• The KIPS Transactions:PartA
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• v.10A no.6
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• pp.665-670
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• 2003

In the applications like automatic masks generation for semiconductor production, a drawing consists of lots of polygons that are partitioned into trapezoids. The addition/deletion of a polygon to/from the drawing is performed through geometric operations such as insertion, deletion, and search of trapezoids. Depending on partitioning algorithm being used, a polygon can be partitioned differently in terms of shape, size, and so on. So, It's necessary to invent some comparison algorithm of sets of trapezoids in which each set represents interested parts of a drawing. This comparison algorithm, for example, may be used to verify a software program handling geometric objects consisted of trapezoids. In this paper, given k sets of trapezoids in which each set forms the regions of interest of each drawing, we present how to compare the k sets to see if all k sets represent the same geometric scene. When each input set has the same number n of trapezoids, the algorithm proposed has O(2$^{k-2}$ $n^2$(log n＋k)) time complexity. It is also shown that the algorithm suggested has the same time complexity O( $n^2$ log n) as the sweeping-based algorithm when the number k(<< n) of input sets is small. Furthermore, the proposed algorithm can be kn times faster than the sweeping-based algorithm when all the trapezoids in the k input sets are almost the same.