Chebyshev Polynomial Fit for Terrain Elevation

摘要

There is currently a desire to use Chebyshev polynomials to fit terrain elevationdata. Such a fit would create a surface function that exactly fits the known elevations, and would describe an elevation at any point on that surface. This note questions the appropriateness of using Chebyshev polynomials for this purpose, as opposed to linear interpolation or use of a cubic spline. A set of elevations in one direction is used to illustrate a point that large transitions in elevation influence the coefficients in the polynomial fit and contribute spectral energy to points far from the transition area. It argues that a linear interpolation process, or a cubic spline interpolation, would be more appropriate.