Korean Journal of Computational Design and Engineering (한국CDE학회논문집)

Society for Computational Design and Engineering (한국CDE학회)
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Efficient Sphere Partition Method for Finding the Maximum Intersection of Spherical Convex Polygons

구 볼록 다각형들의 최대 교차를 찾기 위한 효율적인 구 분할 방식

  • 하종성 (우석대학교 정보통신컴퓨터공학부)
  • Published : 2001.06.01
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Abstract

The maximum intersection of spherical convex polygons are to find spherical regions owned by the maximum number of the polygons, which is applicable for determining the feasibility in manufacturing problems such mould design and numerical controlled machining. In this paper, an efficient method for partitioning a sphere with the polygons into faces is presented for the maximum intersection. The maximum intersection is determined by examining the ownerships of partitioned faces, which represent how many polygons contain the faces. We take the approach of edge-based partition, in which, rather than the ownerships of faces, those of their edges are manipulated as the sphere is partitioned incrementally by each of the polygons. Finally, gathering the split edges with the maximum number of ownerships as the form of discrete data, we approximately obtain the centroids of all solution faces without constructing their boundaries. Our approach is analyzed to have an efficient time complexity Ο(nv), where n and v, respectively, are the numbers of polygons and all vertices. Futhermore, it is practical from the view of implementation since it can compute numerical values robustly and deal with all degenerate cases.

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