Approximation of Surface Texture Profiles

In this paper we are interested in the approximation of continuous surface texture profiles defined only at discretely obtained points. A continuous representation is required in order to be able to apply filtration methods that assume uniform data spacing to practical data that in general is not uniformly spaced. By reconstructing surface profiles as natural cubic spline interpolants accurately using numerically stable fitting algorithms, we can provide a mathematically sound basis on which to compute surface texture profile parameters. As an important direct benefit, parameters involving the integrals of surface profiles can be calculated directly from the spline interpolant. Examples are given to illustrate the advantages of using this reconstruction method.