uniform-cubic-splines

Uniform cubic spline interpolation & inversion.

This crate supports the following types of splines:

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

Curve widget 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.

[dependencies]
uniform-cubic-splines = { version = "0.3" }

Example

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

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

// 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);

Features

• monotonic_check -- The spline_inverse()/spline_inverse_with() code will check if the knot vector is monotonic (enabled by default).

f16 & f128 Support

This crate supports f16 and f128 types on a nightly toolchain if you use this repository as an overlay in your Cargo.toml.

[patch.crates-io]
uniform-cubic-splines = {
    git = "https://github.com/virtualritz/uniform-cubic-splines.git"
}

This will be supported without an overlay once this PR on num-traits is merged and published.

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.

Speed

The code was originally a faithful but idiomatic Rust port of the C++ source. It was optimized quite a bit afterwards. The optimized code is in version 0.3.3 of the crate and after.

For perspective, the current version's spline() function is about twice as fast and the spline_inverse() up to 3.5 times as fast as the original, faithful Rust port.

Benchmarks

Points	spline()	spline_inverse()
10	15.5 ns	95 ns
50	16.4 ns	181.2 ns
100	16.8 ns	277.7 ns
500	20.6 ns	1.275 µs

These were taken on Ubuntu 25.04 with rustc 1.89.0-nightly and target_cpu = "native" on an AMD Ryzen 7 6800H laptop.