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Spacetime Constraints
 Computer Graphics
, 1988
"... Spacetime constraints are a new method for creating character animation. The animator specifies what the character has to do, for instance, "jump from here to there, clearing a hurdle in between;" how the motion should be performed, for instance "don't waste energy," or &quo ..."
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Cited by 335 (6 self)
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Spacetime constraints are a new method for creating character animation. The animator specifies what the character has to do, for instance, "jump from here to there, clearing a hurdle in between;" how the motion should be performed, for instance "don't waste energy," or "come down hard enough to splatter whatever you land on;" the character's physical structurethe geometry, mass, connectivity, etc. of the parts; and the physical resources available to the character to accomplish the motion, for instance the character 's muscles, a floor to push off from, etc. The requirements contained in this description, together with Newton 's laws, comprise a problem of constrained optimization. The solution to this problem is a physically valid motion satisfying the "what" constraints and optimizing the "how" criteria. We present as examples a Luxo lamp performing a variety of coordinated motions. These realistic motions conform to such principles of traditional animation as anticipation, squas...
Mobile Sensor Network Deployment using Potential Fields: A Distributed, Scalable Solution to the Area Coverage Problem
, 2002
"... This paper considers the problem of deploying a mobile sensor network in an unknown environment. A mobile sensor network is composed of a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. Such networks are capable of selfdeployment; ..."
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Cited by 264 (15 self)
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This paper considers the problem of deploying a mobile sensor network in an unknown environment. A mobile sensor network is composed of a distributed collection of nodes, each of which has sensing, computation, communication and locomotion capabilities. Such networks are capable of selfdeployment; i.e., starting from some compact initial configuration, the nodes in the network can spread out such that the area `covered' by the network is maximized. In this paper, we present a potentialfieldbased approach to deployment. The fields are constructed such that each node is repelled by both obstacles and by other nodes, thereby forcing the network to spread itself throughout the environment. The approach is both distributed and scalable.
Using Particles to Sample and Control Implicit Surfaces
, 1994
"... We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement c ..."
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Cited by 233 (3 self)
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We present a new particlebased approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement control points for direct manipulation by specifying particle motions, then solving for surface motion that maintains the constraint. For sampling and rendering, we run the constraint in the other direction, creating floater particles that roam freely over the surface. Local repulsion is used to make floaters spread evenly across the surface. By varying the radius of repulsion adaptively, and fissioning or killing particles based on the local density, we can achieve good sampling distributions very rapidly, and maintain them even in the face of rapid and extreme deformations and changes in surface topology. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling:...
Analytical methods for dynamic simulation of nonpenetrating rigid bodies
 In Proc. of ACM SIGGRAPH ’89
, 1989
"... A method for analytically calculating the forces between systems of rigid bodies in resting (noncolliding) contact is presented. The systems of bodies may either be in motion or static equilibrium and adjacent bodies may touch at multiple points. The analytic formulation of the forces between bodie ..."
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Cited by 201 (9 self)
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A method for analytically calculating the forces between systems of rigid bodies in resting (noncolliding) contact is presented. The systems of bodies may either be in motion or static equilibrium and adjacent bodies may touch at multiple points. The analytic formulation of the forces between bodies in noncolliding contact can be modified to deal with colliding bodies. Accordingly, an improved method for analytically calculating the forces between systems of rigid bodies in colliding contact is also presented. Both methods can be applied to systems with arbitrary holonomic geometric constraints, such as linked figures. The analytical formulations used treat both holonomic and nonholonomic constraints in a consistent manner.
Discrete mechanics and variational integrators
 Acta Numer
, 2001
"... This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the disc ..."
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Cited by 172 (30 self)
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This paper gives a review of integration algorithms for finite dimensional mechanical systems that are based on discrete variational principles. The variational technique gives a unified treatment of many symplectic schemes, including those of higher order, as well as a natural treatment of the discrete Noether theorem. The approach also allows us to include forces, dissipation and constraints in a natural way. Amongst the many specific schemes treated as examples, the Verlet, SHAKE, RATTLE, Newmark, and the symplectic
A survey of deformable modeling in computer graphics
, 1997
"... This paper presents a survey of the work done in modeling deformable objects within the computer graphics research community. The research has a long history and a wide variety of approaches have been used. This paper organizes the diversity of research by the technique used rather than by the appli ..."
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Cited by 166 (1 self)
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This paper presents a survey of the work done in modeling deformable objects within the computer graphics research community. The research has a long history and a wide variety of approaches have been used. This paper organizes the diversity of research by the technique used rather than by the application, although applications are discussed throughout. This paper presents some purely geometric approaches for modeling deformable objects, but focuses on physically based approaches. In the latter category are massspring models, nite element models, approximate continuum models, and low degree of freedom models. Special emphasis is placed on nite element models, which o er the greatest accuracy, but have seen limited use in computer graphics. The paper also suggests important areas for future research. 1
Curved Surfaces and Coherence for Nonpenetrating Rigid Body Simulation
, 1990
"... A formulation for the contact forces between curved surfaces in resting (noncolliding) contact is presented. In contrast to previous formulations, constraints on the allowable tangential movement between contacting surfaces are not required. Surfaces are restricted to be twicedifferentiable surfac ..."
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Cited by 147 (7 self)
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A formulation for the contact forces between curved surfaces in resting (noncolliding) contact is presented. In contrast to previous formulations, constraints on the allowable tangential movement between contacting surfaces are not required. Surfaces are restricted to be twicedifferentiable surfaces without boundary. Only finitely many contact points between surfaces are allowed; however, the surfaces need not be convex. The formulation yields the contact forces between curved surfaces and polyhedra as well. Algorithms for performing collision detection during simulation on bodies composed of both polyhedra and strictly convex curved surfaces are also presented. The collision detection algorithms exploit the geometric coherence between successive time steps of the simulation to achieve efficient running times.
Liegroup methods
 ACTA NUMERICA
, 2000
"... Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Liegroup structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having ..."
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Cited by 110 (19 self)
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Many differential equations of practical interest evolve on Lie groups or on manifolds acted upon by Lie groups. The retention of Liegroup structure under discretization is often vital in the recovery of qualitatively correct geometry and dynamics and in the minimization of numerical error. Having introduced requisite elements of differential geometry, this paper surveys the novel theory of numerical integrators that respect Liegroup structure, highlighting theory, algorithmic issues and a number of applications.
Fast animation and control of nonrigid structures
 Computer Graphics Proceedings, Annual Conference Series (Proc. ACM SIGGRAPH
, 1990
"... We describe a fast method for creating physically based animation of nonrigid objects. Rapid simulation of nonrigid behavior is based on global deformations. Constraints are used to connect nonrigid pieces to each other, forming complex models. Constraints also provide motion control, allowing mod ..."
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Cited by 110 (10 self)
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We describe a fast method for creating physically based animation of nonrigid objects. Rapid simulation of nonrigid behavior is based on global deformations. Constraints are used to connect nonrigid pieces to each other, forming complex models. Constraints also provide motion control, allowing model points to be moved accurately along specified trajectories. The use of deformations that are linear in the state of the system causes the constraint matrices to be constant. Preinverting these matrices therefore yields an enormous benefit in performance, allowing reasonably complex models to be manipulated at interactive speed.