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C¹-continuous Terrain Reconstruction from Sparse Contours

Hormann, Kai and Spinello, Salvatore and Schröder, Peter (2002) C¹-continuous Terrain Reconstruction from Sparse Contours. ASCI Technical Report, ASCI-TR177. . (Unpublished)

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Contour lines from topographic maps are still the most common form of elevation data for the Earth’s surface and in the case of historical landscapes, they often are the only available source of information. In this paper we present a new contour interpolation method that solves this bivariate problem by considering univariate curve interpolation along the approximate gradient directions of the unknown surface. For a point between two contours the height value is computed with Hermite interpolation based on the shortest distances to the contours and height and derivative information at the contours. The surfaces generated are C¹ except at terrain characteristics such as ridges and valleys which are reconstructed as sharp features. The method also faithfully reconstructs summits, pits, and saddles and is especially well-suited for sparse sets of contours. The approach allows for an efficient numerical implementation as we demonstrate with a number of examples.

Item Type:Report or Paper (Technical Report)
Schröder, Peter0000-0002-0323-7674
Additional Information:This work was supported in part by the Deutsche Forschungsgemeinschaft under grant HO 2457/1-1. We would like to thank Nira Dyn and David Levin for inspiring discussions about terrain reconstruction and for pointing us at the work of Gregory and Delbourgo.
Group:Accelerated Strategic Computing Initiative
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)HO 2457/1-1
Series Name:ASCI Technical Report
Issue or Number:ASCI-TR177
Record Number:CaltechAUTHORS:20230209-232128443
Persistent URL:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:119122
Deposited By: George Porter
Deposited On:11 Feb 2023 02:13
Last Modified:11 Feb 2023 02:13

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