’s degrees of freedom. Given a loopfree set of n equality constraints acting between pairs of bodies, the method takes O(n) time to compute the system’s dynamics. The method does not rely on matrix bandwidth, so no assumptions about the constraints’ topology are needed. Bodies need not be rigid, constraints can be of various dimensions, and unlike reducedcoordinate approaches, nonholonomic (e.g. velocitydependent) constraints are allowed. An additional set of k onedimensional constraints which induce loops and/or handle inequalities can be accommodated with cost O(kn). This makes it practical to simulate complicated, closedloop articulated figures with jointlimits and contact at interactive rates. A complete description of a sample implementation is provided in pseudocode. 1
RigidBody Dynamics With Friction and Impact,”
 SIAM Rev.,
, 2000
"... Abstract. Rigidbody dynamics with unilateral contact is a good approximation for a wide range of everyday phenomena, from the operation of car brakes to walking to rock slides. It is also of vital importance for simulating robots, virtual reality, and realistic animation. However, correctly modeli ..."
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Cited by 137 (1 self)
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Abstract. Rigidbody dynamics with unilateral contact is a good approximation for a wide range of everyday phenomena, from the operation of car brakes to walking to rock slides. It is also of vital importance for simulating robots, virtual reality, and realistic animation. However, correctly modeling rigidbody dynamics with friction is difficult due to a number of discontinuities in the behavior of rigid bodies and the discontinuities inherent in the Coulomb friction law. This is particularly crucial for handling situations with large coefficients of friction, which can result in paradoxical results known at least since Painlevé [C. R. Acad. Sci. Paris, 121 (1895), pp. 112115]. This single example has been a counterexample and cause of controversy ever since, and only recently have there been rigorous mathematical results that show the existence of solutions to his example. The new mathematical developments in rigidbody dynamics have come from several sources: "sweeping processes" and the measure differential inclusions of Moreau in the 1970s and 1980s, the variational inequality approaches of Duvaut and J.L. Lions in the 1970s, and the use of complementarity problems to formulate frictional contact problems by Lötstedt in the early 1980s. However, it wasn't until much more recently that these tools were finally able to produce rigorous results about rigidbody dynamics with Coulomb friction and impulses. Key words. rigidbody dynamics, Coulomb friction, contact mechanics, measuredifferential inclu sions, complementarity problems AMS subject classifications. Primary, 70E55; Secondary, 70F40, 74M PII. S0036144599360110 Rigid Bodies and Friction. Rigid bodies are bodies that cannot deform. They can translate and rotate, but they cannot change their shape. From the outset this must be understood as an approximation to reality, since no bodies are perfectly rigid. However, for a vast number of applications in robotics, manufacturing, biomechanics (such as studying how people walk), and granular materials, this is an excellent approximation. It is also convenient, since it does not require solving large, complex systems of partial differential equations, which is generally difficult to do both analytically and computationally. To see the difference, consider the problem of a bouncing ball. The rigidbody model will assume that the ball does not deform while in flight and that contacts with the ground are instantaneous, at least while the ball is not rolling. On the other hand, a full elastic model will model not only the contacts and the resulting deformation of the entire ball while in contact, but also the elastic oscillations of the ball while it is in flight. Apart from the computational complexity of all this, the analysis of even linearly elastic bodies in contact with a *
The Cassowary Linear Arithmetic Constraint Solving Algorithm: Interface and Implementation
 ACM TRANSACTIONS ON COMPUTER HUMAN INTERACTION
, 1998
"... Linear equality and inequality constraints arise naturally in specifying many aspects of user interfaces, such as requiring that one window be to the left of another, requiring that a pane occupy the leftmost 1/3 of a window, or preferring that an object be contained within a rectangle if possibl ..."
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Cited by 116 (10 self)
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Linear equality and inequality constraints arise naturally in specifying many aspects of user interfaces, such as requiring that one window be to the left of another, requiring that a pane occupy the leftmost 1/3 of a window, or preferring that an object be contained within a rectangle if possible. Current constraint solvers designed for UI applications cannot e#ciently handle simultaneous linear equations and inequalities. This is a major limitation. We describe Cassowaryan incremental algorithm based on the dual simplex method that can solve such systems of constraints e#ciently. This informal technical report describes the latest version of the Cassowary algorithm. It is derived from the paper "Solving Linear Arithmetic Constraints for User Interface Applications" by Alan Borning, Kim Marriott, Peter Stuckey, and Yi Xiao [7], published in the UIST'97 Proceedings. The UIST paper also contains a description of QOCA, a closely related solver that finds leastsquares solut...
Nonconvex rigid bodies with stacking
 ACM Trans. Graph
"... We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this d ..."
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Cited by 115 (12 self)
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We consider the simulation of nonconvex rigid bodies focusing on interactions such as collision, contact, friction (kinetic, static, rolling and spinning) and stacking. We advocate representing the geometry with both a triangulated surface and a signed distance function defined on a grid, and this dual representation is shown to have many advantages. We propose a novel approach to time integration merging it with the collision and contact processing algorithms in a fashion that obviates the need for ad hoc threshold velocities. We show that this approach matches the theoretical solution for blocks sliding and stopping on inclined planes with friction. We also present a new shock propagation algorithm that allows for efficient use of the propagation (as opposed to the simultaneous) method for treating contact. These new techniques are demonstrated on a variety of problems ranging from simple test cases to stacking problems with as many as 1000 nonconvex rigid bodies with friction as shown in Figure 1.