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

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Author(s): J E. Lavery; David E. Gilsinn;
Title: Multiresolution Representation of Urban Terrain By L^1^ Splines, L^2^ Splines, and Piecewise Planar Surfaces
Published: December 11, 2000
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 l{opposition} error of the L1 spline is smaller than the l{opposition} 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: Proceedings 22nd Army Science Conference
Location: Baltimore, MD
Dates: December 11-13, 2000
Keywords: cubic splines;data representation;interpolation;multiresolution representation;primal affine algorithm;sibson elements;terrain modeling
Research Areas: Math, Modeling
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