TY - GEN

T1 - Computing depth orders and related problems

AU - Agarwal, Pankaj K.

AU - Katz, Matthew J.

AU - Sharir, Micha

N1 - Publisher Copyright:
© 1994, Springer Verlag. All rights reserved.

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0012681941&partnerID=8YFLogxK

U2 - 10.1007/3-540-58218-5_1

DO - 10.1007/3-540-58218-5_1

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AN - SCOPUS:0012681941

SN - 9783540582182

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 1

EP - 12

BT - Algorithm Theory – SWAT 1994 - 4th Scandinavian Workshop on Algorithm Theory, Proceedings

A2 - Schmidt, Erik M.

A2 - Skyum, Sven

PB - Springer Verlag

T2 - 4th Scandinavian Workshop on Algorithm Theory, SWAT 1994

Y2 - 6 July 1994 through 8 July 1994

ER -