Shape Grammars and their Uses: Artificial Perception, Shape Generation and Computer Aesthetics

257 Pages·1975·8.55 MB·English

by  James Gips (auth.)

Editor 1 Herausgeber:
Praf. Sa/amon Klaczko-Ryndziun, Frankfurt a. M.
Co-Editors 1 Mitherausgeber:
Praf. Ranan Banerji, Temple University, Phi/adelphia
Praf. Jerome A. Feldman, University of Rochester, Rochester
Praf. Mohamed Abdelrahman Mansour, ETH, Zurich
Praf. Ernst Billeter, Universităt Fribourg, Fribourg
Praf. Christof Burckhardt, EPF, Lausanne
Praf. /var Ugi, Technische Universităt Munchen
lnterdisciplinary Systems Research lnterdisziplinăre Systemforschung
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ISR 10
lnterdisciplinary Systems Research
lnterdisziplinăre Systemforschung
JamesGips
Shape Grammars
and their Uses
Artificial Perception, Shape Generation
and Computer Aesthetics
1976 Springer Basel AG
Ali Rights Reserved. No part of this publication may be reproduced. stored in a retrieval
system. ortransmitted. in anyform or by any means. electronic. mechanical. photocopying.
recording or otherwise. without the prior permission of the Copyright owner.
©Springer Basel AG 1975
Originally published by Birkhauser Verlag Basel in 1975
ISBN 978-3-7643-0794-3 ISBN 978-3-0348-5753-6 (eBook)
DOI 10.1007/978-3-0348-5753-6
ACKNOWLEDGMENTS
Important parts of this research were done in collaboration with George Stiny,
a graduale student in System Science at U.C.L.A. In particular, the three formalisms
used (i.e. shape grammars, the formalism for specifying paintings, and the formalism
for specifying aesthetic viewpoints) were developed jointly. Sections 1.1 and
3.1.1.1 - 3.1.1.4 are a revised version of [Stiny and Gips 1972l Portions of
Section 3.2 are expansions of [Gips and Stiny 1973], [Stiny and Gips 1974], and
(Gips and Stiny, in press]. Stiny's research has concentrated on the mathematical
properties of these formalisms, rather than their applications, and will be reported
in his forthcoming dissertation [Stiny, in preparation].
1 would like to thank Professor Jerome Feldman for his lnvaluable help as my
thesis advisor and his consistently good advice throughout my stay at Stanford,
Professors Jeffrey Raskin and Vinton Cerf for serving so conscientiously on my
reading committee, and Professors Thomas Cover, John McCarthy, Roger Shepard,
and Robert Floyd (as well as those previously named) for valuable discussions on
various facets of this research.
Finally, 1 would like to thank my wife, Pat, for her constant support,
understanding, and encouragement.
This research was supported in part by a fellowship from the International
Business Machines Corporation and in part by a student research assistantship at
the Stanford Artificial lntelligence Laboratory under Contract No. SD-183 and
Contract No. DAHC 15-73-C-0435 of the Advanced Research Projects Agency of
the Office of the Secretary of Defense. 1 am most grateful to IBM and to ARPA for
their financial support. The views and conclusions in this document are those of
the author and should not be interpreted as necessarily representing the official
policies, either expressed or implied, of IBM, of ARPA, or of the U.S. government.
This manuscript is a slightly revised version of a dissertation submitted in
March 1974 to the Computer Science Department and the Committee on Graduale
Studies of Stanford University in partial fulfillment of the requirements for the
degree of Doctor of Philosophy.
TABLE OF CONTENTS
lntroduction 1
Section 1 Shape grammars: definitions, examples, related work 3
1.1 Definitions 4
1.2 Restricted shape grammars 6
1.3 Parallel shape grammars 7
1.4 Examples: embedded squares 8
1.5 Example: reversible figure 20
1.6 Examples: mathematical curves 26
1.6.1 Snowflake curve 26
1.6.2 Peano's curve variation 33
1.6.3 Hilbert's curve 37
1.7 Simulation of Turing machines 44
1.8 Related work 48
1.8.1 Array grammars 48
1.8.2 Graph grammars 51
1.8.3 Picture description grammars 54
1.8.4 Grammars with coordinates 57
1.9 A symbolic characterization of shape grammars 60
Table of Contentt (cont.)
Section 2 Analysis of shapes using shape grammars: a program
that performs a three-dimensional perceptual task 63
2.1 The task 65
2.2 Program overview 70
2.3 Preprocessing 71
2.4 Analysis and model building 77
2.5 Comparison of modela 88
2.6 Program results 91
2.7 Limitations and possible extensions 94
Section 3 Generation of shapes using shape grammars:
computer art and aesthetics 97
3.1 Specification of painting using shape grammars 99
3.1.1 Generative specifications 99
3.1.1.1 Shape grammar 10 0
3.1.1.2 Selection rule 106
3.1.1.3 Painting rules 108
3.1.1.4 Limiting shape 110
3.1.1.5 Example: Eve "11 1
3.1.1.6 Example: Yellow Cross 113
3.1.2 Computer implementation 116
3.1.2.1 Interactive definition of shape grammar 118
3.1.2.2 Shape generation 127
Table of Contents (cont.)
3.1.2.3 Display of line drawing 130
3.1.2.4 Transformation of line drawing to image
of the painting 132
3.1.2.5 Display of painting 134
3.1.2.6 The number of memory words used to
represent a generativa specification 137
3.1.2.7 Example: Urform 139
3.1.2.8 Example: Star 142
3.1.2.9 Example: Aleatory 145
3.2 Aesthetics 148
3.2.1 Original motivation 148
3.2.2 General observations on aesthetics 149
3.2.3 Aesthetic systems 154
3.2.3.1 Aesthetic systems: interpretation
and reference 155
3.2.3.2 Aesthetic systems: evaluation
and ordering 163
3.2.4 Aesthetic systems and information theory 166
3.2.5 An aesthetic system for paintings definable by
generativa specifications 169
3.2.6 Computer implementation 172
3.2.7 Example: Anamorphism 1 - VI 178
3.2.8 Comments 187