The muqarnas represents a highly sophisticated three-dimensional application of geometric principles; a muqarnas composition being based on the replication of units arranged in rows corbelled one on top of another. These units, which can be made of wood, stone, stucco or ceramics, provide a flexible system of articulating surfaces, and can be made to fit within any configuration and to visually dematerialize and divide surfaces. As a stereometric formation the muqarnas can be understood as the result of a process of projecting the elements of a plan and carving the curvilinear or angular muqarnas units out of the projected blocks. Most muqarnas volumes are made up of combinations of seven shapes from a total of seventeen types of basic components. From a small number of these basic components with at least one surface area in common, many different interlocking arrangements could be developed.
Systems can be envisaged which consist of some minimum inventory of component types which can be alternatively com¬bined to yield a great diversity of efficient structural form. We call these minimum inventory/maximum diversity systems.
By such a "system" we mean a minimized inventory of component types (a kit of parts) along with rubrics whereby the components may be combined. In the best systems, as we shall see, the rubrics lead not to constriction, but to a maximi¬zation of different, though generically re¬lated, structural forms. We will uncover such rubrics by considering the proper¬ties of space—of form itself. One charac¬teristic of successful systems will be that the rubrics—the rules of assemblage— and the physical components themselves will be seen to be organically related: the rules will be seen to grow out of the parts, the parts out of the rules. In an attempt to understand the concept of minimum inventory/maximum diversity systems we are drawn to nature. Crystal structures, in general, demon¬strate diversity of form as a function of the least-energy internal arrangements of their atomic arrays. 
The general design process is often characterized as mapping needs to function to structure.  It is carried out using many different types of reasoning and many different sources of knowledge.  In general, design is the process of specifying a description of an artifact that satisfies a collection of constraints.  These constraints may arise from a variety of sources.
Because Design is an ill-structured activity requiring intelligence, it is a suitable topic of study for AI. A fundamental hypothesis shared by most AI in Design researchers is that there are core reasoning 'skills', and types of knowledge, that are common across domains. That is, although design problems in different domains require different domain knowledge -- such as knowledge of equations, components, and analysis techniques -- there are underlying similarities in the form of that knowledge and in the way that it is used. An additional type of information that has been added to CAD systems is the Constraint. Constraints restrict the possible values of parameters.  In 2D, a constraint might be added to require that two lines be maintained at a certain angle. As muqarnas is a volumetric component, one could constrain two solids to always touch.  When constraints are used, a single change can propagate through constraints to produce new values for many other parameters, effectively generating a whole new design. Thus, constraint satisfaction provides a Parametric Design capability, (i.e., the system "designs" values for some parameters).
This paper will present the muqarnas as a case study to CAD applications to be gradually turned from being mainly concerned with object representation towards some consideration of the design process (i.e., Design Process Knowledge as opposed to Design Object Knowledge).

