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Publications [#235397] of Pankaj K. Agarwal

Papers Published

  1. Agarwal, PK; Katz, MJ; Sharir, M, Computing depth orders for fat objects and related problems, Computational Geometry, vol. 5 no. 4 (1995), pp. 187-206, ISSN 0925-7721
    (last updated on 2017/12/16)

    Abstract:
    Let K be a set of n non-intersecting objects in 3-space. A depth order of K, if it exists, is a linear order < of the objects in K such that if K, L ε{lunate} K and K lies vertically below L then K < L. We present a new technique for computing depth orders, and apply it to several special classes of objects. Our results include: (i) If K is a set of n triangles whose xy-projections are all 'fat', then a depth order for K can be computed in time O(n log5n). (ii) If K is a set of n convex and simply-shaped objects whose xy-projections are all 'fat' and their sizes are within a constant ratio from one another, then a depth order for K can be computed in time O(nλs 1 2(n) log4n), where s is the maximum number of intersections between the boundaries of the xy-projections of any pair of objects in K, and λs(n) is the maximum length of (n,s) Davenport-Schinzel sequences. © 1995.

 

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