# 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.

### 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

### Citation Source

- Scopus