5.410. two_orth_do_not_overlap
DESCRIPTION | LINKS | GRAPH | AUTOMATON |
- Origin
- Constraint
- Type
- Arguments
- Restrictions
- Purpose
For two orthotopes and enforce that there exists at least one dimension such that the projections on of and do not overlap.
- Example
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FigureΒ 5.410.1 represents the respective position of the two rectangles of the example. The coordinates of the leftmost lowest corner of each rectangle are stressed in bold. The constraint holds since the two rectangles do not overlap.
Figure 5.410.1. The two non overlapping rectangles of the Example slot
- Typical
- Symmetries
Arguments are permutable w.r.t. permutation .
Items of and are permutable (same permutation used).
can be decreased to any value .
can be decreased to any value .
- Used in
- See also
- Keywords
characteristic of a constraint: automaton, automaton without counters, reified automaton constraint.
constraint network structure: Berge-acyclic constraint network.
filtering: arc-consistency, constructive disjunction.
final graph structure: bipartite, no loop.
geometry: geometrical constraint, non-overlapping, orthotope.
- Arc input(s)
- Arc generator
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- Arc arity
- Arc constraint(s)
- Graph property(ies)
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- Graph class
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- Graph model
We build an initial graph where each arc corresponds to the fact that, either the projection of an orthotope on a given dimension is empty, either it is located before the projection in the same dimension of the other orthotope. Finally we ask that at least one arc constraint remains in the final graph.
PartsΒ (A) andΒ (B) of FigureΒ 5.410.2 respectively show the initial and final graph associated with the Example slot. Since we use the graph property, the unique arc of the final graph is stressed in bold. It corresponds to the fact that the projection in dimension 1 of the first orthotope is located before the projection in dimension 1 of the second orthotope. Therefore the two orthotopes do not overlap.
Figure 5.410.2. Initial and final graph of the constraint
(a) (b)
- Automaton
FigureΒ 5.410.3 depicts the automaton associated with the constraint. Let , and respectively be the , the and the attributes of the item of the collection. Let , and respectively be the , the and the attributes of the item of the collection. To each sextuple corresponds a 0-1 signature variable as well as the following signature constraint: .
Figure 5.410.3. Automaton of the constraint
Figure 5.410.4. Hypergraph of the reformulation corresponding to the automaton of the constraint