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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 "come down hard enough to spl ..."
Abstract

Cited by 315 (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...
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 223 (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:...
ThroughtheLens Camera Control
, 1992
"... In this paper we introduce throughthelens camera control, a body of techniques that permit a user to manipulate a virtual camera by controlling and constraining features in the image seen through its lens. Rather than solving for camera parameters directly, constrained optimization is used to com ..."
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Cited by 123 (6 self)
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In this paper we introduce throughthelens camera control, a body of techniques that permit a user to manipulate a virtual camera by controlling and constraining features in the image seen through its lens. Rather than solving for camera parameters directly, constrained optimization is used to compute their time derivatives based on desired changes in userdefined controls. This effectively permits new controls to be defined independent of the underlying parameterization. The controls can also serve as constraints, maintaining their values as others are changed. We describe the techniques in general and work through a detailed example of a specific camera model. Our implementation demonstrates a gallery of useful controls and constraints and provides some examples of how these may be used in composing images and animations.
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 111 (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.
Interactive Dynamics
, 1990
"... Our goal is to use physical simulation as an interactive medium for building and manipulating a wide range of models. A key to achieving this goal is the ability to create complex physical models dynamically by snapping simple pieces together integrating the process of model creation into the ongoin ..."
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Cited by 89 (13 self)
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Our goal is to use physical simulation as an interactive medium for building and manipulating a wide range of models. A key to achieving this goal is the ability to create complex physical models dynamically by snapping simple pieces together integrating the process of model creation into the ongoing simulation. We present a mathematical and computational formulation for constrained dynamics that makes this possible allowing encapsulated objects constraints and forces to be combined dynamically and simulated effciently. The formulation handles arbitrary objects including nonrigid bodies. We describe an implementation for interactive dynamics and discuss applications to mechanism construction geometric modeling interactive optimization data fittting and animation.
Physically Based Modeling: Principles and Practice  Constrained Dynamics
 COMPUTER GRAPHICS
, 1997
"... ..."
Supporting Numerical Computations in Interactive Contexts
, 1993
"... As computational performance becomes more readily available, there will be an increasing variety of interactive graphical applications with iterative numerical techniques at their core. In this paper, we consider how to support the unique demands of such applications. In particular, we focus on how ..."
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Cited by 12 (2 self)
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As computational performance becomes more readily available, there will be an increasing variety of interactive graphical applications with iterative numerical techniques at their core. In this paper, we consider how to support the unique demands of such applications. In particular, we focus on how to set up the numerical problems which must be solved. In the context of interactive systems, this requires the ability to dynamically compose systems of equations and rapidly evaluate them and their derivatives. We present an approach called SnapTogether Mathematics for doing this.
Creating and Manipulating Constrained Models
, 1991
"... The success of constraintbased approaches to geometric modeling has been limited by difficulty in creating constraints, solving them, and presenting them to users. This paper addresses all three issues. We facilitate the creation of constrained models by using placement operations to specify constr ..."
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Cited by 2 (0 self)
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The success of constraintbased approaches to geometric modeling has been limited by difficulty in creating constraints, solving them, and presenting them to users. This paper addresses all three issues. We facilitate the creation of constrained models by using placement operations to specify constraints as well as positions, with no extra work on the part of the user. We augment SnapDragging[Bie89], an earlier successful technique for specifying geometric models, to give the user the option of making persistent the relations it helps create. Because the technique provides both the constraints and an initial solution to them, we can use the techniques of constrained dynamics to maintain the relationships as a user drags the models. This differential approach to constraints avoids many of the difficulties in constraintbased systems, such as solving nonlinear algebraic equations. Our approach suggests methods for displaying and editing constraints as well.
Differential Equation Basics
, 1993
"... is the velocity that the moving point p must have if it ever moves through x (which it may or may not.) Think of f as driving p from point to point, like an ocean current. Wherever we initially deposit p, the "current" at that point will seize it. Where p is carried depends on where we initially dr ..."
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Cited by 1 (0 self)
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is the velocity that the moving point p must have if it ever moves through x (which it may or may not.) Think of f as driving p from point to point, like an ocean current. Wherever we initially deposit p, the "current" at that point will seize it. Where p is carried depends on where we initially drop it, but once dropped, all future motion is determined by f . The trajectory swept out by p through f forms an integral curve of the vector field. See figure 2. We wrote f as a function of both x and t , but the derivative function may or may not depend directly on time. If it does, then not only the point p but the the vector field itself moves, so that p's velocity depends not only on where it is, but on when it arrives there. In that ca
CPSC533B Course Project: Spacetime Constraints 2003/04/25 CPSC533B Course Project: Spacetime Constraints
"... Computer animation has two methods of modeling: one is physicalbased modeling; the other is examplebased modeling. Although the examplebased modeling now is the leading direction, physicalbased modeling has its important as the basement in the area of computer animation. Spacetime constraints ar ..."
Abstract
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Computer animation has two methods of modeling: one is physicalbased modeling; the other is examplebased modeling. Although the examplebased modeling now is the leading direction, physicalbased modeling has its important as the basement in the area of computer animation. Spacetime constraints are a physicalbased method for creating character animation. It specifies what the character should do “moving from here to there, ” how the motion should be performed, for instance “minimize waste energy”, the character’s physical structure—the 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. I experiment as examples a simple accelerate particle and discuss the solution for a swing pendulum and a luxo lamp. These realistic motions conform to such principles of traditional animation as anticipation,