Crate splinefit 

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 = "0.4.1"

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.

Performance

The pure-Rust engine matches or outperforms SciPy’s Fortran-compiled FITPACK. Benchmarks on Apple M1 (macOS), fitting and evaluating sin(x) on [0, 2π]:

1-D smoothing fit

Data points	Rust	SciPy/Fortran
50	17 µs	21 µs
200	57 µs	62 µs
1 000	279 µs	282 µs
5 000	1.35 ms	1.4 ms

1-D evaluation (10× data points)

Data points	Rust	SciPy/Fortran
50	12 µs	18 µs
200	50 µs	61 µs
1 000	254 µs	307 µs
5 000	1.27 ms	1.5 ms

2-D parametric evaluation (10× data points)

Data points	Rust	SciPy/Fortran
50	12 µs	34 µs
200	50 µs	121 µs
1 000	248 µs	611 µs

Reproduce with cargo bench (Rust) and python3 benches/scipy_bench.py (SciPy).

WebAssembly / JavaScript

This crate compiles to WebAssembly via wasm-pack. Enable the wasm feature to expose a CubicSpline class to JavaScript.

<script type="module">
  import init, { CubicSpline } from "https://esm.sh/@harbik/splinefit";
  await init();

  // Fit a smoothing spline to sin(x)
  const x = Float64Array.from({ length: 50 }, (_, i) => i * 2 * Math.PI / 49);
  const y = x.map(Math.sin);
  const spline = CubicSpline.smoothing(x, y, 0.05);

  // Evaluate at 200 points
  const xNew = Float64Array.from({ length: 200 }, (_, i) => i * 2 * Math.PI / 199);
  const yFit = spline.evaluate(xNew);

  // Integration and root-finding
  const area = spline.integral(0, Math.PI);  // ∫₀^π sin(x) dx ≈ 2
  const zeros = spline.roots();               // interior zeros
</script>

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.

All Rust source in this repository is © 2021–2026 Harbers Bik LLC, dual-licensed under:

• 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.

Re-exports

pub use curfit::*;

pub use concur::*;

pub use clocur::*;

pub use util::*;

Modules

clocur

Builder for fitting a closed (periodic) parametric B-spline curve through multi-dimensional data.

concur

Builder for fitting a parametric B-spline curve through multi-dimensional data.

curfit

evaluate

ops

Post-fit operations on SplineCurve values.

util

Structs

FitError

Type Aliases

ClosedCubicSplineFit2D

ClosedCubicSplineFit3D

ClosedLinearSplineFit2D

ClosedLinearSplineFit3D

ClosedQuinticSplineFit2D

ClosedQuinticSplineFit3D

CubicSplineFit

CubicSplineFit1D

CubicSplineFit2D

CubicSplineFit3D

LinearSplineFit

LinearSplineFit1D

LinearSplineFit2D

LinearSplineFit3D

QuinticSplineFit

QuinticSplineFit1D

QuinticSplineFit2D

QuinticSplineFit3D

Result