Abstract
Let H be a collection of n hyperplanes in ℝd, let A denote the arrangement of H, and let σ be a (d - 1)-dimensional algebraic surface of low degree, or the boundary of a convex body in ℝd. The zone of σ in A is the collection of cells of A crossed by σ. We show that the total number of faces bounding the cells of the zone of σ is O(n d−1 log n).
Work on this paper by the second author has been supported by Office of Naval Research Grant N00014-90-J-1284, by National Science Foundation Grant CCR-89-01484, and by grants from the U.S.-Israeli Binational Science Foundation, the G.I.F. — the German Israeli Foundation for Scientific Research and Development, and the Fund for Basic Research administered by the Israeli Academy of Sciences.
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© 1991 Springer-Verlag Berlin Heidelberg
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Aronov, B., Sharir, M. (1991). On the zone of a surface in a hyperplane arrangement. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028245
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DOI: https://doi.org/10.1007/BFb0028245
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