5.260. orth_on_the_ground

DESCRIPTIONLINKSGRAPH
Origin

Used for defining πš™πš•πšŠπšŒπšŽ_πš’πš—_πš™πš’πš›πšŠπš–πš’πš.

Constraint

πš˜πš›πšπš‘_πš˜πš—_πšπš‘πšŽ_πšπš›πš˜πšžπš—πš(π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄,πš…π™΄πšπšƒπ™Έπ™²π™°π™»_𝙳𝙸𝙼)

Arguments
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›)
πš…π™΄πšπšƒπ™Έπ™²π™°π™»_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š…π™΄πšπšƒπ™Έπ™²π™°π™»_𝙳𝙸𝙼β‰₯1
πš…π™΄πšπšƒπ™Έπ™²π™°π™»_𝙳𝙸𝙼≀|π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄|
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™΄)
Purpose

The πš˜πš›πš’ attribute of the πš…π™΄πšπšƒπ™Έπ™²π™°π™»_𝙳𝙸𝙼 th item of the π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄πš‚ collection should be fixed to one.

Example
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

The πš˜πš›πšπš‘_πš˜πš—_πšπš‘πšŽ_πšπš›πš˜πšžπš—πš constraint holds since the πš˜πš›πš’ attribute of its 1th item βŒ©πš˜πš›πš’-1 πšœπš’πš£-2 πšŽπš—πš-3βŒͺ (i.e.,Β 1th item since πš…π™΄πšπšƒπ™Έπ™²π™°π™»_𝙳𝙸𝙼=1) is set to one.

Used in

πš™πš•πšŠπšŒπšŽ_πš’πš—_πš™πš’πš›πšŠπš–πš’πš.

Keywords

geometry: geometrical constraint, orthotope.

Arc input(s)

π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄

Arc generator
π‘†πΈπΏπΉβ†¦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šŽ)

Arc arity
Arc constraint(s)
β€’ πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ.πš”πšŽπš’=πš…π™΄πšπšƒπ™Έπ™²π™°π™»_𝙳𝙸𝙼
β€’ πš˜πš›πšπš‘πš˜πšπš˜πš™πšŽ.πš˜πš›πš’=1
Graph property(ies)
𝐍𝐀𝐑𝐂=1

Graph model

PartsΒ (A) andΒ (B) of FigureΒ 5.260.1 respectively show the initial and final graph associated with the Example slot. Since we use the 𝐍𝐀𝐑𝐂 graph property, the loop of the final graph is stressed in bold.

Figure 5.260.1. Initial and final graph of the πš˜πš›πšπš‘_πš˜πš—_πšπš‘πšŽ_πšπš›πš˜πšžπš—πš constraint
ctrs/orth_on_the_groundActrs/orth_on_the_groundB
(a) (b)
Signature

Since all the πš”πšŽπš’ attributes of the π™Ύπšπšƒπ™·π™Ύπšƒπ™Ύπ™Ώπ™΄πš‚ collection are distinct, because of the first condition of the arc constraint, and since we use the 𝑆𝐸𝐿𝐹 arc generator the final graph contains at most one arc. Therefore we can rewrite the graph property 𝐍𝐀𝐑𝐂=1 to 𝐍𝐀𝐑𝐂β‰₯1 and simplify 𝐍𝐀𝐑𝐂 Β― Μ² to 𝐍𝐀𝐑𝐂 Β―.