SplineFit

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 .

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  • 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.

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基本范例 (1)基本范例 (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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