Direction Similarity Calculation For Vector Polygonal Groups

As one kind of spatial relationship, spatial similarity relationship is an important theoretical problem of GIS. For spatial similarity relationship can reveal the deeper information of geographical entity. Due to the diversity of studied objects(spatial group objects) and research contents(topology similarity, distance similarity and direction similarity) of space similarity relationship, the calculation of spatial similarity needs to complex analyses.In light of this, on the basis of studied existing methods of similarity calculation in-depth, takes vector polygonal groups as the studied target, and proposes a method to calculate the similarity of vector polygons’ direction. The specific work includes the following five areas:(1) Collapse of vector polygonal groupsIt is difficult to calculate the direction of two-dimensional surface targets directly, so adopts the idea of collapse to process vector polygonal groups. From the perspective of geometry, vector polygonal groups can be regard as polygons, and can be divided to regular polygons or irregular polygons. For regular polygon, in order to realize collapse using method of generating its minimum area of MBR, with its long axis direction represents the direction of the regular polygon; for irregular polygon, using method of generating its Convex Hull, with the direction of Convex Hull’s diameter represents the direction of the irregular polygon.(2) Selection of Convex Hull’s diametersAfter collapse, irregular polygon generates Convex Hull’s diameter, a Convex Hull may have more than one diameter, it may cause uncertain of calculation results. Thence, design Convex Hull’s diameter selection method, select qualified diameter to represent the direction of vector polygonal groups.(3) Selection of polygon’s directionAfter collapse polygon changes to line, a line has two directions to choose. In order to avoid the value of directions not unique in similarity calculation combines the cognition difference between the direction of line and polygon; set the direction range of the polygon to generate the appropriate direction vector.(4) Direction similarity calculation for vector polygonal groupsIntegrates the shape and structure feature of polygons, adds weights for the direction vector, according to the parallelogram law of vector computing, integrate direction vector of each polygons into vector of polygonal groups. Calculate the angle between the direction vector of polygonal groups and the horizontal, and then calculate the direction similarity between two polygonal groups by Trigonometric function.(5) Experimental verificationAccording to the proposed method before, experiments are respectively designed for continuous and discrete polygonal groups to calculate the direction similarity, combine with people’s habits of direction similarity cognitive and actual situation to verify the correctness of the method about direction similarity calculation of vector polygonal groups.The main innovations of this paper include the following two points:(1) For irregular polygons of vector polygonal groups, proposes a dimensionality reduction method through calculate and select the appropriate the Convex Hull’s diameter.(2) Integrate the structure feature of polygons, proposes a method to calculate the direction similarity of vector polygonal groups.