Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In ACM SIGGraph, Computer Graphics, volume 24:2, pages 11--21. ACM SIGgraph, March 1990.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....They extended this approach to complex kinematic constraints such as closed loops[12] Barzel and Barr[6] presented a dynamics approach which allows the automatic assembly of articulated structures. Witkin et al. enhanced interactivity by creating and deleting objects and constraints on the fly[20]. Baraff presented a method solving the inequality and complementarity constraints of the Coulomb friction model[4] Gleicher developed a general constraint based approach for interactive scene modeling and animation[10] Baraff presented a fast algorithm for acyclic structures along with an ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In Rich Riesenfeld and Carlo Sequin, editors, Computer Graphics (1990.

....that the constraints be solved analytically at model building time. While this formulation is very ecient, it requires an analytical solution of the constraints to exist. It also precludes modi cation of the constraint structure at run time. Our model instead follows the virtual work formulation [21]. In a virtual work formulation, all the links in a model have full range of unconstrained motion. Hard kinematic constraints on the system are be represented as a special set of forces C: q = W (Q C) 1) These constraints are functions of the systems state, and may also be time varying: C ....

....simulation is required to realize a working system. This sort of system is also computationally rather costly: the system described above consumes nearly 100 of a 500MHz Alpha 21164 processor. The above system can be easily converted to an energybased kinematics engine as describe by Witkin [21], by dropping the integration over acceleration. Here are the update equations for the dynamic case using the synchronous Euler method: q t = W Q q t = q t 1 t q t 1 q t = q t 1 t q t 1 and here are the modi ed equations for the kinematic case: q t = W Q q t = t ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In ACM SIGGraph, Computer Graphics, volume 24:2, pages 11-21. ACM SIGgraph, March 1990.

....In [60] it is shown that using Lagrangian dynamics, the resulting equations of motion are R = Q(t)M Gamma1 (2.7) where M is a constant square matrix that can be precomputed. Q is the generalized force matrix. A method for implementing attachment constraints (point to point) is described in [58] and used in [60] A constraint force is calculated which cancels the applied force acting to separate attached parts. Using the previous linear formulation the constraint matrix is constant (except when constraints are added or deleted) thus its inverse can be precalculated for efficiency. Our ....

....The system implements inequality and conditional constraints, while introducing additional optimizations of the algorithm for efficiency. Constraint methods have animated plastic, elastic, moldable materials [35] a simple figure [59] and a simple arm that throws a ball in a basket [8] In [58, 60], flexible models are addressed. Using linear global deformations a compact representation for flexible models is formulated. The formulation supports constrained dynamics in a fashion similar to that used for rigid bodies. CHAPTER 3. CONTROL 27 OPEN LOOP CONTROL Controller System X Y C ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--22, March 1990.

....system mass matrix. The mass matrix describes the distribution of mass in the system. 4.2.1 Hard Constraints Hard constraints represent absolute limitations imposed on the system. One example is the kinematic constraint of a skeletal joint. The model follows the virtual work formulation of Witkin[51]. The Witkin formulation has several advantages over reduced dimensionality solutions such as that described by Featherstone[17] the constraints can be modified at runtime, and the modularity inherent in the mathematics drastically simplifies the implementation. The one significant disadvantage, ....

....space of some object. Implementing constraints to understand each type of object, possibly having different internal representations for state, would make the constraints unnecessarily complex. Witkin suggests inserting an abstraction layer between objects and constraints, called connectors[51]. Thus c for a constraint between two objects becomes: c(x) f(a(x 1 ) b(x 2 ) 4.16) The constraint Jacobian can then be decomposed by the chain rule: #c #x = #c #a #a #x 1 #c #b #b #x 2 (4.17) 52 x,x x,x x,x x,x x,x x,x,W x,x,W da dx da dx a a Connector da dx da ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In ACM SIGGraph, Computer Graphics, volume 24:2, pages 11--21. ACM SIGgraph, March 1990.

....the problem easier to solve. Snyder[13] addresses geometry awareness but not for articulated objects. The work investigated the generation of stable non interpenetrating configurations of curved surface objects. Interactive dynamics simulation may also be used as a basis for object manipulation[6, 15]. Interactive dynamics simulation can provide fairly physically accurate results, accounting for friction and inertia in addition to geometry awareness. As good haptic feedback interfaces are developed, advanced interactive dynamic approaches should prove quite attractive. The reason for our ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In Symposium on Interactive 3D Graphics, pages 11--21, March1990.

....the inverse of the system mass matrix. The mass matrix describes the distribution of mass in the system. Hard Constraints Hard constraints represent absolute limitations imposed on the system. One example of a kinematic constraint is a skeletal joint. Our model follows the virtual work formulation [23]. In a virtual work formulation, all the links in a model have full range of unconstrained motion. Hard kinematic constraints on the system are enforced by a special set of forces c: q = W (Q c(q; t) 2.2) The formulas governing these constraints can be modified at run time. Figure 2.2: ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In ACM SIGGraph, Computer Graphics, volume 24:2, pages 11--21. ACM SIGgraph, March 1990.

....and guided agent (i.e. graphic images slaved to other human participants) it also tightly couples among human participants and the force feedback devices. It contributes to realistic portrayal of autonomous movements of all virtual objects in the synthetic environments. Most dynamic simulators [4, 7, 25, 88, 89] make simplification of models in simulating the physics of translating and rotating objects, and mostly on frictionless impacts. Recently, Keller applied Routh s frictional impact equations [75] to a few simplified cases with numerous assumptions [49] Wang and Mason also characterize frictional ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--22, March 1990.

....the system mass matrix. The mass matrix describes the distribution of mass in the system. 4.1 Hard Constraints Hard constraints represent absolute limitations imposed on the system. One example of a kinematic constraint is a skeletal joint. Our model instead follows the virtual work formulation [21]. In a virtual work formulation, all the links in a model have full range of unconstrained motion. Hard kinematic constraints on the system enforced by a special set of forces c: q = W Delta (Q c(q; t) 4) The formulas governing these constraints can be modified at run time. It is essential ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In ACM SIGGraph, Computer Graphics, volume 24:2, pages 11--21. ACM SIGgraph, March 1990.

....have studied impact dynamics for robotic applications; their approach is based on Routh s, but deals only with the two dimensional case [17] Finally, a number of researchers have investigated several problems and paradigms for dynamic simulation and physical based modeling. We refer the reader to [5, 18, 19]. 2 Constraint based versus impulse based simulation One of the most difficult aspects of dynamic simulation is dealing with the interactions between bodies in contact. Most of the work which has been done in this area falls into the category of constraint based methods [5, 18, 6, 4] An example ....

....the reader to [5, 18, 19] 2 Constraint based versus impulse based simulation One of the most difficult aspects of dynamic simulation is dealing with the interactions between bodies in contact. Most of the work which has been done in this area falls into the category of constraint based methods [5, 18, 6, 4]. An example will illustrate the approach. Consider a ball rolling along a table top. The normal force which the table exerts on the ball is a constraint force that does not do work on the ball, but only enforces a non penetration constraint. In a constraintbased system, this force is not modeled ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--22, March 1990.

....and constraint based interfaces that led to the development of direct manipulation style interfaces are other examples of this general approach. They too derive from Sutherland and continue to inspire developments. Recent examples include the work of Borning and his students [5] 6] Witkin [18] [34] in particular has taken a physics as interface approach to construction of dynamic interactive interfaces. Smith s Alternate Reality Kit [29] 30] and languages such as Self [33] are also examples of following a physics based strategy for interface design. These systems make use of techniques ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive Dynamics, Computer Graphics, 1990, 24(2), 11-21.

....collision resolution may be extended to constrained systems. We also discuss some important open problems related to developing an efficient simulator that uses both contact interaction paradigms. 1 Introduction Many simulators for simple physical systems employ constraint based approaches [1, 3, 5, 15]. Constraints are used to describe the interactions between objects, which often occur only through physical contact. A large variety of contact interactions can be modeled efficiently and accurately by hard constraints, however the method is not well suited to situations like the one depicted in ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--22, March 1990.

....force expression for a single particle subject to a single scalar constraint. Our goal in this section is to extend this special case to the general one of a whole system of particles, collectively subjected to a number of constraints. The derivation follows the more detailed one presented in [5]. The key to making this a managable task is to adopt a uniform, monolithic view, much as we do in solving ODEs. Rather than considering each particle separately, we lump their positions into a single state vector, which we will call q. Unlike the phase space vector that we hand to the solver, ....

....with damping, to a valid state should drift occur. The final constraint force equation, with feedback, is JWJ T # = J q JWQ k s C k d C. 11) The values assigned to k s and k d are not critical, since this term only plays the relatively undemanding role of absorbing drift. See [1, 3, 5] for further discussion. SIGGRAPH 98 COURSE NOTES F6 PHYSICALLY BASED MODELING 4 Tinkertoys: Implementing Constrained Particle Dynamics The general formula of equation 11 is just a skeleton. To actually simulate anything, a specific constraint function C(q) must be provided, in a form that ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24,

....this simplification is that the body s mass matrix is constant, allowing it to be pre inverted. Attachment constraints. Point to point attachment constraints are used to build complex models from the simple non rigid pieces. Attachment constraints are implemented using a method fully described in [19], and related to those in [4] and [11] The idea is to calculate a constraint force that accurately counters applied forces that would otherwise pull the pieces apart. Ordinarily, obtaining the constraint force requires the solution of a linear system at least once per time step. The linearity ....

....modes, the dimensionality and stiffness of the models are both drastically reduced. The models we develop here yield similar advantages, though we arrive there by a very different route. The use of constraint methods for model creation and motion control has been extensively treated. [3, 18, 7, 9, 4, 12, 11, 20, 19, 13] A number of these entail the use of inverse dynamics to calculate constraint forces. The formulation employed here, which is based on the method of Lagrange multipliers, is described fully in [19] and is also closely related to that presented in [11] 2 Linear Deformations 2.1 The mechanics of ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--22, March 1990.

....is expanding with the availability of computational performance to realize them. For example, the availability of this performance not only facilitates techniques for physically based animation, such as [1, 22] but also causes them to evolve toward techniques for interaction simulation, such as[25, 33]. It also makes such physical simulation viable as an interactive modeling tool, as [2, 21] Related to the methods of physical simulation are those of constrained optimization. Performing these computations at interactive rates permits using these techniques for interaction and animation ....

....these variables. A related technique is to partition the constraint problem into several smaller problems, which is examined extensively by [26] 5 IMPLEMENTATION Our efforts to build general purpose Snap Together Mathematics tools began with our original efforts to construct interactive systems[33]. Our early implementations are discussed in [12] Experience using these tools has caused them to evolve into what has been described here. Our present toolkit, written in C , implements sparse vector passing, scatter and gather variable collections, and a simple timestamping scheme for cache ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--21, March 1990. Proceedings 1990 Symposium on Interactive 3D Graphics.

....If the animator does not like the resulting motion, she must adjust the desired body configurations and start again. We argue that interactivity is essential when aesthetics is a primary concern. Our interactive technique is related to the method for geometric modeling described by Witkin et al. [28]. Similar techniques have also been devised for drawing applications [13] interactive camera control [14] and others. In its treatment of motion discontinuities, our approach most closely resembles that of Harada et al. 17] which combines continuous and discrete optimization for applications in ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive Dynamics. In Proceedings of the 1990 symposium on Interactive 3D graphics, pages 11--21, March 1990.

....force expression for a single particle subject to a single scalar constraint. Our goal in this section is to extend this special case to the general one of a whole system of particles, collectively subjected to a number of constraints. The derivation follows the more detailed one presented in [5]. The key to making this a managable task is to adopt a uniform, monolithic view, much as we do in solving ODEs. Rather than considering each particle separately, we lump their positions into a single state vector, which we will call q. Unlike the phase space vector that we hand to the solver, ....

....with damping, to a valid state should drift occur. The final constraint force equation, with feedback, is JWJ T # = J q JWQ k s C k d C. 11) The values assigned to k s and k d are not critical, since this term only plays the relatively undemanding role of absorbing drift. See [1, 3, 5] for further discussion. SIGGRAPH 97 COURSE NOTES F6 PHYSICALLY BASED MODELING 4 Tinkertoys: Implementing Constrained Particle Dynamics The general formula of equation 11 is just a skeleton. To actually simulate anything, a specific constraint function C(q) must be provided, in a form that ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24, 1990. Proc. 1990 Symposium on 3-D Interactive Graphics.

....this simplification is that the body s mass matrix is constant, allowing it to be pre inverted. Attachment constraints. Point to point attachment constraints are used to build complex models from the simple non rigid pieces. Attachment constraints are implemented using a method fully described in [19], and related to those in [4] and [11] The idea is to calculate a constraint force that accurately counters applied forces that would otherwise pull the pieces apart. Ordinarily, obtaining the constraint force requires the solution of a linear system at least once per time step. The linearity ....

....modes, the dimensionality and stiffness of the models are both drastically reduced. The models we develop here yield similar advantages, though we arrive there by a very different route. The use of constraint methods for model creation and motion control has been extensively treated. [3, 18, 7, 9, 4, 12, 11, 20, 19, 13] A number of these entail the use of inverse dynamics to calculate constraint forces. The formulation employed here, which is based on the method of Lagrange multipliers, is described fully in [19] and is also closely related to that presented in [11] 2 Linear Deformations 2.1 The mechanics of ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--22, March 1990.

....a derivative. All that is required is a method for rapidly displaying the relevant output and receiving the user s desire for the direction of change in that output. We have experimented with an application that connects the outputs of mathematical functions, such as an economic model, to sliders [WGW90, GW91]. 2.3 Implementing Differential Manipulation Implementing differential manipulationinvolves integrating the differential equations of motion in time and periodically displaying the results to the user. These equations are most conveniently expressed in terms of the inverse of the mass matrix, ....

....which may surprise the user. The user can help guide the solution away from incorrect solutions and past places where the solving process gets stuck. 3. 1 Techniques for Constrained Dynamics The techniques for implementing constrained dynamics in physical simulations have been presented elsewhere [WGW90, GW91, Pla89]. The presentation here follows that of [WGW90] except with an emphasis on first order physics and the demands of differential manipulation. We consider here equality constraints, which can be written as f (q) 0; noting that the techniques extend to inequalities. A simple way to implement ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--21, March 1990. Proceedings 1990 Symposium on Interactive 3d Graphics.

....In animation, constraints are popular for holding models together as they move. This is often done by simulating the behavior of physical models [WW90, IC87, Pla89, BB88] The advent of high performance graphics workstations have created an interest in developing interactive simulation techniques[WGW90, SZ90, GW91b] and applying the techniques to domains other than physical objects[GW91a] such as drawings. 3.2. Differential Constraints Because our techniques provide us with a model that initially meets the constraints, the problem of manipulation becomes the differential problem of ....

....the geometric entities as physical objects and the constraints as mechanical connections[GW91a] The continuous motion of a constrained geometric model during dragging is described, as mechanical systems are, by a constrained differential equation. The method of Lagrange Multipliers[Gol80, Pla89, WGW90] provides a technique for converting this to an unconstrained differential equation by solving a linear system, even if the constraints are nonlinear. There are many good techniques for solving the resulting ordinary differential equations[PFTV86] The Lagrange Multiplier technique is well ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--21, March 1990. Proceedings 1990 Symposiumon Interactive 3D raphics.

.... differential methods we use to constrain the motion of particles and surfaces are rooted in classical mechanics (see, e.g. 15] for a discussion of mechanical constraints and constraint forces) and are closely related to constraint methods used in physically based modeling for computer graphics [5,2,3,32,31,4]. Allied methods have also been used for interactive geometric modeling [30,14] 3 The Particle Surface Constraint In this section we derive the basic machinery that allows us to attach moving particles to moving surfaces. First we derive a basic constraint on particle and surface velocities that ....

.... using an arbitrary symmetric positive definite metric tensor, e.g. q Q) T M( q Q) In particular, it is possible to automatically compute a sensitivity matrix, analogous to the mass matrix in mechanics, that compensates for scale differences among the components of Fq (see [31]. The classical method of Lagrange multipliers [13] solves constrained optimization problems by adding to the gradient of the objective a linear combination of constraint gradients, with unknown coefficients. One then solves simultaneously for the original unknowns, and for the coefficients. In ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--21, March 1990. Proc. 1990 Symposium on 3-D Interactive Graphics.

....methods are employed for general object placement and control. The use of these methods for camera placement in animation is described in [30] The differential control methods employed in this paper are formally more closely allied to the methods of constrained dynamic simulationdescribed in [29, 2, 19, 31, 23] than to the positional optimization methods cited above. Some of the issues involved in adapting these methods to differential kinematic control are addressed in [13] while [27] considers their application to the design of free form surfaces, and [12] illustrates their use in a constraint based ....

.... possible to solve for without obtaining the explicit inverse for M by forming a larger linear system (see [8] Under this general linear quadratic formulation, the camera s response to controls can be decoupled from the parameterization, for instance by letting M be a mass matrix for the camera[13, 29, 31]. 3.4 Multiple Points and Other Functions Controlling more than one point involves a simple extension to the foregoing derivation. The matrix J depends on x, so each point being controlled yields a distinct version of equation 5. We combine the m equations into a single one by concatenating the ....

[Article contains additional citation context not shown here]

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--21, March 1990. Proceedings 1990 Symposium on Interactive 3D Graphics.

....and tracking [14] Snakes are essentially simulated springy wires that are attracted to edge features in images, and simultaneously subjected to manipulation forces imposed by the user. The use of constrained dynamics simulations for interactive geometric modeling was described by Witkin et al. [32]. Flexiblesurface simulations for interactive computer vision and free form surface modeling are areas that have also been extensively investigated [29, 28, 30, 5, 31, 33] Constrained dynamics simulations have also been used to support drawing applications [11] and for interactive camera control ....

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. Computer Graphics, 24(2):11--21, March 1990. Proc. 1990 Symposium on 3-D Interactive Graphics.

No context found.

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In ACM SIGGraph, Computer Graphics, volume 24:2, pages 11--21. ACM SIGgraph, March 1990.

No context found.

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In Symposium on Interactive 3D Graphics, pages 11--21, March 1990.

No context found.

Andrew Witkin, Michael Gleicher, and William Welch. Interactive dynamics. In Symposium on Interactive 3D Graphics, pages 11--21, March 1990.

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC