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13
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 91 (8 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.
Animating sand as a fluid
 ACM Trans. Graph. (Proc. SIGGRAPH
, 2005
"... My thesis presents a physicsbased simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulat ..."
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Cited by 74 (4 self)
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My thesis presents a physicsbased simulation method for animating sand. To allow for efficiently scaling up to large volumes of sand, we abstract away the individual grains and think of the sand as a continuum. In particular we show that an existing water simulator can be turned into a sand simulator within frictional regime with only a few small additions to account for intergrain and boundary friction, yet with visually acceptable result. We also propose an alternative method for simulating fluids. Our core representation is a cloud of particles, which allows for accurate and flexible surface tracking and advection, but we use an auxiliary grid to efficiently enforce boundary conditions and incompressibility. We further address the issue of reconstructing a surface from particle data to render each frame. ii Contents ii
Timewarp rigid body simulation
 IN PROC. OF ACM SIGGRAPH
, 2000
"... The traditional highlevel algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson´s timewarp algorithm (Jefferson 85) is ..."
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Cited by 50 (0 self)
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The traditional highlevel algorithms for rigid body simulation work well for moderate numbers of bodies but scale poorly to systems of hundreds or more moving, interacting bodies. The problem is unnecessary synchronization implicit in these methods. Jefferson´s timewarp algorithm (Jefferson 85) is a technique for alleviating this problem in parallel discrete event simulation. Rigid body dynamics, though a continuous process, exhibits many aspects of a discrete one. With modification, the timewarp algorithm can be used in a uniprocessor rigid body simulator to give substantial performance improvements for simulations with large numbers of bodies. This paper describes the limitations of the traditional highlevel simulation algorithms, introduces Jefferson´s algorithm, and extends and optimizes it for the rigid body case. It addresses issues particular to rigid body simulation, such as collision detection and contact group management, and describes how to incorporate these into the timewarp framework. Quantitative experimental results indicate that the timewarp algorithm offers significant performance improvements over traditional highlevel rigid body simulation algorithms, when applied to systems with hundreds of bodies. It also helps pave the way to parallel implementations, as the paper discusses.
OptimizationBased Animation
, 2002
"... A new paradigm for rigid body simulation is presented and analyzed. Current techniques for rigid body simulation run slowly on scenes with many bodies in close proximity. Each time two bodies collide or make or break a static contact, the simulator must interrupt the numerical integration of velocit ..."
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Cited by 36 (1 self)
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A new paradigm for rigid body simulation is presented and analyzed. Current techniques for rigid body simulation run slowly on scenes with many bodies in close proximity. Each time two bodies collide or make or break a static contact, the simulator must interrupt the numerical integration of velocities and accelerations. Even for simple scenes, the number of discontinuities per frame time can rise to the millions. An efficient optimizationbased animation (OBA) algorithm is presented which can simulate scenes with many convex threedimensional bodies settling into stacks and other “crowded” arrangements. This algorithm simulates Newtonian (second order) physics and Coulomb friction, and it uses quadratic programming (QP) to calculate new positions, momenta, and accelerations strictly at frame times. The extremely small integration steps inherent to traditional simulation techniques are avoided. Contact points are synchronized at the end of each frame. Resolving contacts with friction is known to be a difficult problem. Analytic force calculation can have ambiguous or nonexisting solutions. Purely impulsive techniques avoid these ambiguous cases, but still require an excessive and computationally expensive number of updates in the case of
The Computer Modelling of Fallen Snow
, 2000
"... One of nature's greatest beauties is the way fresh snowcovers the world in a perfect blanket of crystalline white. Snow replaces sharp angles with gentle curves, and clings to surfaces to form ghostly silhouettes. It is said the Inuit have 50 di#erentwords for snow, yet even they can be left speechl ..."
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Cited by 23 (0 self)
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One of nature's greatest beauties is the way fresh snowcovers the world in a perfect blanket of crystalline white. Snow replaces sharp angles with gentle curves, and clings to surfaces to form ghostly silhouettes. It is said the Inuit have 50 di#erentwords for snow, yet even they can be left speechless, as snow is one of the most complex natural materials in existence.
Constraintbased Automatic Placement for Scene Composition
 IN GRAPHICS INTERFACE
, 2002
"... The layout of large scenes can be a timeconsuming and tedious task. In most current systems, the user must position each of the objects by hand, one at a time. This paper presents a constraintbased automatic placement system, which allows the user to quickly and easily lay out complex scenes. The ..."
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Cited by 16 (0 self)
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The layout of large scenes can be a timeconsuming and tedious task. In most current systems, the user must position each of the objects by hand, one at a time. This paper presents a constraintbased automatic placement system, which allows the user to quickly and easily lay out complex scenes. The system
ConstraintBased Collision and Contact Handling Using Impulses
 IN PROCEEDINGS OF THE 19TH INTERNATIONAL CONFERENCE ON COMPUTER ANIMATION AND SOCIAL AGENTS (GENEVA (SWITZERLAND
, 2006
"... In this paper a new method for handling collisions and permanent contacts between rigid bodies is presented. Constraintbased methods for computing contact forces with friction provide a high degree of accuracy. The computation is often transformed into an optimization problem and solved with techni ..."
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Cited by 8 (6 self)
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In this paper a new method for handling collisions and permanent contacts between rigid bodies is presented. Constraintbased methods for computing contact forces with friction provide a high degree of accuracy. The computation is often transformed into an optimization problem and solved with techniques like linear or quadratic programming. Impulsebased methods compute impulses to prevent colliding bodies from interpenetrating. The determination of these impulses is simple and fast. The impulsebased methods are very efficient but they are less accurate than the constraintbased methods because they resolve only one contact between two colliding bodies at the same time. The presented method uses a constraintbased approach. It can handle multiple contacts between two colliding bodies at the same time. For every collision and contact a nonpenetration constraint is defined. These constraints are satisfied by iteratively computing impulses. In the same iteration loop impulses for dynamic and static friction are determined. The new method provides the accuracy of a constraintbased method and is efficient and easy to implement like an impulsebased one.
A fast impulsive contact suite for rigid body simulation
 IEEE Transactions on Visualization and Computer Graphics
, 2004
"... Abstract—A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) p ..."
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Cited by 8 (1 self)
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Abstract—A suite of algorithms is presented for contact resolution in rigid body simulation under the Coulomb friction model: Given a set of rigid bodies with many contacts among them, resolve dynamic contacts (collisions) and static (persistent) contacts. The suite consists of four algorithms: 1) partial sequential collision resolution, 2) final resolution of collisions through the solution of a single convex QP (positive semidefinite quadratic program), 3) resolution of static contacts through the solution of a single convex QP, 4) freezing of “stationary ” bodies. This suite can generate realisticlooking results for simple examples yet, for the first time, can also tractably resolve contacts for a simulation as large as 1,000 cubes in an “hourglass. ” Freezing speeds up this simulation by more than 25 times. Thanks to excellent commercial QP technology, the contact resolution suite is simple to implement and can be “plugged into” any simulation algorithm to provide fast and realisticlooking animations of rigid bodies. Index Terms—Quadratic programming, computer graphics, physicallybased modeling, simulation, animation. æ
Rotational Polygon Overlap Minimization and Compaction
 Computational Geometry: Theory and Applications
, 1998
"... An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P 1 ,P 2 ,P 3 ,...,P k in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any p ..."
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Cited by 5 (1 self)
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An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P 1 ,P 2 ,P 3 ,...,P k in a container polygon Q, translate and rotate the polygons to diminish their overlap to a local minimum. A (local) overlap minimum has the property that any perturbation of the polygons increases the overlap. Overlap minimization is modified to create a practical algorithm for compaction: starting with a nonoverlapping layout in a rectangular container, plan a nonoverlapping motion that diminishes the length or area of the container to a local minimum. Experiments show that both overlap minimization and compaction work well in practice and are likely to be useful in industrial applications. 1998 Published by Elsevier Science B.V. Keywords: Layout; Packing or nesting of irregular polygons; Containment; Minimum enclosure; Compaction; Linear programming 1. Introduction A number of industries generate new parts by cutting them from stock mater...
Rotational Polygon Overlap Minimization
 Computational Geometry: Theory and Applications
, 1997
"... An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1 ; P2 ; P3 ; : : : ; Pk in a container polygon C, translate and rotate the polygons to a layout that minimizes an overlap measure. A (local) overlap minimum has the property that ..."
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Cited by 4 (1 self)
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An effective and fast algorithm is given for rotational overlap minimization: given an overlapping layout of polygons P1 ; P2 ; P3 ; : : : ; Pk in a container polygon C, translate and rotate the polygons to a layout that minimizes an overlap measure. A (local) overlap minimum has the property that any perturbation of the polygons increases the chosen measure of overlap. Experiments show that the algorithm works well in practice. It is shown how to apply overlap minimization to create algorithms for other layout tasks: compaction, containment, and minimal enclosure. Compaction: starting with a nonoverlapping layout in a rectangular container, plan a nonoverlapping motion that minimizes the length or area of the container. Containment: place the polygons into a (possibly nonconvex container) without overlapping. Minimal enclosure: find a nonoverlapping layout inside a minimumlength, fixedwidth rectangle or inside a minimum area rectangle. All of these algorithms have important i...