3.7.175. Orthotope

Figure 3.7.46. Illustration of the notion of orthotope for various number of dimensions n

A constraint involving orthotopes. An orthotope corresponds to the generalisation of the rectangle and box to the n-dimensional case. In addition its sides are parallel to the axes of the Β placement space. FigureΒ 3.7.46 illustrates the notion of orthotope for n=1,2,3 and 4. A collection usually named π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄, declared as π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄-πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πš˜πš›πš’-πšπšŸπšŠπš›,πšœπš’πš£-πšπšŸπšŠπš›,πšŽπš—πš-πšπšŸπšŠπš›), defines for each dimension d (with d∈[1,n]) the coordinate of its lower corner, the size and the coordinate of its upper corner in dimension d. FigureΒ 3.7.47 illustrates the representation of an orthotope for n=2.

Figure 3.7.47. Representation of an orthotope when the number of dimensions n=2 in term of the collection π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄-πšŒπš˜πš•πš•πšŽπšŒπšπš’πš˜πš—(πš˜πš›πš’-πšπšŸπšŠπš›,πšœπš’πš£-πšπšŸπšŠπš›,πšŽπš—πš-πšπšŸπšŠπš›)