Introduction to
Computing with
Geometry Adrian Bowyer and John Woodwark
INFORMATION GEOMETERS
First published 1993 Information Geometers Ltd 47 Stockers Avenue Winchester SO22 5LB UK
[email protected]
ISBN 1-874728-03-8
This PDF version is basically the master at 110% enlargement from which the original edition was printed. Necessary changes have been made to pagination, typefaces and gures, and some typographical errors have been corrected.
c
Information Geometers Ltd 1993.
Typeset and designed by the author.
. . . we are geometricians only by chance.
Dr Johnson
Contents
Foreword
5
1.
Introduction
6
2.
Geometric basics
16
3.
Parametric curves and surfaces
31
4.
Bernstein-basis curves and surfaces
51
5.
General implicit curves and surfaces
67
6.
Tessellations
77
7.
Approximations
88
8.
Storing geometry
102
9.
Transforms
116
10.
Intersections
127
11.
Distances and osets
139
12.
Geometric algorithms
13.
Geometric programming
159
References and Bibliography
173
??
Foreword
Information Geometers has run its Computing with Geometry course a number of times in the last few years with the authors as presenters. This book is the material presented on the course. Computing with geometry is a large (and in some places muddy) eld. Here we have tried to cover all of it to a more-