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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 ...
Single knots at 1/3 and 2/3 establish a spline of three cubic polynomials meeting with C 2 parametric continuity. Triple knots at both ends of the interval ensure that the curve interpolates the end points. In mathematics, a spline is a function defined piecewise by polynomials.
In these applications, each coordinate of the plane or space is separately interpolated by a cubic spline function of a separate parameter t. Cubic polynomial splines are also used extensively in structural analysis applications, such as Euler–Bernoulli beam theory. Cubic polynomial splines have also been applied to mortality analysis [2] and ...
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.
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 modified to ensure the monotonicity of the resulting Hermite spline.
The resulting function is called a spline. For instance, the natural cubic spline is piecewise cubic and twice continuously differentiable. Furthermore, its second derivative is zero at the end points. The natural cubic spline interpolating the points in the table above is given by
This is a list of Wikipedia articles about curves used in ... Splines. B-spline; Nonuniform rational B-spline ... An elementary treatise on cubic and quartic curves ...
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]