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Controlling Rigid Bodies with Dynamic Constraints

IP.com Disclosure Number: IPCOM000127962D
Original Publication Date: 1988-Dec-31
Included in the Prior Art Database: 2005-Sep-14

Publishing Venue

Software Patent Institute

Related People

R.onen Barzel: AUTHOR [+3]

Abstract

Mod- eling Computer graphics "picture making" can be divided into two pants: modeling and rendering (see Fig. 1.1). To create an image, we first create a model, a mathe-matical representation of the object or objects being imaged. The model must include all aspects of the objects that we wish to have affect the final image. Once we have created the model, we render its image; typically, by computing the interaction of light with the elements of the model, and projecting the results onto a two-dimensional "film." The computer graphics modeling technique most commonly used today, which we shall refer to as the "traditional" technique, is purely spatial -- the mod-els represent the shapes and positions of objects. The traditional model consists of a collection of objects, with a description of the position and orientation of each object, as well as parameters describing the shape of each object (see Fig. 1.2). For animations, the models are parametrized by time. Thin traditional approach to modeling is power-ful and easy to use. Unfortunately, as models be-come complex, traditional modeling becomes overly cumbersome---specifying each detail by hand is te-dious at best, and if complex relationships between objects are to be maintained as objects animate, specifying the details by hand becomes virtually im-possible. Furthermore, if we wish traditional models to exhibit physically realistic behavior, it is up to the human modeler/animator to create this behavior by hand. The traditional modeling & animation tools ignore physical realism, tending to impart "puppet-like" behavior to models. This thesis presents a modeling technique, called "Dynamic Constraints," that alleviates some of the problems of the traditional modeling technique. "Dy-namic Constraints" is based on four principles: * Generality: A model is built from a collection Computer Graphics: Modeling: , Rendering: Create a model- Create an image a mathematical of the model representation

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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.

Controlling Rigid Bodies with Dynamic Constraints

R.onen Barzel California Institute of Technology Pasadena, CA 91125

November 16, 1988

Caltech-CS-T R- 88-19

Acknowledgement s

My advisor, Al Barr, had the seminal idea for constraint-based control of dynamic rigid bodies; we have worked jointly in developing the "Dynamic Constraints" technique, and the inverse dynamics method it is based on. Some people who additionally deserve mention: Jed Lengyel, for being a "guinea pig" user of the modeling system, and for putting together the video system that was used in making animations; John Snyder, for the rendering.of the animations; John Platt, for discussions and for numerical software; and Brian Von Herzen, for the motivation and modeling for the space-station self-assembly animations. Supporters of the graphics lab, who made available equipment that was used in this work: Ampex, a VPR-3 video tape recorder; Hewlett-Packard, several HP9000 machines that were used for rendering; Schlumberger Palo Alto Research Center and Symbolics, Inc., Symbolics Lisp Machines that were used to implement the Dynamic Constraints technique. Finally, I have been personally supported, initially by Caltech, and now by the AT&T Foundation, as the recipient of an AT&T Bell Laboratories Ph.D. Scholarship.

INDEX OF FIGURES

List of Symbols

Conventions: 9 A Super-arrow indicates a vector; e.g. Boldface indicates a matrix; e.g. I . The superscript a is used as a a label for a body; e.g. F' is the net force on the ith body. If only one body is being discussed, the superscript is sometimes left off. ~ The subscripts j and k are typically used as labels for a constraint; e.g. Dt is the devia-tion function for kth constraint. If only one constraint is being discussed, the subscript is sometimes left off.

9 The subscript body indicates a quantity that is represented in the body coordinate system of a body; e.g. Iboag.

Other subscrIpts are part of the "name" of an object, e.g. F, the net force on a body, vs. FN, the net non-constraint force on a body. Calligraphic font is used for single quantities that contain values for the entire model; e.g. .r is the collection of forces acting on bodies in the model. Greek symbols: The part of D'ka~(y,.7~ ,T,t) independent of force and torque; a dk-component vector. [Fig. 3.6] Qk with the subscript dropped, when there is only one constraint. (Eqn. 3.61 ri k A matrix that acts on the net force on body i, yielding a contribution to Dk21(y,.F,T,t). (Fig.

California Institute of Technology Page 1 Dec 31, 1988

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Controlling Rigid Bodies with Dynamic Constraints

3.61 ri with the subscript dropped, when there is only one constraint. (Eqn. 3.6] r' with the superscript i dropped, for a model with only a single body. A matrix that acts on the net torque on body i, yielding a contribution to D,(2) (y,.F,T,t). (Fig. 3.61 A` Ay with the subscript dropped, when there is...