Towards a shape editor: the implementation of a shape generation system

A fundamental problem in editing shapes is the recognition of partial shapes in a drawing to which changes are to be made. In this paper the possibility of using shape rules as a mechanism for effecting such changes is explored. Shape rules represent spatial relationships between two shapes a and /? with the interpretation that any instance of a in a shape can be replaced by a 'similar' instance of /?. A shape generation system implemented in PROLOG is described. Introduction As the title suggests, this paper is concerned with the implementation of a shape generation system. However, the implementation details in themselves are of relatively little importance. The motivation for this paper stems from an interest in the problematic issues associated with 'shape editing', and how they may be approached within a shape generation system. Shape editing is difficult to define precisely and no definition will be proffered in this paper. This is partly because of our present limited understanding of shapes. However, it is worthwhile briefly to examine editors in general. There are two main aspects to an editor. First, the subject of a typical editor in any domain—namely, some sort of 'document', be it a manuscript, a programme, a table, a memo, or a drawing etc—may be regarded as satisfying certain rules of form and meaning that we can loosely classify as the particular 'document rules'. In other words, we may state as a belief that document construction—spatial or otherwise—can be set within an environment that is based on some rules. Second, the tasks associated with an editor include the creation, deletion, change, arrangement, and copy of documents (Meyrowitz and van Dam, 1982). These tasks involve some process of recognition and some process of alteration. Consider interactive text editors as implemented in computers. Alteration to text is basically some form of text replacement. Text recognition, in its simplest form, corresponds to some form of pattern matching. However, in principle, recognition of text can be driven by other considerations that rely on knowledge about either the form or the content of the document. In other words, recognition may be carried out either syntactically or semantically. Of the two, semantic recognition is much harder. As an extreme example, imagine trying to scan for a piece of text that has the same 'meaning' as the given text! By analogy, a shape editor is feasible only when the problems of shape recognition and shape replacement are resolved—albeit partially. A shape editor deals with drawings. Drawings are a medium through which people communicate. Drawings reflect, in part, a person's perception of a spatial problem and, in part, his or her conception of a spatial solution. Drawings represent pictorial descriptions of abstract (and perhaps nonspatial) relationships. The relationships between the 392 R Krishnamurti, C Giraud shapes in a drawing and the nonspatial descriptions to which they refer constitute the semantics of the drawing. Drawings often materialise through a trial and error sequence with each successive drawing arising out of changes made to the preceding drawing. These changes generally correspond to spatial alterations—for example, the introduction of a wall into a plan, or a rearrangement of room spaces within a plan. These changes involve some sort of shape replacements. Let us clarify this. Imagine a person sitting in front of a drawing board or a graphics terminal. Let us suppose that the person initially produces an outline drawing. Then, finer details are gradually introduced into the drawing. The details may be replicated in various parts of the drawing. The details may be subjected to further spatial editing either globally or locally. The details may of course be associated with partial semantic information, often illustrated through text in the drawing. Although conventional graphics systems perform these and other tasks reasonably, they do have their drawbacks. Such systems typically employ representations for objects that distinguish between a segment, an object made up of segments, assemblies made up of sets of objects, and so on. Composite objects are named. Composite objects are essential if they are replicated in the various parts of the drawing. Two principal problems, when one attempts to edit drawings, can be identified. First, changes made to composite objects tend to have a global effect. That is, the changes are manifested in every occurrence of the object in the drawing. Second, it is difficult to recognise and modify just parts of objects. The problem is important in situations where semantic links are attached to those parts of the shape. For instance, 'the corner of a room' may have to be identified in order to carry out a spatial consistency check. The concept of spatial relations (Stiny, 1980b; Earl and Krishnamurti, 1984) promises a mechanism whereby such shape editing tasks may be carried out. In its simplest form a spatial relationship can be expressed as a shape rule relating two shapes, a and /3. Figure 1 shows examples of edit rules for tiling the plane. A shape rule is interpreted as follows. Any occurrence of a in a specified shape under some transformation can be replaced by an occurrence of (5 under the same transformation. Shape rules work' in much the same way as string replacement rules in text processing, except that they have also to take into account the possible geometric transformations associated with a and /?. Figure 2 illustrates shape rule application.