CubicSpline

A performant cubic spline.

Usage

    import CubicSpline
    import CubicSplineUI

    let points:[SIMD2<Double>] = [[0.0,0.9],[0.3,1.0],[0.7,0.0],[0.9,0.6],[1.4,0.6],[2,1.0]]
    
    let spline = CubicSpline(points:points)

Create a SwiftUI view like this:

SplineView(spline:spline)

This view will stretch the spline to fit the available space. If that is not do exactly what you want, you can obtain a path from the spline :

let path = spline.path

This path will be in the same coordinate system as the points used to create the spline. You can then transform the path as needed and construct your own shape.

The spline is callable, with a value in the range 0...1 :

    let u = spline(t: 0.1)

You can get an array of cubic curves, which are also callable in the range 0...1:

    let curve = spline.cubicCurves.first!
    let v = curve(t: 0.5)

Closed Splines

To create a closed spline from an array of points just pass true for closed:

    let spline = CubicSpline(points:points, closed:true)

Higher Dimensions

CubicSpline also supports splines in 3 and higher dimensions. All SIMD types where the scalar is a Double will work.

Performance

$O(n)$

CubicSpline uses the Accelerate framework (or LAPack on Linux) to speed up the linear algebra. Building a spline with 10 000 points takes 0.02 s on a M1 Max Mac Pro.

Linux

I have not tested on Linux yet, but it should work. You will need install LAPack:

sudo apt-get install liblapacke-dev

Note that CubicSplineUI is not available on Linux, as it requires SwiftUI.

References

https://mathworld.wolfram.com/CubicSpline.html