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Besides, the spatial planning theory derived from spatial qualitative reasoning
can be used in distributed design which looks for a group of satisfying constraints
for a group of geometric objects. Related approaches are mainly used in the fields
of automatic design and qualitative modeling, etc. Some results that are of
practical significance have been gained in this field, such as solving theory of
constraint satisfaction problems (CSP). In fact, lots of spatial qualitative planning
are geometric constraint satisfaction problems.
4.7.1
Spatial logic
The main task to carry out geometric simulation about spatial geometric object
and its movement is to produce envisionment about its possible states.
Envisionment is to model the system and generate spanning tree of its possible
states. There are two kinds of envisionment, total envisionment and attainable
envisionment. Attainable envisionment is to build the possible state spanning tree
from some special states for the modeling system. While total envisionment can
generate all the possible states of the system (Cui,1992).
In 1992, Randell, etc, have built up RCC spatial temporal logic in order to
carry out stainable envisionment about spatial problem, which has been realized.
Similar to QSIM approach of Kuipers, the simulation algorithm based on RCC
logic begins with structural description of the system. Initial state is considered
as the root node of spanning tree. Possible behaviors are the paths from the root
node to the leaf node in the tree.
The foundation of spatial logic is to assume a primitive binary relation C(x,y).
Among that, x and y indicate two regions and predicate C indicates sharing more
than one public point, which means touching each other and is of reflexivity and
symmetry.
1. The definitions of eight basic relations
With relation C(
x,y
), a group of basic binary relation can be defined as:
(1) DC(
x,y
): indicating the two regions don't have touch with each other.
(2) EC(
x,y
): indicating the two regions have external touch with each other.
(3) PO(
x,y
): indicating the tow regions partly cover with each other.
(4) = (
x,y
): indicating the tow regions are totally the same.
(5) TPP(
x,y
): indicating
x
is a strict part of
y
and they are tangent(inside).
(6) NTPP(
x,y
): indicating
x
is a strict part of
y
but they don't touch each other.
