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Multiresolution Representation of Urban Terrain By L^1^ Splines, L^2^ Splines, and Piecewise Planar Surfaces

Published

Author(s)

J E. Lavery, David E. Gilsinn

Abstract

Cubic L1 and L2 interpolating splines based on C1 smooth piecewise cubic Sibson elements on a tensor-product grid are investigated. Computational tests were carried out for a 102.4 km area of Fort Hood, Texas represented by a 1025 x 1025 set of 100-meter-spacing(posting) DTED1 terrain data obtained from the National Imagery and Mapping Agency. L1 and L2 interpolating splines were calculated for this area using data at coarser spacings of 800 m, 1600 m, 3200 m, 6400 m, 12800 m and 25600 m. The l1 and l2 errors of the L1 spline for a given spacing. In half of the cases, the lopposition} error of the L1 spline is smaller than the lopposition} error of the corresponding L2 spline. In the other half of the cases, it is larger. Overall, this evidence indicates that L1 splines preserve shape better for this terrain data set than do L2 splines.
Proceedings Title
Proceedings 22nd Army Science Conference
Conference Dates
December 11-13, 2000
Conference Location
Baltimore, MD, US

Keywords

cubic splines, data representation, interpolation, multiresolution representation, primal affine algorithm, sibson elements, terrain modeling

Citation

Lavery, J. and Gilsinn, D. (2000), Multiresolution Representation of Urban Terrain By L^1^ Splines, L^2^ Splines, and Piecewise Planar Surfaces, Proceedings 22nd Army Science Conference, Baltimore, MD, US, [online], https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=150797 (Accessed May 31, 2023)
Created December 10, 2000, Updated October 12, 2021