splinefit: B-Spline Curve and Surface Fitting

A pure-Rust B-spline fitting library with an ergonomic high-level API, backed by a line-by-line Rust translation of Paul Dierckx' classic Fortran fitting library.

No Fortran compiler, no C compiler, no build-time dependencies — just Rust.

The original Fortran library was written by Paul Dierckx in the mid-1980s and remains one of the most complete and mathematically rigorous B-spline fitting libraries available. It is described in detail in his book: Curve and Surface Fitting with Splines, Oxford University Press, 1993.

Numerical output is verified against scipy, which wraps the original Fortran library.

Usage

Add this to your Cargo.toml:

[dependencies]
splinefit = "0.1.0"

Example

Fit a smoothing cubic spline to noisy data, then evaluate it:

use splinefit::{CubicSplineFit, evaluate};
use std::f64::consts::PI;

let m = 20usize;
let x: Vec<f64> = (0..m).map(|i| i as f64 * 2.0 * PI / (m - 1) as f64).collect();
let y: Vec<f64> = x.iter().map(|&xi| xi.sin()).collect();

let spline = CubicSplineFit::new(x.clone(), y)
    .smoothing_spline(0.05)
    .expect("fit failed");

let y_fit = evaluate::evaluate(&spline, &x).expect("evaluate failed");
assert!((y_fit[0] - x[0].sin()).abs() < 0.1);

Fit types

Type alias	Description
`CubicSplineFit`	Smoothing / interpolating 1-D cubic spline
`LinearSplineFit` / `QuinticSplineFit`	Same, degree 1 or 5
`CubicSplineFit2D`	Parametric cubic curve in 2-D
`CubicSplineFit3D`	Parametric cubic curve in 3-D
`ClosedCubicSplineFit2D`	Closed (periodic) parametric curve in 2-D
`ClosedCubicSplineFit3D`	Closed (periodic) parametric curve in 3-D

Each fit type exposes three methods:

Method	Description
`.interpolating_spline()`	Exact interpolation through all data points
`.smoothing_spline(rms)`	Fewest knots with RMS error ≤ `rms`
`.cardinal_spline(dt)`	Weighted least-squares on a fixed equidistant knot grid

Relationship to `dierckx-sys` and `splinify`

dierckx-sys wrapped the original Fortran sources via gfortran, requiring a Fortran compiler at build time. splinify used dierckx-sys as its backend.

This crate (splinefit) combines the high-level API from splinify with a pure-Rust translation of the Fortran engine, so it builds anywhere Rust builds with no external toolchain dependencies.

License

The original Dierckx Fortran algorithms (on which this translation is based) were downloaded from netlib.org and carry no license restrictions. Please acknowledge Paul Dierckx' work in your projects.

Apache License, Version 2.0 (LICENSE-APACHE)
MIT license (LICENSE-MIT)

at your option.

Contribution

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

splinefit 0.1.0