![]() ![]() ![]() Weiser & Zarantonello (1988), "A Note on Piecewise Linear and Multilinear Table Interpolation in Many Dimensions", Mathematics of Computation 50 (181), p.If a reference-counting scheme is used for the memory containing the underlying data, an optional reference-counting type may be passed as a template parameter.įor a description of the two interpolation algorithms, see: The underlying data may be shared or copied. The number type is user-specified as a template parameter. Compared to the multilinear algorithm, this becomes much faster in higher dimensions, at the cost of decreased accuracy (since less neighboring points are used to control the interpolated value). Each hypercube of the rectangular grid is split into simplices the simplex containing a point x is determined by sorting the coordinates of x. Simplicial: This uses the values at the N+1 vertices of the N-dimensional simplex containing the point.In two dimensions, this is equivalent to bilinear interpolation in 3 dimensions, trilinear, etc. Multilinear: This uses the values at the 2^N vertices of the N-dimensional hypercube containing the point.Two algorithms for computing the interpolated value are available: Arbitrary dimensions are supported, but the number of dimensions must be specified as a template parameter at compile time. For interpolation on unstructured data, take a look at delaunay_linterp. Gridding is the process of converting irregularly spaced data to a regular grid (gridded data).Linterp is a C++ header-only library for N-dimensional linear interpolation on a rectangular grid, similar to Matlab's interpn command. Radial basis function ( Polyharmonic splines are a special case of radial basis functions with low degree polynomial terms).Polyharmonic spline (the thin-plate-spline is a special case of a polyharmonic spline).tetrahedron) interpolation (see barycentric coordinate system) ![]() Triangulated irregular network-based linear interpolation (a type of piecewise linear function).Triangulated irregular network-based natural neighbor.They should all work on a regular grid, typically reducing to another known method. Schemes defined for scattered data on an irregular grid are more general. The cubic Hermite spline article will remind you that C I N T x ( f − 1, f 0, f 1, f 2 ) = b ( x ) ⋅ ( f − 1 f 0 f 1 f 2 ) -dimensional summation. Tensor product splines for N dimensions Ĭatmull-Rom splines can be easily generalized to any number of dimensions. See also Padua points, for polynomial interpolation in two variables. The colours represent the interpolated values. Three of the methods applied on the same dataset, from 25 values located at the black dots. ![]()
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