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Bicubic interpolation on the square [,] [,] consisting of 25 unit squares patched together. Bicubic interpolation as per Matplotlib's implementation. Colour indicates function value. The black dots are the locations of the prescribed data being interpolated. Note how the color samples are not radially symmetric.
Lagrange and other interpolation at equally spaced points, as in the example above, yield a polynomial oscillating above and below the true function. This behaviour tends to grow with the number of points, leading to a divergence known as Runge's phenomenon ; the problem may be eliminated by choosing interpolation points at Chebyshev nodes .
Multivariate interpolation is the interpolation of functions of more than one variable. Methods include nearest-neighbor interpolation, bilinear interpolation and bicubic interpolation in two dimensions, and trilinear interpolation in three dimensions. They can be applied to gridded or scattered data.
Bicubic splines (Bicubic interpolation) are often used to interpolate data on a regular rectangular grid, such as pixel values in a digital image or altitude data on a terrain. Bicubic surface patches, defined by three bicubic splines, are an essential tool in computer graphics. Cubic splines are often called csplines, especially in computer ...
In the mathematical field of numerical analysis, spline interpolation is a form of interpolation where the interpolant is a special type of piecewise polynomial called a spline. That is, instead of fitting a single, high-degree polynomial to all of the values at once, spline interpolation fits low-degree polynomials to small subsets of the ...
In numerical analysis, multivariate interpolation or multidimensional interpolation is interpolation on multivariate functions, having more than one variable or defined over a multi-dimensional domain. [1] A common special case is bivariate interpolation or two-dimensional interpolation, based on two variables or two dimensions.
Examples of algorithms for this task include New Edge-Directed Interpolation (NEDI), [1] [2] Edge-Guided Image Interpolation (EGGI), [3] Iterative Curvature-Based Interpolation (ICBI), [citation needed] and Directional Cubic Convolution Interpolation (DCCI). [4] A study found that DCCI had the best scores in PSNR and SSIM on a series of test ...
In the mathematical field of numerical analysis, monotone cubic interpolation is a variant of cubic interpolation that preserves monotonicity of the data set being interpolated. Monotonicity is preserved by linear interpolation but not guaranteed by cubic interpolation .