Approximating centroids for the maximum intersection of spherical polygons

Authors:
Jong-Sung Ha;Kwan-Hee Yoo
Affiliations:
Department of Computer Engineering, Woosuk University, 490 Hujongri, Samrae-Up, Wanju-Kun, Chonbuk 565-701, South Korea;Department of Computer Education and Dept. of Information Industrial Engineering, Chungbuk National University, San 48 Gaesin-Dong, Cheongju Chungbuk 361-763, South Korea
Venue:
Computer-Aided Design
Year:
2005

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Abstract

This paper considers the problem of investigating the spherical regions owned by the maximum number of spherical polygons. We present a practical O(n(v+I)) time algorithm for finding the approximating centroids for the maximum intersection of spherical polygons, where n, v, and I are, respectively, the numbers of polygons, all vertices, and intersection points. In order to elude topological errors and handle geometric degeneracies, our algorithm takes the approach of edge-based partitioning of the sphere. Furthermore, the numerical complexity is avoided since the algorithm is completely spherical.