Computing depth orders and related problems
Published
Conference Paper
© 1994, Springer Verlag. All rights reserved. Let K: be a set of n non-intersecting objects in 3-space. A depth order of K, if exists, is a linear order < of the objects in K such that if K, L ε 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 log6 n). (ii) If K: is a set of n convex and simply-shaped objects whose xy-projections are all ‘fat’ and their sizes axe within a constant ratio from one another, then a depth order for K: can be computed in time O(nλs1/2 12 (n)log4 n), where s is the maximum number of intersections between the xy-projections of the boundaries of any pair of objects in/C.
Full Text
Duke Authors
Cited Authors
- Agarwal, PK; Katz, MJ; Sharir, M
Published Date
- January 1, 1994
Published In
Volume / Issue
- 824 LNCS /
Start / End Page
- 1 - 12
Electronic International Standard Serial Number (EISSN)
- 1611-3349
International Standard Serial Number (ISSN)
- 0302-9743
International Standard Book Number 13 (ISBN-13)
- 9783540582182
Digital Object Identifier (DOI)
- 10.1007/3-540-58218-5_1
Citation Source
- Scopus