Visibility maps of realistic terrains have linear smoothed complexity

M.T. Berg, de; H.J. Haverkort; C.P. Tsirogiannis

doi:10.1145/1542362.1542397

Visibility maps of realistic terrains have linear smoothed complexity

M.T. Berg, de, H.J. Haverkort, C.P. Tsirogiannis

Algorithms

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

2 Citations (Scopus)

Abstract

We study the complexity of the visibility map of terrains whose triangles are fat, not too steep and have roughly the same size. It is known that the complexity of the visibility map of such a terrain with n triangles is ¿(n2) in the worst case. We prove that if the elevations of the vertices of the terrain are subject to uniform noise which is proportional to the edge lengths, then the worst-case expected (smoothed) complexity is only ¿(n). This provides an explanation why visibility maps of superlinear complexity are unlikely to be encountered in practice.

Original language	English
Title of host publication	Proceedings 25th Annual ACM Symposium on Computational Geometry (SoCG'09, Aarhus, Denmark, June 8-10, 2009)
Place of Publication	New York NY
Publisher	Association for Computing Machinery, Inc
Pages	163-168
ISBN (Print)	978-1-60558-501-7
DOIs	https://doi.org/10.1145/1542362.1542397
Publication status	Published - 2009

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title = "Visibility maps of realistic terrains have linear smoothed complexity",

abstract = "We study the complexity of the visibility map of terrains whose triangles are fat, not too steep and have roughly the same size. It is known that the complexity of the visibility map of such a terrain with n triangles is ¿(n2) in the worst case. We prove that if the elevations of the vertices of the terrain are subject to uniform noise which is proportional to the edge lengths, then the worst-case expected (smoothed) complexity is only ¿(n). This provides an explanation why visibility maps of superlinear complexity are unlikely to be encountered in practice.",

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Visibility maps of realistic terrains have linear smoothed complexity. / Berg, de, M.T.; Haverkort, H.J.; Tsirogiannis, C.P.
Proceedings 25th Annual ACM Symposium on Computational Geometry (SoCG'09, Aarhus, Denmark, June 8-10, 2009). New York NY: Association for Computing Machinery, Inc, 2009. p. 163-168.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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AU - Haverkort, H.J.

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N2 - We study the complexity of the visibility map of terrains whose triangles are fat, not too steep and have roughly the same size. It is known that the complexity of the visibility map of such a terrain with n triangles is ¿(n2) in the worst case. We prove that if the elevations of the vertices of the terrain are subject to uniform noise which is proportional to the edge lengths, then the worst-case expected (smoothed) complexity is only ¿(n). This provides an explanation why visibility maps of superlinear complexity are unlikely to be encountered in practice.

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M3 - Conference contribution

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BT - Proceedings 25th Annual ACM Symposium on Computational Geometry (SoCG'09, Aarhus, Denmark, June 8-10, 2009)

PB - Association for Computing Machinery, Inc

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ER -

Visibility maps of realistic terrains have linear smoothed complexity

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