# 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.