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Efficient viewshed computation on terrain in external memory

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Abstract

The recent availability of detailed geographic data permits terrain applications to process large areas at high resolution. However the required massive data processing presents significant challenges, demanding algorithms optimized for both data movement and computation. One such application is viewshed computation, that is, to determine all the points visible from a given point p. In this paper, we present an efficient algorithm to compute viewsheds on terrain stored in external memory. In the usual case where the observer’s radius of interest is smaller than the terrain size, the algorithm complexity is θ(scan(n 2)) where n 2 is the number of points in an n × n DEM and scan(n 2) is the minimum number of I/O operations required to read n 2 contiguous items from external memory. This is much faster than existing published algorithms.

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Notes

  1. θ(f(n)) grows proportionally to f(n) as n → ∞. Formally, \(g(n)=\theta(f(n))\Rightarrow\exists n_0>0, c_1>c_2>0\) such that \(n>n_0\Rightarrow c_1f(n)>g(n)>c_2f(n)\). Hein [23, page 334].

  2. For 45° < α ≤ 90°, interchange x and y and use a similar idea.

  3. If the observer is close to the terrain border, the square might not be completely contained in the terrain.

  4. To compare the efficiency of our algorithm and the Haverkort et al. algorithm, we used terrain of size similar to those used by them.

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Acknowledgements

This work was partially supported by CNPq—the Brazilian Council of Technological and Scientific Development, FAPEMIG—the Research Support Foundation of the State of Minas Gerais (Brazil) and by NSF grants CCR-0306502 and DMS-0327634 and by DARPA/DSO/GeoStar.

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Authors and Affiliations

  1. DPI, Universidade Federal de Viçosa, Viçosa, Brasil

    Marcus V. A. Andrade, Salles V. G. Magalhães & Mirella A. Magalhães

  2. ECSE Dept., Rensselaer Polytechnic Institute, Troy, NY, USA

    Marcus V. A. Andrade & W. Randolph Franklin

  3. CS Dept., Rensselaer Polytechnic Institute, Troy, NY, USA

    Barbara M. Cutler

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  1. Marcus V. A. Andrade
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  2. Salles V. G. Magalhães
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  3. Mirella A. Magalhães
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Correspondence to Marcus V. A. Andrade.

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Andrade, M.V.A., Magalhães, S.V.G., Magalhães, M.A. et al. Efficient viewshed computation on terrain in external memory. Geoinformatica 15, 381–397 (2011). https://doi.org/10.1007/s10707-009-0100-9

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  • DOI: https://doi.org/10.1007/s10707-009-0100-9

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