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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.
The relations are n − 1 linear equations for the n + 1 values k 0, k 1, ..., k n. For the elastic rulers being the model for the spline interpolation, one has that to the left of the left-most "knot" and to the right of the right-most "knot" the ruler can move freely and will therefore take the form of a straight line with q′′ = 0.
Spline interpolation — interpolation by piecewise polynomials Spline (mathematics) — the piecewise polynomials used as interpolants; Perfect spline — polynomial spline of degree m whose mth derivate is ±1; Cubic Hermite spline. Centripetal Catmull–Rom spline — special case of cubic Hermite splines without self-intersections or cusps
1 Mathematics (Geometry) Toggle Mathematics (Geometry) subsection ... This is a list of Wikipedia articles about curves used in different fields: ... Splines. B-spline;
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
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.