Results 1  10
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14
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 98 (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
Adding force feedback to graphics systems: Issues and solutions
 In Proceedings of SIGGRAPH ’96
, 1996
"... Integrating force feedback with a complete realtime virtual environment system presents problems which are more difficult than those encountered in building simpler forcefeedback systems. In particular, lengthy computations for graphics or simulation require a decoupling of the haptic servo loop f ..."
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Cited by 75 (0 self)
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Integrating force feedback with a complete realtime virtual environment system presents problems which are more difficult than those encountered in building simpler forcefeedback systems. In particular, lengthy computations for graphics or simulation require a decoupling of the haptic servo loop from the main application loop if highquality forces are to be produced. We present some approaches to these problems and describe our forcefeedback software library which implements these techniques and provides other benefits including haptictextured surfaces, device independence, distributed operation and easy enhancement.
Planning Paths for Elastic Objects Under Manipulation Constraints
 International Journal of Robotics Research
, 2001
"... This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to ..."
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Cited by 38 (7 self)
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This paper addresses the problem of planning paths for an elastic object from an initial to a final configuration in a static environment. It is assumed that the object is manipulated by two actuators and that it does not touch the obstacles in its environment at any time. The object may need to deform in order to achieve a collisionfree path from the initial to the final configuration. Any required deformations are automatically computed by our planner according to the principles of elasticity theory from mechanics. The problem considered in this paper differs significantly from that of planning for a rigid or an articulated object. In the first part of the paper we point out these differences and highlight the reasons that make planning for elastic objects an extremely difficult task. We then present a randomized algorithm for computing collisionfree paths for elastic objects under the abovementioned restrictions of manipulation.
Hierarchical Geometric Approximations
, 1994
"... This dissertation explores some techniques for automatic approximation of geometric objects. My thesis is that using and extending concepts from computational geometry can help us in devising efficient and parallelizable algorithms for automatically constructing useful detail hierarchies for geometr ..."
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Cited by 36 (4 self)
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This dissertation explores some techniques for automatic approximation of geometric objects. My thesis is that using and extending concepts from computational geometry can help us in devising efficient and parallelizable algorithms for automatically constructing useful detail hierarchies for geometric objects. We have demonstrated this by developing new algorithms for two kinds of geometric approximation problems that have been motivated by a single driving problem  the efficient computation and display of smooth solventaccessible molecular surfaces. The applications of these detail hierarchies are in biochemistry and computer graphics. The smooth solventaccessible surface of a molecule is useful in studying the structure and interactions of proteins, in particular for attacking the proteinsubstrate docking problem. We have developed a parallel lineartime algorithm for computing molecular surfaces. Molecular surfaces are equivalent to the weighted ffhulls. Thus our work is pot...
Towards Planning for Elastic Objects
 ROBOTICS: THE ALGORITHMIC PERSPECTIVE
, 1998
"... This paper investigates the problem of path planning for a thin elastic plate. The underlying geometric model for the plate is provided by a Bezier representation. The geometric model is augmented by a realistic mechanical model. The latter permits the computation of the shape of the plate with resp ..."
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Cited by 35 (6 self)
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This paper investigates the problem of path planning for a thin elastic plate. The underlying geometric model for the plate is provided by a Bezier representation. The geometric model is augmented by a realistic mechanical model. The latter permits the computation of the shape of the plate with respect to a set of grasping constrints by minimizing the elastic energy of the deformation. We use a probabilistic roadmap planner to compute paths for the plate and we present a number of experimental results to illustrate our approach. Our work is a first step towards considering the physical properties of objects when planning.
Dynamic simulation of articulated rigid bodies with contact and collision
 IEEE TVCG
, 2006
"... We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. In order to leverage existing algorithms for nonconvex bodies, multiple collisions, large contact groups, stacking, etc., we use maximal rather than generaliz ..."
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Cited by 28 (4 self)
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We propose a novel approach for dynamically simulating articulated rigid bodies undergoing frequent and unpredictable contact and collision. In order to leverage existing algorithms for nonconvex bodies, multiple collisions, large contact groups, stacking, etc., we use maximal rather than generalized coordinates and take an impulse based approach that allows us to treat articulation, contact and collision in a unified manner. Traditional constraint handling methods are subject to drift, and we propose a novel prestabilization method that does not require tunable potentially stiff parameters as does Baumgarte stabilization. This differs from poststabilization in that we compute allowable trajectories before moving the rigid bodies to their new positions, instead of correcting them after the fact when it can be difficult to incorporate the effects of contact and collision. A poststabilization technique is used for momentum and angular momentum. Our approach works with any black box method for specifying valid joint constraints, and no special considerations are required for arbitrary closed loops or branching. Moreover, our implementation is linear both in the number of bodies and in the number of auxiliary contact and collision constraints, unlike many other methods that are linear in the number of bodies but not in the number of auxiliary constraints.
Interactive PhysicallyBased Manipulation of Discrete/Continuous Models
, 1995
"... Physicallybased modeling has been used in the past to support a variety of interactive modeling tasks including freeform surface design, mechanism design, constrained drawing, and interactive camera control. In these systems, the user interacts with the model by exerting virtual forces, to which t ..."
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Cited by 24 (1 self)
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Physicallybased modeling has been used in the past to support a variety of interactive modeling tasks including freeform surface design, mechanism design, constrained drawing, and interactive camera control. In these systems, the user interacts with the model by exerting virtual forces, to which the system responds subject to the active constraints. In the past, this kind of interaction has been applicable only to models that are governed by continuous parameters. In this paper we present an extension to mixed continuous /discrete models, emphasizing constrained layout problems that arise in architecture and other domains. When the object being dragged is blocked from further motion by geometric constraints, a local discrete search is triggered, during which transformations such as swapping of adjacent objects may be performed. The result of the search is a "nearby" state in which the target object has been moved in the indicated direction and in which all constraints are satisfied. ...
Interactive Topological Drawing
, 1998
"... The research presented here examines topological drawing, a new mode of constructing and interacting with mathematical objects in threedimensional space. In topological drawing, issues such as adjacency and connectedness, which are topological in nature, take precedence over purely geometric issues ..."
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Cited by 18 (1 self)
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The research presented here examines topological drawing, a new mode of constructing and interacting with mathematical objects in threedimensional space. In topological drawing, issues such as adjacency and connectedness, which are topological in nature, take precedence over purely geometric issues. Because the domain of application is mathematics, topological drawing is also concerned with the correct representation and display of these objects on a computer. By correctness we mean that the essential topological features of objects are maintained during interaction. We have chosen to limit the scope of topological drawing to knot theory, a domain that consists essentially of one class of object (embedded circles in threedimensional space) yet is rich enough to contain a wide variety of difficult problems of research interest. In knot theory, two embedded circles (knots) are considered equivalent if one may be smoothly deformed into the other without any cuts or selfintersections. This notion of equivalence may be thought of as the heart of knot theory. We present methods for the computer construction and interactive manipulation of a
A Novel HapticsBased Interface and Sculpting System for PhysicsBased Geometric Design
 INTERNATIONAL JOURNAL OF SHAPE MODELING
, 2001
"... Standard freeform splines such as Bsplines and NURBS are widely employed in a wide range of CAD/CAM systems. Conventional geometric modeling and design techniques using these popular splines often requires tedious controlpoint manipulation and/or painstaking constraint specification (for funct ..."
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Cited by 17 (3 self)
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Standard freeform splines such as Bsplines and NURBS are widely employed in a wide range of CAD/CAM systems. Conventional geometric modeling and design techniques using these popular splines often requires tedious controlpoint manipulation and/or painstaking constraint specification (for functional requirements) via unnatural mousebased computer interfaces. In this paper, we propose a novel and natural haptic interface and present a physicsbased geometric modeling approach that supports the interactive sculpting of splinebased virtual material. Our desktop modeling system permits both expert and nonexpert users to interactively deform virtual materials with real properties using force feedback. Using commercially available (and lowcost) haptic devices, modelers can feel the physically realistic presence of virtual spline objects such as Bsplines throughout the design process. Our hapticsbased Bspline is a special case of more powerful dynamic NURBS (DNURBS) models. We develop various haptic sculpting tools to expedite the deformation of Bspline surfaces with haptic feedback and constraints. The most significant contribution of this paper is that point, normal, and curvature constraints can be specified interactively and modified naturally using forces. To achieve the realtime sculpting performance, we devise a novel dual representation for Bspline surfaces in both physical and mathematical space: the physicsbased massspring model is mathematically constrained by the Bspline surface throughout the sculpting session. We envision that the integration of haptics with traditional computeraided design makes it possible to realize all the potential offered by both haptic sculpting and physicsbased modeling in computerintegrated design, vir...
Kinematic Manipulation of Molecular Chains Subject to Rigid Constraints
 In Proceedings of 2nd International Symposium on Molecular Biology
, 1994
"... We present algorithms for kinematic manipulation of molecular chains subject to fixed bond lengths and bond angles. They are useful for calculating conformations of a molecule subject to geometric constraints, such as those derived from twodimensional NMR experiments. Other applications include sea ..."
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Cited by 14 (0 self)
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We present algorithms for kinematic manipulation of molecular chains subject to fixed bond lengths and bond angles. They are useful for calculating conformations of a molecule subject to geometric constraints, such as those derived from twodimensional NMR experiments. Other applications include searching out the full range of conformations available to a molecule such as cyclic configurations. We make use of results from robot kinematics and recently developed algorithms for solving polynomial systems. In particular, we model the molecule as a serial chain using the DenavitHartenberg formulation and reduce these problems to inverse kinematics of a serial chain. We also highlight the relationship between molecular embedding problems and inverse kinematics. As compared to earlier methods, the main advantages of the kinematic formulation are its generality to all molecular chains without any restrictions on the geometry and efficiency in terms of performance. The algorithms give us real...