5.344. two_orth_include

DESCRIPTIONLINKSGRAPH
Origin

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

Constraint

𝚝𝚠𝚘_πš˜πš›πšπš‘_πš’πš—πšŒπš•πšžπšπšŽ(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, either P 1 is included in P 2 , either P 2 is included in P 1 .

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’-1 πšœπš’πš£-2 πšŽπš—πš-3,πš˜πš›πš’-2 πšœπš’πš£-3 πšŽπš—πš-5,1
Figure 5.344.1. Initial and final graph of the 𝚝𝚠𝚘_πš˜πš›πšπš‘_πš’πš—πšŒπš•πšžπšπšŽ constraint
ctrs/two_orth_includeActrs/two_orth_includeB
(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š’πš—πšŒπš•πšžπšπšŽ.

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.

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‡’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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