5.342. two_orth_column

DESCRIPTIONLINKSGRAPH
Origin

Used for defining πšπš’πšπšπš—_πšŒπš˜πš•πšžπš–πš—.

Constraint

𝚝𝚠𝚘_πš˜πš›πšπš‘_πšŒπš˜πš•πšžπš–πš—(π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1,π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2,𝙳𝙸𝙼)

Type
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›)
Arguments
π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄
π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄
π™³π™Έπ™Όπš’πš—πš
Restrictions
|π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄|>0
πš›πšŽπššπšžπš’πš›πšŽ_𝚊𝚝_πš•πšŽπšŠπšœπš(2,π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄,[πš˜πš›πš’,πšœπš’πš£,πšŽπš—πš])
π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄.πšœπš’πš£β‰₯0
π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄.πš˜πš›πš’β‰€π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄.πšŽπš—πš
|π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1|=|π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2|
πš˜πš›πšπš‘_πš•πš’πš—πš”_πš˜πš›πš’_πšœπš’πš£_πšŽπš—πš(π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1)
πš˜πš›πšπš‘_πš•πš’πš—πš”_πš˜πš›πš’_πšœπš’πš£_πšŽπš—πš(π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2)
𝙳𝙸𝙼>0
𝙳𝙸𝙼≀|π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1|
Purpose

Let P 1 and P 2 respectively denote the projections of π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1 and π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2 in dimension 𝙳𝙸𝙼. If P 1 and P 2 overlap then the size of their intersection is equal to the size of π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1 in dimension 𝙳𝙸𝙼, as well as to the size of π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2 in dimension 𝙳𝙸𝙼.

Example
πš˜πš›πš’-1 πšœπš’πš£-3 πšŽπš—πš-4,πš˜πš›πš’-1 πšœπš’πš£-1 πšŽπš—πš-2,πš˜πš›πš’-4 πšœπš’πš£-2 πšŽπš—πš-6,πš˜πš›πš’-1 πšœπš’πš£-3 πšŽπš—πš-4,1
Figure 5.342.1. Initial and final graph of the 𝚝𝚠𝚘_πš˜πš›πšπš‘_πšŒπš˜πš•πšžπš–πš— constraint
ctrs/two_orth_columnActrs/two_orth_columnB
(a) (b)
Symmetry

Arguments are permutable w.r.t. permutation (π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1,π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2) (𝙳𝙸𝙼).

Used in

πšπš’πšπšπš—_πšŒπš˜πš•πšžπš–πš—.

See also

related: πšπš’πšπšπš—Β (an extension of the πšπš’πšπšπš— constraint).

Keywords

geometry: geometrical constraint, positioning constraint, orthotope, guillotine cut.

Arc input(s)

π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄1 π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄2

Arc generator
π‘ƒπ‘…π‘‚π·π‘ˆπΆπ‘‡(=)β†¦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š˜πšπš˜πš™πšŽ1,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2)

Arc arity
Arc constraint(s)
β‹€πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πš”πšŽπš’=𝙳𝙸𝙼,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πš˜πš›πš’<πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2.πšŽπš—πš,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2.πš˜πš›πš’<πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πšŽπš—πš,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πšœπš’πš£>0,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2.πšœπš’πš£>0β‡’β‹€πš–πš’πš—(πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πšŽπš—πš,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2.πšŽπš—πš)-πš–πšŠπš‘(πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πš˜πš›πš’,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2.πš˜πš›πš’)=πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πšœπš’πš£,πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ1.πšœπš’πš£=πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ2.πšœπš’πš£
Graph property(ies)
𝐍𝐀𝐑𝐂=1