Crate uniform_cubic_splines

Uniform cubic spline interpolation & inversion.

This crate supports the following types of splines:

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

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.

Cargo Features

• monotonic_check – The spline_inverse() code will check if the knot vector is monotonic (on by default).

The crate does not depend on the standard library (i.e. is marked no_std).

Example

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

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

// 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, None, None).unwrap();
let y = spline::<CatmullRom, _, _>(v, &knots);

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

Background

The code is a Rust port of the resp. implementations 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.

Modules

• basis

Functions

• is_len_ok
  Returns true if a knots slice you want to feed into spline() has the correct length for the choosen Basis.
• spline
  As x varies from 0 to 1, this function returns the value of a cubic interpolation of uniformly spaced knots. The input value x will be clamped to the range [0, 1].
• spline_inverse
  Computes the inverse of the spline() function. This returns the value x for which spline(x) would return y.