SplineFit

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


generates a SplineFunction object of the specified type from the points .

DetailsDetails

  • 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 thirdorder 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 thirdorder 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.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

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returns a SplineFunction of the appropriate type:

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

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Plot the resulting splines:

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works in arbitrary dimensions:

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