Object models for computer aided design

Page 54

43 􁪽􋴚􁪽􋵥e s􁪽􋵲rr?lic􁪽􋵴ty and rnatheITat􁪽􋵣cal foundat􁪽􋵯on of the relat􁪽􋵯o􁪽􋵡al sc􁪽􋵥e􁪽􋵥e allow opera:io􁪽􋵳s to be def􁪽􋵮ned w􁪽􋵩ich let s orr.e part of the data base without specify􁪽􋵮n􁪽􋵥 explicit 􁪽􋵡att traversals. A relational algebra has bee􁪽􋵤 defined Khich contains operators which forrr ne􁪽􋵲 relations cy "selectingll, "restrictinq", "jo:'nin911, etc. exist:ng rela:ions. F􁪽􋵲rst oreer predicate calculus can linkage mecb.ar.ism which is used to build up also be usee t􁪽􋵡 access relational structures. General query languages have been defined based on both the relaticnal al􁪽􋵥etra and the f􁪽􋵲rst crder precicate calculus. A possible representation scheme for a polyhedron using relations is shown in figure 3.3. For any relation, there rn􁪽􋵳st b􁪽􋵡 a sccset of the do􁪽􋵡ains, called a key, which serves to un􁪽􋴚􁪽􋵵uely identify each tuple in the relation. For e x a IT, :: 1 e, i n f i sur e 3. 3 the II n am e" do IT, a i n i s the key for €2ch of 􁪽􋵨he 􁪽􋵣ci􁪽􋵴ts, edges, faces, and polyhecra relations. The key of the incidence relation is the pair ( po i n t r e dc e ) • The po􁪽􋵮nt oc􁪽􋵡a:n of the i n c i de r.c e relation is also "f o r e i c n xe y ? , that is it 'contains a key into the p o i n t r e Le t i c r.. Keys and forei9n keys constitute a syrrbolic ir.ter-rela:io􁪽􋵡al structures. Kote that this relational structure is, in fact, very sirrilar to the D2TG exarr􁪽􋵬le. The incieence relation