ArcLength
2D/3D

• ArcLength[spline] returns a 1D cubic SplineFunction object approximately representing the arc length of the given spline. The spline must be a 2D or 3D SplineFunction object such as is returned by SplineFit.

• The spline must be a single SplineFunction of higher dimensionality, not a list of 1D SplineFunction objects.
• ArcLength uses NIntegrate to approximate the arc length of each segment of the spline.

Further Examples

Load the Modeler2D package.

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Create a SplineFunction representing the path between a sequence of 2D points, and evaluate it halfway between the first and second points. Each end of the spline will have zero curvature.

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The spline is a 2D parametric function, and can be plotted as such.

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Here is a spline with the ends closed upon themselves.

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Here is a spline with specific direction vectors at the ends.

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Here are all three splines shown together.

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Here is a SplineFunction with values given for the independent variable at each knot point.

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Here is the arc length of the spline, also expressed as a function of the independent variable.

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