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Relation Shape Shape 2 ~----~•x Pictorial Equivalence (a) Congruence (b) Si mil ari tv ( c) Fi qure 1-5 Pictorial equiv•lence, conqruence, and s i mil arity between two shapes. 12 terms of shape union and pictorial equivalence, one shape is a subshape of a second shape if and only if the shape union of the two shapes is pictorially equivalent to the second shape. examples of subshape. eve~ Figure 1-6 shows some Notice that the empty shape is a subshape of shape. The shape union of two shapes may have subshapes which are not subshapes of the original two shapes.

Artists) and at the same time to be readi1y adaptable for the rigorous mathematical 26 Fi gure 1-13 Some shapes resultino frorn the recursive application of rule (ii) to the shapP. in Figure l-12a. 27 investigation of shape (see Chapter 2). Shape grammars are similar to phrase structure grammars [13] which were originally used by Chomsky [14] in linguistics. Where a phrase structure grammar is defined over an alphabet of symbols and generates languages of strings of symbols, shape grammars are defined over alphabets of shapes and generate languages of shapes.

In the definitions of shape grammar and languages of shapes, shapes, subshape, and the Euclidean transformations on shapes are used as primitives. Thesedefinitions are recast along traditional mathematical lines in Chapter 2. 2 A Simple Example Figure 1-14 shows a shape grammar SGl which incorporates rule (i) of Figure 1-lla. VT contains a line as its only element. shapes in the language defined by SGl will be composed of VM contains a ci1·cle as its only element. distinguishable from the shapes in VM+ rules.

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