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Bicubic Spline


A bicubic spline is a special case of bicubic interpolation which uses an interpolation function of the form

y(x_1,x_2)=sum_(i=1)^(4)sum_(j=1)^(4)c_(ij)t^(i-1)u^(j-1)
(1)
y_(x_1)(x_1,x_2)=sum_(i=1)^(4)sum_(j=1)^(4)(i-1)c_(ij)t^(i-2)u^(j-1)
(2)
y_(x_2)(x_1,x_2)=sum_(i=1)^(4)sum_(j=1)^(4)(j-1)c_(ij)t^(i-1)u^(j-2)
(3)
y_(x_1x_2)=sum_(i=1)^(4)sum_(j=1)^(4)(i-1)(j-1)c_(ij)t^(i-2)u^(j-2),
(4)

where c_(ij) are constants and u and t are parameters ranging from 0 to 1. For a bicubic spline, however, the partial derivatives at the grid points are determined globally by one-dimensional splines.


See also

B-Spline, Spline

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References

Press, W. H.; Flannery, B. P.; Teukolsky, S. A.; and Vetterling, W. T. Numerical Recipes in FORTRAN: The Art of Scientific Computing, 2nd ed. Cambridge, England: Cambridge University Press, pp. 118-122, 1992.

Referenced on Wolfram|Alpha

Bicubic Spline

Cite this as:

Weisstein, Eric W. "Bicubic Spline." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/BicubicSpline.html

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