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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.
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spatial rules to define orientation, linear ordering, and cyclic ordering of spatial objects in sketch maps
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