- Origin
Inspired by and .
- Constraint
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- Arguments
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- Restrictions
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- Purpose
Consider a set of rectangles described by the
collection. Enforces that at each point of the
plane, the cumulated height of the set of rectangles that overlap
that point, does not exceed a given limit.
- Example
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PartΒ (A) of FigureΒ 5.85.1
shows the 4 parallelepipeds of height 4, 2, 3 and 1
associated with the items of the collection
(parallelepipeds since each rectangle also has a height).
PartΒ (B) gives the corresponding cumulated 2-dimensional profile,
where each number is the cumulated height of all the rectangles
that contain the corresponding region.
The constraint holds since the
highest peak of the cumulated 2-dimensional profile does not
exceed the upper limit 4 imposed by the last argument of the
constraint.
- Typical
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- Symmetries
Items of are permutable.
Attributes of are permutable w.r.t. permutation (permutation applied to all items).
can be decreased to any value .
One and the same constant can be added to the and attributes of all items of .
One and the same constant can be added to the and attributes of all items of .
can be increased.
- Usage
The constraint is a necessary
condition for the constraint in 3 dimensions
(i.e.,Β the placement of parallelepipeds in such a way that
they do not pairwise overlap and that each parallelepiped
has his sides parallel to the sides of the placement space).
- Algorithm
A first natural way to handle this constraint would be to accumulate
the compulsory partΒ [Lahrichi82] of
the different rectangles in a quadtreeΒ [Samet89].
To each leave of the quadtree we associate
the cumulated height of the rectangles containing the corresponding
region.
- Systems
geost in Choco.
- See also
related:
Β ( is a necessary condition for : forget one dimension when the number of dimensions is equal to 3).
specialisation:
Β ( of size 1 with a replaced by of 1),
Β ( with a replaced by with same ).
- Keywords
characteristic of a constraint:
derived collection.
constraint type:
predefined constraint.
filtering:
quadtree,
compulsory part.
geometry:
geometrical constraint.
