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For detail information read published paper:
https://www.researchgate.net/publication/279449408_Spatial_Rules_for_Capturing_Qualitatively_Equivalent_Configurations_in_Sketch_maps
Using the CLP(QS) framework, we define spatial rules to
compute qualitative information between nearby objects. For
the linear ordering and orientation information of adjacent
landmarks, we use connected street segments as reference
objects, while junctions are used as reference objects for cyclic
ordering. The adjacency of landmarks is defined via relative
metric distances.
Preliminaries
CLP(QS) includes a library of qualitative spatial relations
encoded as polynomial constraints over a set of real variables
X, which are solved via constraint logic programming [2].
In this subsection we present the CLP(QS) library implementations
of projection, distance, and orientation relations that
we build on in subsequent sections. A set of spatial relations
is consistent in CLP(QS) if there exists some assignment of
reals to the variables X such that all of the corresponding
polynomial constraints are satisfied. CLP(QS) uses a variety of
polynomial solvers including CLP(R), SAT Modulo Theories,
quantifier elimination by Cylindrical Algebraic Decomposition,
and geometric constraint solvers.
Projection. A point is projected onto a line using the dot
product. This is extended to segment-line projection by projecting
both end points. Polygons are projected onto lines by
projecting all vertices and taking the maximum and minimum
projected values as the projected interval. Points are projected
onto segments by clamping the projected value to lie within
the projection of the segment and the line collinear with the
segment, i.e. let v; a; b be reals such that a b then
Euclidean distance. We employ CLP(QS) Euclidean distances
between points, and between points and segments
Relative Orientation. We employ CLP(QS) relative orientation
predicates between points and lines.
A- Rules for Linear Ordering as Constraints
B- Qualitative Cyclic Ordering
C- Orientation Relations.