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TERRAIN APPROXIMATION BY FIXED GRID POLYNOMIAL
Author(s) -
Segu W. P.
Publication year - 1985
Publication title -
the photogrammetric record
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.638
H-Index - 51
eISSN - 1477-9730
pISSN - 0031-868X
DOI - 10.1111/j.1477-9730.1985.tb00525.x
Subject(s) - least squares function approximation , mathematics , interpolation (computer graphics) , residual , polynomial , terrain , grid , chebyshev nodes , degree (music) , explained sum of squares , degree of a polynomial , generalized least squares , lack of fit sum of squares , total least squares , polynomial interpolation , polynomial regression , multivariate interpolation , chebyshev polynomials , mathematical analysis , geometry , statistics , algorithm , linear interpolation , non linear least squares , computer science , regression analysis , geography , computer graphics (images) , estimator , bilinear interpolation , acoustics , animation , physics , cartography
A method of describing terrain by a fixed grid polynomial is described. The method employs a Chebyshev polynomial with a least squares criterion of fit. The least squares fit is carried out on an iterative basis to a prescribed degree of fit, either of a root mean square residual, or of a standard deviation of the fitted surface, or of a percentage of the total sum of squares of the residuals. The fitting data overlap along the common boundaries of the grids. Interpolation at any new point is carried out patchwise. An application of the method in highway engineering is described.