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An efficient output-sensitive hidden surface removal algorithm and its parallelization

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SCG '88: Proceedings of the fourth annual symposium on Computational geometry

Pages 193 - 200

https://doi.org/10.1145/73393.73413

Published: 06 January 1988 Publication History

Abstract

In this paper we present an algorithm for hidden surface removal for a class of polyhedral surfaces which have a property that they can be ordered relatively quickly like the terrain maps. A distinguishing feature of this algorithm is that its running time is sensitive to the actual size of the visible image rather than the total number of intersections in the image plane which can be much larger than the visible image. The time complexity of this algorithm is Ο((k +n)lognloglogn) where n and k are respectively the input and the output sizes. Thus, in a significant number of situations this will be faster than the worst case optimal algorithms which have running time Ω(n²) irrespective of the output size (where as the output size k is Ο(n²) only in the worst case). We also present a parallel algorithm based on a similar approach which runs in time Ο(log⁴(n+k)) using Ο((n + k)/log(n+k)) processors in a CREW PRAM model. All our bounds are obtained using ammortized analysis.

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Cited By

Franklin Wde Magalhães SAndrade M(2018)Data Structures for Parallel Spatial Algorithms on Large Datasets (Vision paper)Proceedings of the 7th ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data10.1145/3282834.3282839(16-19)Online publication date: 6-Nov-2018
https://dl.acm.org/doi/10.1145/3282834.3282839
Sang NGold CMiller D(2016)The topological viewshed: embedding topological pointers into digital terrain models to improve GIS capability for visual landscape analysisInternational Journal of Digital Earth10.1080/17538947.2016.11922299:12(1185-1205)Online publication date: 22-Sep-2016
https://doi.org/10.1080/17538947.2016.1192229
Floriani LMagillo P(2016)Algorithms for Visibility Computation on Terrains: A SurveyEnvironment and Planning B: Planning and Design10.1068/b1297930:5(709-728)Online publication date: 30-Nov-2016
https://doi.org/10.1068/b12979
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cover image ACM Conferences

SCG '88: Proceedings of the fourth annual symposium on Computational geometry

January 1988

403 pages

ISBN:0897912705

DOI:10.1145/73393

Chairman:
H. Edelsbrunner
Univ. of Illinois, Urbana-Champaign

Copyright © 1988 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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SIGACT: ACM Special Interest Group on Algorithms and Computation Theory

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Association for Computing Machinery

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Publication History

Published: 06 January 1988

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CG88: Symposium on Computational Geometery

June 6 - 8, 1988

Illinois, Urbana-Champaign, USA

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

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Cited By

Franklin Wde Magalhães SAndrade M(2018)Data Structures for Parallel Spatial Algorithms on Large Datasets (Vision paper)Proceedings of the 7th ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data10.1145/3282834.3282839(16-19)Online publication date: 6-Nov-2018
https://dl.acm.org/doi/10.1145/3282834.3282839
Sang NGold CMiller D(2016)The topological viewshed: embedding topological pointers into digital terrain models to improve GIS capability for visual landscape analysisInternational Journal of Digital Earth10.1080/17538947.2016.11922299:12(1185-1205)Online publication date: 22-Sep-2016
https://doi.org/10.1080/17538947.2016.1192229
Floriani LMagillo P(2016)Algorithms for Visibility Computation on Terrains: A SurveyEnvironment and Planning B: Planning and Design10.1068/b1297930:5(709-728)Online publication date: 30-Nov-2016
https://doi.org/10.1068/b12979
Jia Duan Yuan Yan Tang Chu Yu Guo Chi Fang Xian Chuan Hu (2013)Boundary expansion: An hidden surface removal method based on boundary detection for discrete points2013 International Conference on Wavelet Analysis and Pattern Recognition10.1109/ICWAPR.2013.6599301(110-114)Online publication date: Jul-2013
https://doi.org/10.1109/ICWAPR.2013.6599301
Hurtado FLöffler MMatos ISacristán VSaumell MSilveira RStaals F(2013)Terrain Visibility with Multiple ViewpointsAlgorithms and Computation10.1007/978-3-642-45030-3_30(317-327)Online publication date: 2013
https://doi.org/10.1007/978-3-642-45030-3_30
Dévai F(2011)An optimal hidden-surface algorithm and its parallelizationProceedings of the 2011 international conference on Computational science and its applications - Volume Part III10.5555/2029312.2029314(17-29)Online publication date: 20-Jun-2011
https://dl.acm.org/doi/10.5555/2029312.2029314
de Berg MGray C(2010)Computing the visibility map of fat objectsComputational Geometry: Theory and Applications10.1016/j.comgeo.2008.12.01043:4(410-418)Online publication date: 1-May-2010
https://dl.acm.org/doi/10.1016/j.comgeo.2008.12.010
Coll NMadern NSellarès J(2010)Good-visibility maps visualizationThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-009-0380-y26:2(109-120)Online publication date: 12-Jan-2010
https://dl.acm.org/doi/10.1007/s00371-009-0380-y
Ben-Moshe BCarmi PKatz M(2008)Approximating the Visible Region of a Point on a TerrainGeoinformatica10.1007/s10707-006-0017-512:1(21-36)Online publication date: 1-Mar-2008
https://dl.acm.org/doi/10.1007/s10707-006-0017-5
de Berg MGray C(2007)Computing the visibility map of fat objectsProceedings of the 10th international conference on Algorithms and Data Structures10.5555/2394893.2394925(251-262)Online publication date: 15-Aug-2007
https://dl.acm.org/doi/10.5555/2394893.2394925
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