Natural-neighbour interpolation (Sibson and Laplace coordinates)
Source:R/NaturalNeighbour.R
NaturalNeighbourWeights.RdNaturalNeighbourWeights: Sibson (area-stealing) or Laplace
(non-Sibsonian: facet length over distance) coordinates of a query point,
positive only on its natural neighbours, summing to one and reproducing
linear functions. NnInterpolate: \(f(x) = \sum_i w_i z_i\), with the
natural-neighbour variance and the bounds of the neighbours' values;
NA outside the convex hull unless outside = "extrapolate".
NnGradientInterpolate: \(\sum_i w_i (z_i + g_i \cdot (x - x_i))\)
with gradients from inverse-squared-distance weighted planes through each
datum and its natural neighbours. NnCrossValidation: leave-one-out
predictions and RMSE. NnInDomain: the convex-hull domain (Sibson 1981;
Belikov et al. 1997; Watson 1992). Identical to the Python arm
morie.fn.natnbr; weight names are 1-based point indices.
Usage
NaturalNeighbourWeights(points, x, method = "sibson")
NnInterpolate(points, values, xs, method = "sibson", outside = "nan")
NnGradientInterpolate(points, values, xs, method = "sibson")
NnCrossValidation(points, values, method = "sibson")
NnInDomain(points, xs)References
Sibson, R. (1981). A brief description of natural neighbour interpolation. In V. Barnett (ed.), Interpreting Multivariate Data, 21-36. Wiley.
Belikov, V. V. et al. (1997). The non-Sibsonian interpolation: a new method of interpolation of the values of a function on an arbitrary set of points. Computational Mathematics and Mathematical Physics 37, 9-15.
Watson, D. F. (1992). Contouring: A Guide to the Analysis and Display of Spatial Data. Pergamon.