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Example showing non-monotone cubic interpolation (in red) and monotone cubic interpolation (in blue) of a monotone data set. Monotone interpolation can be accomplished using cubic Hermite spline with the tangents m i {\displaystyle m_{i}} modified to ensure the monotonicity of the resulting Hermite spline.
Download QR code; Print/export Download as PDF; Printable version; In other projects ... The most familiar example is the cubic smoothing spline, ...
Dynamic cubic splines with JSXGraph; Lectures on the theory and practice of spline interpolation; Paper which explains step by step how cubic spline interpolation is done, but only for equidistant knots. Numerical Recipes in C, Go to Chapter 3 Section 3-3; A note on cubic splines; Information about spline interpolation (including code in ...
Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing , bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling , when speed is not an issue.
In applied mathematics, an Akima spline is a type of non-smoothing spline that gives good fits to curves where the second derivative is rapidly varying. [1] The Akima spline was published by Hiroshi Akima in 1970 from Akima's pursuit of a cubic spline curve that would appear more natural and smooth, akin to an intuitively hand-drawn curve.
A discrete spline is a piecewise polynomial such that its central differences are continuous at the knots whereas a spline is a piecewise polynomial such that its derivatives are continuous at the knots. Discrete cubic splines are discrete splines where the central differences of orders 0, 1, and 2 are required to be continuous. [1]
Again, suitably constrained cubic polynomial splines may have this property as well, but, being a more general concept than the very specific Wilson-Fowler spline, discussion with cubic polynomial splines customarily entail differentiation with respect to the parameter — so-called C n continuity.
English: Geometric interpretation of cubic interpolation of the black point with uniformly spaced abscissae using a Catmull-Rom spline and Lagrange basis polynomials by CMG Lee. On the left third, the yellow horizontal distance is negative as the black point is on the left of the yellow point; on the right third, the green horizontal distance ...