Concepts of Complexity

In this paper the term "CAD model" refers to one or more computer filesthat are intended to describe or represent the visual, or any other, propertiesof a design.

'Complex' and 'Complexity'

The adjectives representing the focus of this project are defined in theWebsterUniversal Dictionary (Wyld,Partridge, 1975) as follows:
"Composite, complicated, consisting of two or more closely connected orinterwoven parts, elements, strands etc.: not simple"
State or quality of being complex; intricacy.

Interpretations of Complexity

Although the broad sense of complexity is defined it is still necessaryto evaluate a variety of common interpretations of the term and selectonly those which are relevant. These are described below.

Degree of Difficulty

It is recognised that complexity of a CAD task is associated withits difficulty. Complexity influences difficulty. However, as many otherthings also influence task difficulty, this relationship is not exploredin this project.

Real Complexity

There is a difference between complexity, which is real or objectivelymeasurable and substantially irreducible, and apparent complexity, whichis a matter of perception and interpretation, varying from one person toanother. In this project we plan to measure real complexity.

Necessary Complexity

Human artefacts typically contain both necessary and unnecessary elements,both intended and unintended. The CAD complexity of this study is thatwhich may be regarded as intended and necessary. This project does notexplore the area of CAD intentions but acknowledges that CAD models producedfor one purpose are frequently put to other uses.

Organised Complexity

Weaver (1948)distinguishes between disorganised and organised complexity. Since CADmodels can be considered ordered systems,we focus on organised complexity in this project.

Complex System

CAD models are systems, to the extent that they combine any of the above mentioned aspects of complexity within some integrated form. This is clear from the following definitions, found in the Fontana Dictionary of Modern Thought (Bullock et al., 1988) and the Webster Universal Dictionary (Wyld, Partridge, 1975):
Complex CAD models are complex systems, based on the description of complexsystems by Simon (1996,p.183), to the extent that they are "made up of a large number of partsthat have many interactions."

Ordered System

Research into complex systems has been stimulated in recent years by studiesof chaos. One outcome of this research has been a greater interest in thestudy of complexity in its own right (Salingaros,1997a; Simon,1996, p.181) including the study of complex systems that are orderedand not at all chaotic.

It is proposed that CAD models, at least as we currently understandthem, belong in the former group, in both

It is acknowledged that this need not always be true. Some aspects of design complexity, and some functions of CAD modelling, such as surface representation, may involve intentional chaos or utilisation of chaos, for artistic purposes, for example. In this project, these aspects of complexity are not explored.

Complexity - Characteristics

Simon (1996) includesthe following characteristics, in a series of observations about complexsystems:In applying these observations to CAD models one may conclude that a practical first step towards achieving an economical description of CAD complexity is to identify CAD hierarchies.

Complexity Criteria for Graphic Systems

A number of different criteria have been identified and used as measures of complexity for graphic objects. One of the earliest measures was by Birkhoff (1933), who based shape complexity on the number of sides of a polygon, leading to a formula for measuring aesthetic values. Attneave (1957) used matrix grain, curvedness, symmetry, number of turns, degree of compactness and angular variability as parameters for his measures in his experiments. Stiny and Gips (1978) suggested that the lengths of shape descriptions and generative specifications define shape complexity, following similar work in information theory (Chaitin, 1975; Kolmogorov, 1968). Salingaros (1997b) has used an analogy with thermodynamic complexity to describe the complexity of drawings of buildings by measuring thermodynamic temperature and architectural harmony. A recent Ph.D thesis by Cha (1998) describes shape complexity measurement using pattern representations.

We plan to incorporate many of the criteria formulated in these works in our formal model.

CAD Versus Design Complexity

Complexity of a CAD model is influenced by design complexity to the extentthat properties of the design or modelled object are represented in itsCAD embodiment.

It may be inferred that the distinguishing elements of CAD complexitymust derive from something other than these properties. Looking beyondthe properties, it is evident that a CAD embodiment is a representationof an object, either whole or part. It is equally clear that similar objectsmay be interpreted and represented in different ways by designers for avariety of reasons, and by CAD systems simply as a result of variationsin functionality. Looking at this another way, one could observe that distinctionsbetween CAD embodiment and the designed object arise from the fact of representation.Therefore, it may be expected that distinguishing elements of CAD complexitywill arise from characteristics of CAD interpretation and representation. 


In the following research we identify CAD subsystems that contribute tothe measurement of several different aspects of complexity. Selection ofparticular measures and evaluation criteria form the initial stage of theproject, but some informal observations can be made here.

Complexity, like intelligence or the weather, includes interdependentcomponents and others that act separately. Unlike intelligence, CAD complexityitself is not an objective. The objectives are to optimise and manage complexity.Unlike the weather, complexity can be controlled. Measurement of CAD complexityis fundamental to both optimisation and control. The research proposedhere will focus on a small aspect of CAD complexity. Future research inthis area will focus on relationships between the individual subsystemsof CAD organisation, design type, model scope and other CAD requirements.

The implications of these observations are far reaching. Ultimately,CAD is about communication, and that is changing everywhere as technologyprogresses. CAD usage is evolving beyond single task "throw away" functions,of project based design and construction, towards interoperability andlonger term applications, such as large scale system simulations and facilitymanagement. Interoperability requires greater consistency in the use ofCAD as well as the design of CAD software. Longer term applications demandboth consistency and durability of CAD models. As these factors grow inimportance so will the need to further develop and refine principles andconcepts of CAD organisation, based on objective measurement.