Plans composed from elements of rectangular grids are considered. A general approach towards the generation and enumeration of nonequivalent plans is presented. It is shown that for these plans there is a minimum colouring which permits easy detection of isomorphs without the need for external storage devices. The notions of threading patterns and colour rules are introduced. Four specific algorithms for different types of plans involving rectangular elements are developed.
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References
1.
BiggsN, 1969“Rectangulations”Proceedings of the Cambridge Philosophical Society65399–408
2.
BlochC J, 1976“On the set and number of minimal gratings for rectangular dissections”Environment and Planning B371–74
3.
BlochC JKrishnamurtiR, 1978“The counting of rectangular dissections”Environment and Planning B5207–214
4.
EarlC F, 1977“A note on the generation of rectangular dissections”Environment and Planning B4241–246
5.
EarlC F, 1978“Joints in two- and three-dimensional rectangular dissections”Environment and Planning B5179–187
6.
GipsJ, 1975Shape Grammars and Their Uses: Artificial Perception, Shape Generation and Computer Generation and Computer Aesthetics (Birkhaüser, Basel)
7.
GropiusWTangeKIshimotoY, 1960Katsura Tradition and Creation in Japanese Architecture (Yale University Press, New Haven, Conn.)
8.
KirbyJ B, 1962From Castle to Teahouse (Charles E Tuttle, Tokyo)
9.
KrishnamurtiRRoeP H O'N, 1979“On the generation and enumeration of tessellation designs” (in preparation)
10.
MorseE S, 1961Japanese Homes and Their Surroundings (Dover, New York); originally published by Ticknor and Company in 1886
11.
ReingoldE MNeivergeltJDeoN, 1977Combinatorial Algorithms: Theory and Practice (Prentice-Hall, Englewood Cliffs, NJ)
12.
StinyG, 1975Pictorial and Formal Aspects of Shape and Shape Grammars: On Computer Generation of Aesthetic Objects (Birkhaüser, Basel)
13.
StinyG, 1977“Ice-ray: A note on the generation of Chinese lattice designs”Environment and Planning B489–98
14.
StinyG, 1979The Grammar of Form (Pion, London) forthcoming
15.
StinyGMitchellW J, 1978a“The Palladian grammar”Environment and Planning B55–18
16.
StinyGMitchellW J, 1978b“Counting Palladian plans”Environment and Planning B5189–198
17.
YoshidaT, 1955The Japanese House and Garden (Praeger, New York)