Splines`

SplineFit

As of Version 7.0, some of the functionality of the Splines Package is now built into the Wolfram Language kernel. »

SplineFit[{pt₁,pt₂,…},type]

generates a SplineFunction object of the specified type from the points pt₁,pt₂,….

Details and Options

To use SplineFit, you first need to load the Splines Package using Needs["Splines`"].
A SplineFunction object is a function that parametrizes a curve specified by the points pt₁,pt₂,…, such that an argument of 0 corresponds to pt₁, 1 corresponds to pt₂, 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 n–1 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 pt₁,pt₂,… are not restricted to two dimensions.

SplineFit returns a SplineFunction of the appropriate type:

Fit three types of splines to a random set of five points:

Plot the resulting splines:

SplineFit works in arbitrary dimensions:

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