Physically-Based Modeling for Computer Graphics: A Structured Approach

Ronen Barzel
California Institute of Technology

San Diego: Academic Press, 1992.
ISBN 0-12-079880-8

Based on:

Barzel, Ronen, Physically-Based Modeling for Computer Graphics: A Structured Approach. Ph.D. thesis, Computer Science Department, California Institute of Technology, 1992.

Abstract

This thesis presents a framework for the design of physically-based computer graphics models. The framework includes a paradigm for the structure of physically-based models, techniques for ``structured'' mathematical modeling, and a specification of a computer program structure in which to implement the models. The framework is based on known principles and methodologies of structured programming and mathematical modeling. Because the framework emphasizes the structure and organization of models, we refer to it as ``Structured Modeling.''

The Structured Modeling framework focuses on clarity and ``correctness'' of models, emphasizing explicit statement of assumptions, goals, and techniques. In particular, we partition physically-based models, separating them into conceptual and mathematical models, and posed problems. We control complexity of models by designing in a modular manner, piecing models together from smaller components.

The framework places a particular emphasis on defining a complete formal statement of a model's mathematical equations, before attempting to simulate the model. To manage the complexity of these equations, we define a collection of mathematical constructs, notation, and terminology, that allow mathematical models to be created in a structured and modular manner.

We construct a computer programming environment that directly supports the implementation of models designed using the above techniques. The environment is geared to a tool-oriented approach, in which models are built from an extensible collection of software objects, that correspond to elements and tasks of a ``blackboard'' design of models.

A substantial portion of this thesis is devoted to developing a library of physically-based model ``modules,'' including rigid-body kinematics, rigid-body dynamics, and dynamic constraints, all built with the Structured Modeling framework. These modules are intended to serve both as examples of the framework, and as potentially useful tools for the computer graphics community. Each module includes statements of goals and assumptions, explicit mathematical models and problem statements, and descriptions of software objects that support them. We illustrate the use of the library to build some sample models, and include discussion of various possible additions and extensions to the library.

Structured Modeling is an experiment in modeling: an exploration of designing via strict adherence to a dogma of structure, modularity, and mathematical formality. It does not stress issues such as particular numerical simulation techniques or efficiency of computer execution time or memory usage, all of which are important practical considerations in modeling. However, at least so far as the work carried on in this thesis, Structured Modeling has proven to be a useful aid in the design and understanding of complex physically-based models.