Computing Realistic Terrains from Imprecise Elevations

Abstract: In the imprecise 2.5D terrain model, each vertex of a triangulated terrain has precise x- and y-coordinates, but the elevation (z-coordinate) is an imprecise value only known to lie within some interval. The goal is to choose elevation values from the intervals so that the resulting precise terrain is "realistic" as captured by some objective function. We consider four objectives: #1 minimizing local extrema; #2 optimizing coplanar features; #3 minimizing surface area; #4 minimizing maximum steepness. We also consider the problems down a dimension in 1.5D, where a terrain is a poly-line with precise x-coordinates and imprecise y-coordinate elevations. In 1.5D we reduce problems #1, #3, and #4 to a shortest path problem, and show that problem #2 can be 2-approximated via a minimum link path. In 2.5D, problem #1 was proved NP-hard by Gray et al.~[Computational Geometry, 2012]. We give a polynomial time algorithm for a triangulation of a polygon. We prove that problem #2 is strongly N.... https://www.cgt-journal.org/index.php/cgt/article/view/29

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Computing Realistic Terrains from Imprecise Elevations ; volume:2 ; number:2 ; year:2023 ; Computing in Geometry and Topology ; 2, Heft 2 (2023)

Contributors, Places and Time

• Creator: Lubiw, Anna ; Stroud, Graeme

Further information

• DOI: 10.57717/cgt.v2i2.29
• URN: urn:nbn:de:101:1-2023090216541402931578
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:44 AM CEST