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1
Getting Computers to Read The Architectural Semantics of
Drawings
John S. Gero and Han J. Jun
Key Centre of Design Computing
Department of Architectural and Design Science
University of Sydney
Sydney NSW 2006 Australia
email: {john, han}@arch.su.edu.au
Abstract. This paper presents an approach to the reading of the architectural semantics of drawings.
Topological constraints on objects are used to represent various types of groups where the groups produce
repeating patterns. A process model of visual rhythm discovery is developed. Discovery of visual rhythms in
an architectural facade is demonstrated.
1. Introduction
Drawn shapes play a critical role in various design domains and particularly in architectural
design not only in representing a design concept but also in allowing the designer to reinterpret
them to develop new ideas. In the conceptual and creative aspects of designing this
reinterpretation of what has been drawn appears to play an important role. Working in a visual
medium - drawing - the designer sees what is there, draws in relation to it, and interprets what
has been drawn, thereby informing further designing. In all this seeing, the designer not only
visually registers information but also constructs and discovers visual patterns in it [Schön and
Wiggins, 1992].
From seeing what was intended to be drawn, intentional and/or unintentional patterns of shapes
are identified. The patterns can be grouped into dominant themes or formative ideas which can
conceivably be used in the generation of designs. A formative idea is understood to be a
concept which a designer uses to influence or give form to a design. Formative ideas from
shapes are considered as shape semantics. Emergent shape semantics in architectural design
from plans and/or facades include visual symmetry, visual rhythm, visual movement and visual
balance.
Shape semantics play an important role in organising decisions, providing order, and
generating a final form in visually-oriented design. They appear to have a special role in
architectural design in particular. Architecture reflects its main design concept through the
structure of visual organization. Visual organization can be treated as the visual semantics of
the design and is perceivable by designers. However, current computer-aided drawing,
computer-aided drafting and computer-aided design systems prevent the discovery and use of
visual shape semantics because most computer-aided design systems treat shapes as sets of
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ACADIA'95
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primitives, such as line segments and their endpoints [Mitchell et al, 1987]. Inadvertently such
systems have enforced fixation so that it is not surprising that they are not used in the early
stages of architectural design. This is one obstacle in using computers to provide significant
assistance to human creativity. Symbolic models related to shapes and, to a lesser extent, to
shape emergence have been studied [Stiny, 1994]. However there has been very little work on
emergence of shape semantics at a symbolic level or on the development of a computational
process model of it. Thus, the major aim of this paper is to describe a computational model for
the emergence of shape semantics and to discuss their potential to improve the capability of
CAAD systems to support a designer's creativity at the conceptual design stage in architectural
design.
2. Shape Semantics in Architecture
2.1. Definitions
Shape semantics provide ways to interpret shapes. A primary shape semantic is a visual pattern
of relationships of shapes which is represented explicitly and intentionally. An emergent shape
semantic is a visual pattern of shapes that exists only implicitly in the relationships of shapes,
and that was not explicitly input and was not represented at input time. Many such patterns
have predefined labels. Figure 1 shows a plan from which examples of primary shapes,
primary shape semantics and emergent semantics can be inferred. Shape semantics emergence
is the process of recognizing both emergent and primary shape semantics from primary and /or
emergent shapes.
Figure 1: The plan of the Indian Institute of Management of Ahmedabad in India from which
many architectural semantics can be discovered (Louis I. Kahn, 1963- ) (from Giurgola, R.
and Mehta, J. (1975), Louis I. Kahn, A.D.A. EDITA Tokyo, Tokyo, p.77)
2.2. Visual Rhythm
There is a vast array of possible architectural shape semantics which could be emerged. Four
types of shape semantics of architectural design are of interest through interpretations of the
visual patterns from plans and facades as shown in Figure 2: visual symmetry, visual rhythm,
visual movement and visual balance. The representation of visual symmetry and a process
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model to discover it have been developed [Gero and Jun, 1994]. In this paper we will describe
the representation of visual rhythm and a process model for its discovery. The term 'rhythm'
has been used widely. Nature around us is throbbing with complex rhythms and these rhythms
serve the purpose of life [Gombrich, 1984]. Even though rhythm reminds most of people of
its musical sense, there is no concrete definition of rhythm itself in music because of the
complexity of relations with other elements [Cooper and Weyer, 1960; Porter, 1986]. The
concept of rhythm in architecture, sculpture and painting has played an important role in
accomplishing and judging designers' works. The principle of composition in the works of the
great masters has been investigated at a mathematical level [Richter, 1932]. Other research into
rhythm has been in the area of psychology. The laws of perceptual grouping in Gestalt
psychology could be used to explain visual rhythm as visual phenomena [Arnheim, 1966;
Palmer, 1983]. Some principles in the laws of perception can be applied to architectural design
[Meiss, 1986].
(a)
(d)
(c)
(b)
Figure 2: Emergence of architectural semantics from plans: (a) reflective symmetry:
Montmorency (Claude-Nicolas Ledoux) (from Mitchell, W., Liggett, R. and Kvan, T. (1987)
The Art of Computer Graphics Programming, Van Nostrand Reinhold , New York, p.443); (b)
visual rhythm: Master Plan & Headquarters Office Development for the Langley Court Site
(Richard Rogers, 1986) (from Anonymous (1988) Richard Rogers, Yoshio Yoshida, Tokyo.);
(c) visual movement: Holy Trinity Ukrainian Church (Radoslav Zuk, 1977) (from Clark, R. H.
and Pause, M. (1985) Precedents in Architecture, Van Nostrand Reinhold, New York, p.207);
(d) visual balance: Annex to Oita Medical Hall (Arata Isozaki, 1970-1972) (from Clark, R. H.
and Pause, M. (1985) Precedents in Architecture, Van Nostrand Reinhold, New York, p.180)
However, there appears to be no adequate representation of visual rhythm at a symbolic level.
Therefore, in this paper we present two contributions which assist in the discovery of visual
rhythm. The first is concerned with a representation of visual rhythm at the symbolic level.
The second is concerned with a process model of visual rhythm discovery.
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We define visual rhythm as the perception of patterns of relationships of equivalent objects or
groups of objects such that the patterns contain repetition along one or more axes. Emergence
of visual rhythm in architectural designs may be discovered when repetitions of visual patterns
of shapes exist.
3. Representation
3.1 Introduction
The general representation of forms constructed of objects is [Gero and Jun, 1994]
F = {No; constraints}
where No is the number of objects constituting form F and the constraints, which constrain
behaviours or properties resulting from the objects, based upon which particular forms are
defined.
When the constraints on forms are constraints on visual rhythm, visual rhythm exists.
Therefore the symbolic representation of visual rhythm R is
R = {No; constraints}.
Objects are treated as units of visual rhythm. When the units are grouped into identical
patterns, the pattern is regarded as the unit in visual rhythm.
The group G is represented by the number of objects (n) and constraints on units.
G = n(constraints on units).
Therefore, the representation of visual rhythm becomes
R = ng (constraints on groups)
where ng is the number of groups which produce the repeating patterns. For generality a group
may contain a single line segment, a single enclosed shape, a group of line segments or a group
of enclosed shapes.
3.2 Constraints
Eight symbols, , , Æ, , ª, , and , for representing topological constraints on objects
in visual rhythm are introduced. These define the topological constraints on objects.
O2 is right of O1 and τ(O2) = O1 => O1 O2.
O1 is left of O2 and τ(O1) = O2 => O1 O2.
O1 is below O2 and τ(O1) = O2 => O1 Æ O2.
O1 is above O2 and τ(O1) = O2 => O1 O2.
O2 is below right of O1 and τ(O2) = O1 => O1 ª O2.
O1 is below left of O2 and τ(O1) = O2 => O1 O2.
O2 is above right of O1 and τ(O2) = O1 => O1 O2.
O1 is above left of O2 and τ(O1) = O2 => O1 O2.
Where Oi denotes objects and τ(Oi) = Oj means Oi is translated into Oj.
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For example, R = ng{G()} represents identical groups, G, translated from left to right. The
group may contain various types of objects or groups of objects such as: a single segment,
denoted by L; a group of line segments, denoted Lg; a single enclosed shape, S; or a group of
enclosed shapes, Sg. When a group is a group of enclosed shapes, the same symbols are used
for topological constraints on shapes. For example,
G = (, )
=> S1 S2 S3
=> τ1(S1) = S2 and S1 is left of S2 ∧ τ2(S2) = S3 and S2 is above left of S3
Various types of visual rhythm as repeating units of a group of line segments are shown in
Figure 3. Representation of each type of visual rhythm shown in Figure 3 is as follows:
Figure 3(a):
Group of units: G = (Lg1),
Representation of visual rhythm: R = 4[17{G()} ],
where Lg1 = ;
Figure 3(b):
Group of units: G = (Lg2),
Representation of visual rhythm: R = 3[4{G()} ],
where Lg2 = ;
Figure 3(c):
Group of units: G = (Lg3),
Representation of visual rhythm: R = 3[Ci, 14{G()}, Ct ],
where Lg3 = , Ci denotes initial condition ( ) and Ct is terminal condition ( );
Figure 3(d):
Group of units: G = (Lg4),
Representation of visual rhythm: R = n[3{G()} ],
where Lg4 = .
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(a)
(b)
(c)
(d)
Figure 3: Examples of various types of visual rhythm as repeating groups of line segments in
the Filigree Warehouse elevation (from Blaser W. (1980). Filigree Architecture, Wepf, Basel,
p.131)
Various types of visual rhythm as repeating units of group of enclosed shapes are shown in
Figure 4. Representation of each type of visual rhythm shown in Figure 4 is as follows:
Figure 4(a):
Unit = ,
Group of units: G = (3, , 2, Æ),
Representation of visual rhythm: R= 2[n{G()} ];
Figure 4(b):
Unit = ,
Group of units: G = (),
Representation of visual rhythm: R = 2[4{G()} ];
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Figure 4(c):
Unit = ,
Group of units: G = (2)
Representation of visual rhythm: R = 8{G()};
Figure 4(d):
Unit = ,
Group of units: G = (4, 4),
Representation of visual rhythm: R = 4{G()}.
(a)
(b)
(c)
(d)
Figure 4: Examples of various types of visual rhythm as repeating groups of shapes
4. Process Model for Visual Rhythm Discovery
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Visual rhythm is discovered when groups of identical units repeat in a uniform sequence.
Equivalent properties of elements in primary objects are searched by a process called object
correspondence. Corresponding structures of objects are inferred by constraints on structures
of objects resulting from behaviours of the structures. Through the process of object
correspondence, corresponding structures are found. After corresponding structures are
found, groups from various objects are searched in the grouping process. Consequently visual
rhythms are discovered by the process of rhythm emergence, as shown in Figure 5. Various
types of visual rhythm based on their repetition sequence are discovered through the process.
Thus, visual rhythm discovery involves three steps: (1) searching for corresponding structures
of objects, so called object correspondence; (2) searching for groups, so called grouping; and
(3) discovering repetitions of groups, so called visual rhythm emergence.
primary objects
object correspondence
grouping
groups
corresponding structures
rhythm emergence
visual rhythm
Figure 5: A process model of visual rhythm emergence
4.1 Object correspondence
Object correspondence confirms corresponding structures of elements in primary objects. Line
segments are regarded as basic structural units for groups in visual rhythm. Corresponding
line segments as units are searched for when line segments lie in parallel infinite maximal lines
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and dimensional constraints on the line segments are equal [Gero and Jun, 1994]. Given two
infinite maximal lines and segments in lines respectively:
lp and lj and (iap, ibp) ∈ lp and (ijc, ijd), (ije, ijf) and (ijg, ijk) ∈ lj.
Line segment correspondence exists when
lp // lj ∧ d(iap, ibp) = d(ijc, ijd) = d(ije, ijf) = d(ijg, ijk) =>
(iap, ibp) ↔ (ijc, ijd) ↔ (ije, ijf) ↔ d(ijg, ijk).
Where lp // lj means two infinite maximal lines, lp and lj, are parallel to each other, iap
represents the intersections of two lines, la and lp, (iap, ibp) represents segment of a line, lp and
the dimension of the segment is represented as d(iap, ibp).
4.2 Grouping
Grouping is the process of searching various types groups of line segments, enclosed shapes
and groups of enclosed shapes resulting from grouping line segments. Grouping involves two
steps as shown in Figure 6: (i) searching groups of line segments, called line segment
grouping; and (ii) searching groups of enclosed shapes after searching enclosed shapes, called
shape grouping.
In line segment grouping, a group of line segments as continuous patterns and enclosed shapes
are searched by grouping adjacent intersections. Enclosed shapes are found by enclosed
groups of intersections [Gero and Yan, 1994]. Otherwise various groups of continuous line
segments are emerged.
corresponding structures
(corresponding line segments)
line segments grouping
enclosed shapes
shape grouping
groups of line segments
groups of enclosed shapes
groups
Figure 6: Process of grouping
4.3 Visual rhythm emergence
Visual rhythm emergence is the process of discovering possible visual rhythm from the shapes.
Through processes of object correspondence and grouping, various groups of line patterns and
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groups of enclosed shapes are discovered. When identical groups are repeated, the pattern
from repeating identical groups is searched by examining topological constraints on groups.
Visual rhythms are discovered as repetitions of identical groups of objects. In other words,
they are discovered when equivalent translational constraints exist for all groups. A visual
rhythm is discovered, for example, when the following rule is satisfied.
Discovered: G1 = (2, ), G2= (2, ), G3= (2, ),
Find: visual rhythm
τ(G1) = G2, τ(G2) = G3,
∧ G1 G2 G3
=> ∃ R = 3{G()}
5. Visual Rhythm in Architectural Design
The architectural facade of the Palace of Justice designed by Le Corbusier is analysed to
discover various types of visual rhythms. Only some emergent visual rhythms could be
presented. The facade of the building is shown in Figure 7.
Figure 7: Example of facade design from the Palace of Justice designed by Le Corbusier, 1956
(from Boesiger, W. and Girsberger, H. (1967), Le Corbusier 1910-1965, Thames and
Hudson, London, p.201).
5.1 Object correspondence
Grids of facades are one way for determining facade design for a building. Here, the grids are
taken as infinite maximal lines for inferring corresponding line segments through this process.
Four different types of primary corresponding line segments and numbers of emergent
corresponding line segments are searched for in primary object representation using infinite
maximal lines in Figure 8.
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Figure 8: Primary object representation (shown as heavy lines) of Figure 7 using infinite
maximal lines (shown as light lines).
5.2 Grouping
Using the process outlined in Section 4.2 groups are discovered. Some examples of groups of
line segments and enclosed groups are shown in Figure 9.
(a)
(b)
(c)
Figure 9: (a) Primary groups of line segments; (b) primary groups of enclosed shapes; and (c)
some emergent groups of enclosed shapes.
5.3 Visual rhythm emergence
Various emergent visual rhythms are discovered from the repeating identical groups through
this process. The units are groups of line segments or groups of enclosed shapes. Some
emergent visual rhythms from groups of line segments are shown in Figure 10 (a) and some
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emergent visual rhythms from groups of enclosed shapes are shown in Figure 10 (b), (c), (d),
(e) and (f).
(a)
(b)
(c)
(d)
(e)
(f)
Figure 10: Examples of various types of emergent visual rhythms of Figure 7
6. Discussion
The ability to discover architectural semantics from drawings readily offers opportunities to
develop design-oriented graphics system which may be more amenable to augment designers
during the early conceptual stage of design than current systems. We have developed a
symbolic representation of shape semantics, in particular visual rhythm, from two dimensional
shapes in this work.
We can conceive of a variety of visual semantics from architectural drawings such as visual
movement and visual balance. These shape semantics can be symbolically represented at
different levels of abstraction, where the symbolic representation can be characterised to allow
it to be mapped onto the various semantics. So far we have been only concerned with
discovering architectural semantics from existing drawings. An appropriate question to raise is
how can the various architectural semantics be introduced into a design. It appears that there are
two distinct situations to examine. The first is when the architectural semantics have been
discovered in an existing drawing and the second is when the designer wishes to enforce a
particular semantic in a design. Both these cases can be treated a constraint satisfaction
problems using constraint-based graphics languages.
Acknowledgments
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Valuable discussions were had with Dr. Routley of the Department of Music and Associate
Professor Purcell of the Department of Architectural and Design Science both in the University
of Sydney. Part of this work is supported by a grant from the Australian Research Council.
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