Minimum curvature

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Minimum curvature

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Minimum curvature is similar to bi-cubic spline fitting, in that the surface is modeled assuming that a smooth elastic-like membrane is used to approximate the surface. However, the interpolation is not exact, but close to exact, and is designed to ensure that the amount of surface curvature is as small as possible. This is achieved through a multi-stage process. As mentioned in Section 6.6.10, Polynomial regression, the first stage is simple linear regression and extraction of residuals. The procedure uses these residuals for interpolation rather than the original data points, but then it adds the regression surface data values back on completion. The interpolation process itself involves an iterative procedure that seeks to smooth the interpolated grid to a pre-specified parameter setting using a grid which is progressively made increasingly fine. The procedure is quite complex and is described in detail in Smith and Wessel (1990).