Acta Geodaetica et Cartographica Sinica

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Boolean Operations on Polygons by Using Trapezoidal Decomposition

  

  • Received:2009-09-25 Revised:2010-08-06 Online:2011-02-25 Published:2011-02-25

Abstract: Boolean operations on planar polygons, including “Union”, ”Erase”, “Identity”, “Intersect”, etc., are fundemental operations in GIS to extract new information which may contribute to resolve geological application problems. In this paper, a new algorithm for Boolean operations is presented, which incorporates trapezoidal decomposition. The decomposition of polygons into trapezoids has been studied in the area of computer graphics. It is comparatively easier to process a simple shape like a trapezoid than a polygon. However, so far it has seldom been used into GIS applications. In the proposed method, the involved polygons are decomposed into two sets of trapezoids by the sweep-line, therefore Boolean operations on polygons are transformed into the Boolean operations on the decomposed trapezoids. Since these trapezoids are organized and stored by row, thus the Boolean operations between them are confined within one row; in consequence, the computation efficiency could be improved effectively. Once the resulting set of trapezoids is obtained by implementing Boolean operations on the two original sets of trapezoids, the resulting polygons need to be constructed by means of boundary tracing. The proposed method avoids the complex computation of spatial relationship between polygons’ edges in most vector algorithms for Boolean operation, thus making the whole procedures more efficient and understandable. In addition, by adopting multi-attribute condition extraction, this method could realize various Boolean operations in a unified way, without the necessity of designing respective methods targeting at each operation.