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A description of linear interpolation can be found in the ancient Chinese mathematical text called The Nine Chapters on the Mathematical Art (九章算術), [1] dated from 200 BC to AD 100 and the Almagest (2nd century AD) by Ptolemy. The basic operation of linear interpolation between two values is commonly used in computer graphics.
In numerical analysis and approximation theory, basis functions are also called blending functions, because of their use in interpolation: In this application, a mixture of the basis functions provides an interpolating function (with the "blend" depending on the evaluation of the basis functions at the data points).
Trilinear interpolation is the extension of linear interpolation, which operates in spaces with dimension =, and bilinear interpolation, which operates with dimension =, to dimension =. These interpolation schemes all use polynomials of order 1, giving an accuracy of order 2, and it requires 2 D = 8 {\displaystyle 2^{D}=8} adjacent pre-defined ...
In the mathematical subfield of numerical analysis, a B-spline or basis spline is a spline function that has minimal support with respect to a given degree, smoothness, and domain partition. Any spline function of given degree can be expressed as a linear combination of B-splines of that degree.
Radial basis function (RBF) interpolation is an advanced method in approximation theory for constructing high-order accurate interpolants of unstructured data, possibly in high-dimensional spaces. The interpolant takes the form of a weighted sum of radial basis functions .
The figure also includes the radial basis functions φ = exp(−r 2) which gives a good interpolation as well. Finally, the figure includes also the non-polyharmonic spline phi = r 2 to demonstrate, that this radial basis function is not able to pass through the predefined points (the linear equation has no solution and is solved in a least ...
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In computer graphics, hierarchical RBF is an interpolation method based on radial basis functions (RBFs). Hierarchical RBF interpolation has applications in the construction of shape models in 3D computer graphics (see the Stanford bunny image below), treatment of results from a 3D scanner, terrain reconstruction, and others.