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  "body": "\n## Summary\n\nMultivariate interpolation is the construction of a function of several variables that takes given values at given points of $\\R^d$ with $d \\ge 2$.\nIn one variable, polynomials of degree at most $n$ always interpolate uniquely at $n + 1$ distinct points.\nIn several variables, this depends on the position of the points, see [[unisolvent point set|5276MDSDQV]].\nFor gridded data one uses tensor products of one-dimensional methods, such as bilinear and bicubic interpolation.\nFor scattered data one uses methods adapted to the points, such as [[radial basis function interpolation|XZ33P3HBB9]], [[inverse distance weighting|QHN67MSH8S]], [[moving least squares|T0JZN6WP5X]] and [[kriging|VP9S3PNJQ0]].\n\n## Explanations\n\n### L1 human\n\nImagine temperature readings taken at weather stations scattered over a country.\nMultivariate interpolation fills in a temperature map that agrees with the readings at the stations.\nOn a regular grid one can interpolate first along rows and then along columns.\nFor example, bilinear interpolation on the unit square with corner values $f_{00}, f_{10}, f_{01}, f_{11}$ gives $f_{00}(1 - x)(1 - y) + f_{10} x (1 - y) + f_{01} (1 - x) y + f_{11} x y$.\nFor scattered stations other methods are needed.\nThe [[definition|C4B5FB6A34]] states the problem.\n",
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