5.120. diffn_include
DESCRIPTION | LINKS | GRAPH |
- Origin
- Constraint
- Type
- Arguments
- Restrictions
- Purpose
Extension of the generalised multi-dimensional non-overlapping diffn constraint. Holds if, for each pair of orthotopes the following conditions hold:
and do not overlap. Two orthotopes do not overlap if one of the orthotopes has zero size or if there exists at least one dimension where their projections do not overlap.
Let and respectively denote the projections of and onto dimension . If and overlap then, either is included in , either is included in .
- Example
-
FigureΒ 5.120.1 represents the respective position of the twelve rectangles of the example. The coordinates of the leftmost lowest corner of each rectangle are stressed in bold. The constraint holds since (1)Β the twelve rectangles do not overlap and since (2)Β when their projection onto dimension overlap one of the projections is included within the other one.
Figure 5.120.1. Illustration of the Example slot: twelve non-overlapping rectangles such that, for each pair of rectangles , , if the projections onto dimension 1 of rectangles and intersect then one of the projections is included within the other projection
- Typical
- Symmetries
Items of are permutable.
One and the same constant can be added to the and attributes of all items of .
- Arg. properties
Contractible wrt. .
- See also
common keyword: Β (geometrical constraint,orthotope), Β (geometrical constraint,orthotope,positioning constraint).
- Keywords
constraint type: decomposition.
geometry: geometrical constraint, positioning constraint, orthotope.
- Arc input(s)
- Arc generator
-
- Arc arity
- Arc constraint(s)
- Graph property(ies)
-
- Graph model
Since showing all items produces too big graphs, partsΒ (A) andΒ (B) of FigureΒ 5.120.2 respectively show the initial and final graph associated with the first three items of the Example slot. Since we use the graph property, the arcs of the final graph are stressed in bold.
Figure 5.120.2. Initial and final graph of the constraint
(a) (b)