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  Computing Large Planar Regions in Terrains, with an Application to Fracture Surface

Smid, M., Ray, R., Wendt, U., & Lange, K. (2004). Computing Large Planar Regions in Terrains, with an Application to Fracture Surface. Discrete Applied Mathematics, 139, 253-264.

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Datensatz-Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-295E-1 Versions-Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-295F-0
Genre: Zeitschriftenartikel

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 Urheber:
Smid, Michiel1, Autor           
Ray, Rahul1, Autor           
Wendt, Ulrich, Autor
Lange, Katharina, Autor
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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Schlagwörter: -
 Zusammenfassung: We consider the problem of computing the largest region in a terrain that is approximately contained in some two-dimensional plane. We reduce this problem to the following one. Given an embedding of a degree-3 graph $G$ on the unit sphere $\IS^2$, whose vertices are weighted, compute a connected subgraph of maximum weight that is contained in some spherical disk of a fixed radius. We give an algorithm that solves this problem in $O(n^2 \log n (\log\log n)^3)$ time, where $n$ denotes the number of vertices of $G$ or, alternatively, the number of faces of the terrain. We also give a heuristic that can be used to compute sufficiently large regions in a terrain that are approximately planar. We discuss an implementation of this heuristic, and show some experimental results for terrains representing three-dimensional (topographical) images of fracture surfaces of metals obtained by confocal laser scanning microscopy.

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Sprache(n): eng - English
 Datum: 2005-05-302004
 Publikationsstatus: Erschienen
 Seiten: -
 Ort, Verlag, Ausgabe: -
 Inhaltsverzeichnis: -
 Art der Begutachtung: Expertenbegutachtung
 Identifikatoren: eDoc: 231227
Anderer: Local-ID: C1256428004B93B8-4E3CC2F3E3C394C8C1256D1F00452FBA-Rahul2003
 Art des Abschluß: -

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Titel: Discrete Applied Mathematics
Genre der Quelle: Zeitschrift
 Urheber:
Affiliations:
Ort, Verlag, Ausgabe: -
Seiten: - Band / Heft: 139 Artikelnummer: - Start- / Endseite: 253 - 264 Identifikator: -