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Crate spliny

Crate spliny 

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§Spliny: Working with Spline Curves

Spine curves are piecewise polynomial (parametric) curves, used for interpolation, curve fitting, and data smoothing.

Spliny is a (tiny) pure Rust library for using spline curves, based a spliny’s knots and control points in SplineCurve<K,N>, and to plot splines –currently limited to 1 and 2D splines– to check the results. It does not fit spline functions to data-sets: see the Splinify-crate for that purpose.

§Example 1: Lissajous Curve Fit

Get a spline curve for a Lissajous-dataset, with plot and JSON representation:

Lissajous curve fit plot
ⓘ
use splinify::{CubicSplineFit2D, Result};

fn lissajous(t:f64, a: f64, kx: f64, b: f64, ky: f64) -> [f64;2] {
    [
        a * (kx * t).cos(),
        b * (ky * t).sin()
    ]
}

fn main() -> Result<()> {

    // Generate Lissajous data points, with angle parameter `u`
    // ranging from 0 to 180º, with 1º-steps.
    let u: Vec<f64> = (0..=180u32).into_iter().map(|v|(v as f64).to_radians()).collect();
    let xy: Vec<f64> = u.iter().flat_map(|t|lissajous(*t,1.0, 3.0, 1.0, 5.0)).collect();

    // fit Cubic Spline with Splinify's CubicSplineFit
    let s = CubicSplineFit2D::new(u, xy)?.smoothing_spline(5e-3)?;

    // Output fit results as JSON file and plot
    println!("{}", serde_json::to_string_pretty(&s)?);
    s.plot_with_control_points("lissajous.png", (800,800))?;

    Ok(())
}

And here is its associated `Spliny`` JSON representation

{
  "t": [
    0.0, 0.0, 0.0, 0.0, 0.4014257279586958, 0.7853981633974483, 
    0.9948376736367679, 1.1868238913561442, 1.3788101090755203, 
    1.5707963267948966, 1.7802358370342162, 1.9722220547535925, 
    2.1642082724729685, 2.356194490192345, 2.7576202181510405, 
    3.141592653589793, 3.141592653589793, 3.141592653589793, 
    3.141592653589793
  ],
  "c": [
    0.9961805460172887, 1.01581609212485, 0.45785551737300106, 
    -0.6743400479743561, -1.04606086926188, -0.9655723250526262, 
    -0.5757280827332156, 0.017487591989126007, 0.610401362313724, 
    0.9866605336566671, 1.0335232431543322, 0.6453772441164307, 
    -0.4846359310719992, -1.014195365951515, -0.9964502165043656,
    -0.027374797128379907, 0.770580186441133, 1.5844468932141083, 
    -0.7504988105159386, -1.1533053154158592, -0.39940623356854926, 
    0.669953241001308, 1.1822672685309246, 0.6182210556297563, 
    -0.493261782484514, -1.1530136311265229, -0.6885569654105621, 
    1.6217843337199846, 0.7207977628265237, -0.02317389641793977
  ],
  "k": 3,
  "n": 2
}

§Example 2: 4 Control Point Cubic Spline

Here a Cubic Spline is constructed from 4 control points:

Cubic spline curve with 4 control points
ⓘ
use spliny::{CubicSpline2D, Result};

pub fn main() -> Result<()> {

    let spline = CubicSpline2D::new(
        vec![1.0, 1.0, 1.0, 1.0, 2.0, 2.0, 2.0, 2.0],
        vec![0.0, 0.5, 1.0, 3.0, 2.0, -3.0, 3.0, -3.0]
    );

    spline.plot_with_control_points("cubic2d.png", (800,800))?;

    Ok(())
}

The control points are four control points: (0,2), (.5,-3), (1,3), and (3,-3), and the curve has 8 knots.

§Usage

Spliny is developed as part of a family of three crates but can be used independently too:

  • splinify fits (non-uniform) B-Spline curves to input data, and results in a fitted as a spliny-crate CurveSpline. Data inputs are x and y vectors for 1-dimensional curves, and u and xyn vectors in case of N-dimensional curves.

  • Use spliny to to use the generated splines, for example, to calculate curve coordinates or spline curves derivatives. This package also implements basic tools for the input and output of spline representations in JSON files and spline plots. It is written in Rust and does not require a Fortran compiler.

  • dierckx-sys contains Fortran foreign function interfaces to Paul Dierckx’ FITPACK library. It is used by splinify, but —unless you want to explore Paul Dierckx library yourself— can be ignored as concerned to using splinify and spliny.

To use this library, add this to your Cargo.toml file:

[dependencies]
spliny = "0.3"

§Spline Curve

The base spline representation in Spliny is the SplineCurve<K,N> object —a wrapper for a vector of knots, and fit coefficients— with K the spline degree, N the space dimension of the curve spline.

For convenience, the following aliases have been defined:

AliasKN
LinearSpline11
CubicSpline31
QuinticSpline51
LinearSpline2D12
CubicSpline2D32
QuinticSpline2D52
LinearSpline3D13
CubicSpline3D33
QuinticSpline3D53

§License

All content ©2022 Harbers Bik LLC, and licensed under either of

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 spline::*;
pub use splines::*;

Modules§

spline
splines

Type Aliases§

CubicSpline
1D cubic spline. Supports plotting with the plot feature.
CubicSpline2D
2D cubic spline. Supports plotting with the plot feature.
CubicSpline3D
3D cubic spline. Plotting is not supported.
LinearSpline
1D linear spline. Supports plotting with the plot feature.
LinearSpline2D
2D linear spline. Supports plotting with the plot feature.
LinearSpline3D
3D linear spline. Plotting is not supported.
QuinticSpline
1D quintic spline. Supports plotting with the plot feature.
QuinticSpline2D
2D quintic spline. Supports plotting with the plot feature.
QuinticSpline3D
3D quintic spline. Plotting is not supported.
Result
Convenience Result type used throughout this crate, with a boxed dynamic error.