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An Introduction to Tonal Theory by Peter Westergaard

By Peter Westergaard

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In our object-oriented approach graphical relations will be modelled by means of graphical relation classes. 10 ( graphical relation class) A graphical relation class [G R] E C is an object class that defines, besides name: [G R] I-t String, a finite set of attributes specifying the graphical object classes on which the graphical relation is defined. LetWOC] denote the set ofgraphical object classes, then graphDomaini : [GR] I-t {o E DID I oid- 1 (o) E gOC}forl ::; i ::;-·n. The set of objects generatedfrom [GR], that is {gr = (gl ...

Kamps, Diagram Design © Springer-Verlag Berlin Heidelberg 1999 22 Chapter 3. Data Structure • Boolean domain: {trueJalse} operations: V,/\,etc: Boolean x Boolean -,: Boolean f-t Boolean. • String domain: the set offinite strings operations: ~: String x String String f-t String, etc. • OlD domain: the set ofobject ids operations: =: OlD x OlD f-t f-t f-t Boolean, Boolean, concatenation: String x Boolean. • domain: 0 the empty set 0 operations: the set ofoperations defined for aU other types. Any operation applied to the empty type will result in the empty type.

Because the transitivity is graphically not expressed. Diagram b), in constrast, is conflict free. Network diagram b) is free from conflicts although it is based on the same design decisions applied to the same type of data. The difference results from the fact that the connectivity of R 2 is different from that of R I . Diagram b) illustrates that graphical relations are not per se incompatible. Instead, resource allocation conflicts rather need to be detected on the tuple level. This problem represents a typical constraint solving task which is particularly difficult when the tuple set is large.

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