5.124. disjoint_sboxes
DESCRIPTION | LINKS | LOGIC |
- Origin
Geometry, derived from [RandellCuiCohn92]
- Constraint
- Synonym
.
- Types
- Arguments
- Restrictions
- Purpose
Holds if, for each pair of objects , , and are disjoint 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 .
Two objects and object are disjoint 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 at least one dimension such that (1)Β the origin of in dimension is strictly greater than the end of in dimension , or (2)Β the origin of in dimension is strictly greater than the end of in dimension .
- Example
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FigureΒ 5.124.1 shows the objects of the example. Since these objects are pairwise disjoint the constraint holds.
Figure 5.124.1. (D)Β the three mutually disjoint 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.
can be decreased to any value .
- Arg. properties
Suffix-contractible wrt. .
- Remark
One of the eight relations of the Region Connection CalculusΒ [RandellCuiCohn92]. Unlike the constraint, which just prevents objects from overlapping, the constraint in addition enforces that borders and corners of objects are not directly in contact.
- See also
common keyword: , , , , , Β (rcc8), Β (geometrical constraint,logic), Β (rcc8).
implies: .
- Keywords
- Logic