This book is concerned with aspects of boundary representation (B-rep) solid

modelling, describes several algorithms illustrating both general principles of

modelling algorithms and their versatility and outlines the general principles

behind the development of such algorithms and the extensions for handling in-

formation in models. It goes on to describe feature modelling, graphics, model

input and output, and applications. It represents a collection of work partly

by the author but also by many other people whose results are described.

The purpose of the book is not to give a general introduction to solid mod-

elling. A variety of techniques are available and to go into detail about each

one would require much more space than is reasonable. This book attempts

to cover basic techniques for one branch. It is not intended to be a review of

commercial systems nor to describe any one system. The aim is to describe

the techniques behind different systems.

The first two chapters describe the background to solid and product mod-

elling and what has already been done. Chapter 1 gives a brief outline of

computer modelling, and chapter 2 describes in more detail the background

to B-rep modelling specifically, because this forms the basis for the book.

Chapter 3 describes an idealised, or recommended B-rep modelling en-

vironment, the basic operations or tools that provide a basis for the work

described in the book. This idealised representation can be implemented in

several ways, so the chapter first describes the various options and the basic

datastructures available when designing a modelling system. Datastructure

definitions of the B-rep entities are described in Appendix A. The chapter

goes on to identify and describe various basic tools, i.e. elementary modelling

operations, which provide a uniform functional shell surrounding any particu-

lar implementation. Chapter 4 also describes basic tools, the Euler operators,

and the theory behind decomposition of modelling operations into sequences

of Euler operators. Chapter 5 describes variations on the basic datastructure,

the non-manifold, degenerate, and partial object representations.

Chapter 6 describes several modelling algorithms for manipulating B-

rep models, including modelling with degenerate models. These algorithms

demonstrate the versatility of the B-rep technique. The algorithms are not

a complete set, because one characteristic of B-rep systems is that they can

be adapted to provide a diversity of tools suitable for different users and ap-

viiviii Preface

plication environments. Instead the algorithms are intended to represent a

broad selection of algorithms to illustrate B-rep modelling and the principles

of stepwise construction. Chapter 7 outlines some general principles for de-

veloping modelling algorithms and demonstrates the use of these principles

with two detailed examples.

Chapter 8 describes some techniques for creating and maintaining infor-

mation and auxiliary structures with B-rep models. These extra facilities are

necessary to extend the model so that it can be used for a more complete

communication in a distributed application environment.

Chapter 9 discusses some aspects of features which are an extension to

the basic representation domain to include sets of model elements with some

meaning. There are two basic approaches: feature recognition to recover

feature information from a model and ”design by/with features” to include

feature information directly. These approaches are briefly discussed as well as

some other aspects, such as feature verification and feature datastructures.

Chapter 10 describes some basic graphics techniques for presenting mod-

els. Chapter 11 describes disc formats and disc transfer of models. Chapter

12 describes command interpreter techniques. Chapter 13 describes some

techniques for introducing free-form geometry into the model and chapter 14

describes, sketchily, some application areas. Chapter 15 describes the me-

dial axis transform calculation for volumetric reasoning applications. Finally,

chapter 16 describes some miscellaneous aspects of modelling: tolerances and

debugging.