5.251. meet_sboxes
DESCRIPTION | LINKS | LOGIC |
- Origin
Geometry, derived from [RandellCuiCohn92]
- Constraint
- Synonym
.
- Types
- Arguments
- Restrictions
- Purpose
Holds if, for each pair of objects , , and meet with respect to a set of dimensions depicted by . 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 .
Two objects and object meet with respect to a set of dimensions depicted by if and only if the two following conditions hold:
For all shifted box associated with and for all shifted box associated with there exists a dimension such that (1)Β the start of in dimension is greater than or equal to the end of in dimension , or (2)Β the start of in dimension is greater than or equal to the end of in dimension (i.e.,Β there is no overlap between the shifted box of and the shifted box of ).
There exists a shifted box of and there exists a shifted box of such that for all dimensions (1)Β the end of in dimension is greater than or equal to the start of in dimension , and (2)Β the end of in dimension is greater than or equal to the start of in dimension (i.e.,Β at least two shifted box of and are in contact).
- Example
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FigureΒ 5.251.1 shows the objects of the example. Since all the pairs of objects meet the constraint holds.
Figure 5.251.1. (D)Β the three pairwise meeting objects , , of the Example slot respectively assigned shapes , , ; (A), (B), (C)Β shapes , , and are respectively made up from 1, 3, 3 and 1 disjoint shifted box.
- Typical
- Symmetries
Items of are permutable.
Items of are permutable.
Items of , and are permutable (same permutation used).
- Arg. properties
Suffix-contractible wrt. .
- Remark
One of the eight relations of the Region Connection CalculusΒ [RandellCuiCohn92].
- See also
common keyword: , , , , , Β (rcc8), Β (geometrical constraint,logic), Β (rcc8).
- Keywords
- Logic