Function Repository Resource:

# LeeInterpolatingNodes

Generate interpolating nodes from points on a curve

Contributed by: Jan Mangaldan
 ResourceFunction["LeeInterpolatingNodes"][{{x1,y1,…},{x2,y2,…},…}] yields centripetal interpolating nodes suitable for use with Interpolation from points assumed to be lying on a space curve. ResourceFunction["LeeInterpolatingNodes"][{{x1,y1,…},{x2,y2,…},…},a] yields Lee's interpolating nodes with parameter a.

## Details

The parameter a is usually taken to be between 0 and 1.
Typical values of a used are:
 0 uniform parametrization 1/2 centripetal parametrization 1 chord length parametrization

## Examples

### Basic Examples (3)

Generate centripetal interpolating nodes from a given set of points:

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Use Interpolation to get an interpolating curve:

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Plot the curve along with the original points:

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### Scope (3)

A set of 3D points:

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Generate an interpolating curve with uniform parametrization:

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Generate an interpolating curve with chord length parametrization:

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### Applications (3)

A set of 3D points:

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Generate the corresponding knots and control points for a B-spline curve:

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Visualize the B-spline curve and the points:

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### Neat Examples (1)

Demonstrate the effect of varying the parameter for the Lee interpolating nodes:

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## Version History

• 1.0.0 – 05 April 2021