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I/o-efficient efficient algorithms for computing contours on a terrain

Authors:

Pankaj K. Agarwal,

Thomas Mølhave,

Bardia SadriAuthors Info & Claims

SCG '08: Proceedings of the twenty-fourth annual symposium on Computational geometry

Pages 129 - 138

https://doi.org/10.1145/1377676.1377698

Published: 09 June 2008 Publication History

Abstract

A terrain M is the graph of a bivariate function. We assume that M is represented as a triangulated surface with N vertices. A contour (or isoline) of M is a connected component of a level set of M. Generically, each contour is a closed polygonal curve; at "critical" levels these curves may touch each other or collapse to a point. We present I/O efficient algorithms for the following two problems related to computing contours of M:

(i) Given a sequence l₁ < ... < l_s of real numbers, we present an I/O-optimal algorithm that reports all contours of M at heights l₁, ..., l_s using O(sort(N) + T/B) I/Os, where T is the total number edges in the output contours, B is the "block size," and sort(N) is the number of I/Os needed to sort N elements. The algorithm uses O(N/B) disk blocks. Each contour is generated individually with its composing segments sorted in clockwise or counterclockwise order. Moreover, our algorithm generates information on how the contours are nested.

(ii) We can preprocess M, using O(sort(N)) I/Os, into a linear-size data structure so that all contours at a given height can be reported using O(log_B N + T/B) I/Os, where T is the output size. Each contour is generated individually with its composing segments sorted in clockwise or counterclockwise order.

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Cited By

Agarwal DPuri SPrasad S(2018)Crayons: Empowering CyberGIS by Employing Cloud InfrastructureCyberGIS for Geospatial Discovery and Innovation10.1007/978-94-024-1531-5_7(115-141)Online publication date: 27-Jun-2018
https://doi.org/10.1007/978-94-024-1531-5_7
Toma L(2014)Terrain Modeling for the GeosciencesComputing Handbook, Third Edition10.1201/b16812-36(1-22)Online publication date: 8-May-2014
https://doi.org/10.1201/b16812-36
Agarwal D(2012)CrayonsProceedings of the 2012 SC Companion: High Performance Computing, Networking Storage and Analysis10.1109/SC.Companion.2012.315(1542-1543)Online publication date: 10-Nov-2012
https://dl.acm.org/doi/10.1109/SC.Companion.2012.315
Show More Cited By

Index Terms

I/o-efficient efficient algorithms for computing contours on a terrain
1. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Conferences

SCG '08: Proceedings of the twenty-fourth annual symposium on Computational geometry

June 2008

304 pages

ISBN:9781605580715

DOI:10.1145/1377676

Program Chair:
Monique Teillaud
INRIA Sophia Antipolis - Méditerranée, France

Copyright © 2008 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 09 June 2008

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SoCG08

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SoCG08: 24th Annual Symposium on Computational Geometry

June 9 - 11, 2008

MD, College Park, USA

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Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Cited By

Agarwal DPuri SPrasad S(2018)Crayons: Empowering CyberGIS by Employing Cloud InfrastructureCyberGIS for Geospatial Discovery and Innovation10.1007/978-94-024-1531-5_7(115-141)Online publication date: 27-Jun-2018
https://doi.org/10.1007/978-94-024-1531-5_7
Toma L(2014)Terrain Modeling for the GeosciencesComputing Handbook, Third Edition10.1201/b16812-36(1-22)Online publication date: 8-May-2014
https://doi.org/10.1201/b16812-36
Agarwal D(2012)CrayonsProceedings of the 2012 SC Companion: High Performance Computing, Networking Storage and Analysis10.1109/SC.Companion.2012.315(1542-1543)Online publication date: 10-Nov-2012
https://dl.acm.org/doi/10.1109/SC.Companion.2012.315
Agarwal DPuri SHe XPrasad S(2012)A System for GIS Polygonal Overlay Computation on Linux Cluster - An Experience and Performance ReportProceedings of the 2012 IEEE 26th International Parallel and Distributed Processing Symposium Workshops & PhD Forum10.1109/IPDPSW.2012.180(1433-1439)Online publication date: 21-May-2012
https://dl.acm.org/doi/10.1109/IPDPSW.2012.180
Huttunen JStark P(2012)Cheap contouring of costly functions: the Pilot Approximation Trajectory algorithmComputational Science & Discovery10.1088/1749-4699/5/1/0150065:1(015006)Online publication date: 30-Aug-2012
https://doi.org/10.1088/1749-4699/5/1/015006
Arge LDeleuran LMølhave TRevsbæk MTruelsen J(2012)Simplifying massive contour mapsProceedings of the 20th Annual European conference on Algorithms10.1007/978-3-642-33090-2_10(96-107)Online publication date: 10-Sep-2012
https://dl.acm.org/doi/10.1007/978-3-642-33090-2_10
Agarwal PMølhave TSadri BRandall D(2011)I/O-efficient contour queries on terrainsProceedings of the twenty-second annual ACM-SIAM symposium on Discrete algorithms10.5555/2133036.2133059(268-284)Online publication date: 23-Jan-2011
https://dl.acm.org/doi/10.5555/2133036.2133059

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