- Origin
Geometry, derived from [BeldiceanuCarlssonPoderSadekTruchet07]
- Constraint
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- Synonyms
,
.
- Types
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- Arguments
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- Restrictions
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- Purpose
Holds if, for each pair of objects , , and do not overlap
with respect to a set of dimensions depicted by .
and are objects that take a shape among a set of shapes.
Each shape is defined as a finite set of shifted boxes, where each
shifted box is described by a box in a -dimensional space
at a given offset (from the origin of the shape) with given sizes. More
precisely, a shifted box is an entity defined by its shape id ,
shift offset , and sizes . Then, a shape is defined as the union of
shifted boxes sharing the same shape id. An object is an entity
defined by its unique object identifier , shape id and origin .
An object does not overlap an object
with respect to a set of dimensions depicted by
if and only if,
for all shifted box associated with and
for all shifted box associated with ,
there exists a dimension such that
the start of in dimension is greater than or equal to the end of in dimension , or
the start of in dimension is greater than or equal to the end of in dimension .
- Example
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FigureΒ 5.280.1 shows the objects of the example.
Since and do not overlap,
since and do not overlap, and
since and also do not overlap,
the constraint holds.
- Typical
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- Symmetries
Items of are permutable.
Items of are permutable.
Items of , and are permutable (same permutation used).
can be decreased to any value .
- Arg. properties
Suffix-contractible wrt. .
- Remark
In addition from preventing objects to overlap,
the constraint also enforces
that borders and corners of objects are not directly in contact.
- See also
common keyword:
,
,
Β (geometrical constraint between shifted boxes),
Β (geometrical constraint,non-overlapping),
,
Β (geometrical constraint between shifted boxes),
,
Β (geometrical constraint,non-overlapping),
,
,
Β (geometrical constraint between shifted boxes),
Β (geometrical constraint).
implied by:
.
- Keywords
constraint type:
logic.
geometry:
geometrical constraint,
non-overlapping.
- Logic
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