As of Version 7.0, some of the functionality of the Splines Package is now built into the Mathematica kernel.
generates a SplineFunction object of the specified type from the points .
- To use , you first need to load the Splines Package using .
- A SplineFunction object is a function that parametrizes a curve specified by the points , such that an argument of 0 corresponds to , 1 corresponds to , etc.
- Supported types are Cubic, Bezier and CompositeBezier.
- A cubic spline is made of piecewise third-order polynomials, with continuity, and interpolates each of the points it is created from. The second derivative of the spline at the endpoints is set to 0.
- A Bézier spline interpolates only the endpoints. The other points control the spline, forming a convex hull. Given n points, a spline of degree is created.
- A composite Bézier spline is made up of a series of third-order Bézier curves with continuity. It alternates interpolating points and control points.
- In a composite Bézier spline generated from an even number of points the last two points are reversed so that the final point is interpolated and the next to last is a control point for the final segment; if the spline is generated from an odd number of points, then the final vertex is doubled.
- The points are not restricted to two dimensions.