5.194. inside_sboxes
| DESCRIPTION | LINKS | LOGIC |
- Origin
Geometry, derived from [RandellCuiCohn92]
- Constraint
- Synonym
.
- Types
- Arguments
- Restrictions
- Purpose
Holds if, for each pair of objects , , is inside 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 is inside an object with respect to a set of dimensions depicted by if and only if, for all shifted boxes associated with , there exists a shifted box of such that is inside . A shifted box is inside a shifted box if and only if, for all dimensions , (1)Β the start of in dimension is strictly less than the start of in dimension , and (2)Β the end of in dimension is strictly less than the end of in dimension .
- Example
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FigureΒ 5.194.1 shows the objects of the example. Since is inside and , and since is also inside , the constraint holds.
Figure 5.194.1. (D)Β the three nested objects , , of the Example slot respectively assigned shapes , , ; (A), (B), (C)Β shapes , and are made up from a single shifted box.
- Typical
- Symmetries
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]. The constraint is a restriction of the original relation since it requires that each box of an object is contained by one box of the other object.
- See also
common keyword: , , , , , Β (rcc8), Β (geometrical constraint,logic), Β (rcc8).
- Keywords
- Logic