Abstract
We study optimization problems in an imprecision model for polyhedral terrains. An imprecise terrain is given by a triangulated point set where the height component of the vertices is specified by an interval of possible values. We restrict ourselves to 1.5-dimensional terrains: an imprecise terrain is given by an x-monotone polyline, and the y-coordinate of each vertex is not fixed but constrained to a given interval. Motivated by applications in terrain analysis, in this paper we present two linear-time approximation algorithms, for minimizing the largest turning angle and for maximizing the smallest one. In addition, we also provide linear time exact algorithms for minimizing and maximizing the sum of the turning angles.
This research was partially supported by the Netherlands Organisation for Scientific Research (NWO) through the project GOGO and project no. 639.023.301. A preliminary version of this paper was presented at the 24th European Workshop on Computational Geometry (EuroCG 2008), under the title “Smoothing imprecise 1-dimensional terrains”.
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Gray, C., Löffler, M., Silveira, R.I. (2009). Smoothing Imprecise 1.5D Terrains. In: Bampis, E., Skutella, M. (eds) Approximation and Online Algorithms. WAOA 2008. Lecture Notes in Computer Science, vol 5426. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-93980-1_17
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DOI: https://doi.org/10.1007/978-3-540-93980-1_17
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