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The choices made in forming the extended knot vector, for example: using single knots for C n–1 continuity and spacing these knots evenly on [a,b] (giving us uniform splines) using knots with no restriction on spacing (giving us nonuniform splines) Any special conditions imposed on the spline, for example:
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.
Print/export Download as PDF; Printable version; In other projects Wikidata item; Appearance. move to sidebar hide ... Spline (mathematics) Hermite spline.
1 Mathematics (Geometry) Toggle Mathematics (Geometry) subsection ... Download as PDF; Printable version; In other projects ... Splines. B-spline;
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]
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.