Uniform Cubic Spline Interpolation & Inversion

This crate supports the following types of splines:

• B-spline
• Bezier
• Catmull-Rom
• Hermite
• Linear
• Power

UI with a 1D Catmull-Rom spline with non-uniform knot spacing and knot multiplicity using this crate for interpolation (drawn using tiny-skia).

The crate uses generics to allow interpolation of any type for which certain traits are defined.

I.e. you can use this crate to interpolate splines in 1D, 2D, 3D, etc.

Example

Using a combination of spline() and spline_inverse() it is possible to compute a full spline-with-nonuniform-abscissæ:

use uniform_cubic_splines::{
    spline, spline_inverse, basis::CatmullRom
};

// We want to evaluate the spline at knot value 0.3.
let x = 0.3;

// The first and last points are never interpolated.
let knot_spacing = [0.0, 0.0, 0.1, 0.3, 1.0, 1.0];
let knots        = [0.0, 0.0, 1.3, 4.2, 3.2, 3.2];

let v = spline_inverse::<CatmullRom, _>(x, &knot_spacing).unwrap();
let y = spline::<CatmullRom, _, _>(v, &knots);

assert!(y - 4.2 < 1e-6);

Background

The code is a Rust port of the implementation found in the Open Shading Language C++ source.

If you come from a background of computer graphics/shading languages used in offline rendering this crate should feel like home.