splines/README.md

This crate provides [splines](https://en.wikipedia.org/wiki/Spline_(mathematics)), mathematic curves
defined piecewise through control keys a.k.a. knots.

Feel free to dig in the [online documentation](https://docs.rs/splines) for further information.

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# Spline interpolation made easy.

This crate exposes splines for which each sections can be interpolated independently of each
other – i.e. it’s possible to interpolate with a linear interpolator on one section and then
switch to a cubic Hermite interpolator for the next section.

Most of the crate consists of three types:

  - [`Key`], which represents the control points by which the spline must pass.
  - [`Interpolation`], the type of possible interpolation for each segment.
  - [`Spline`], a spline from which you can *sample* points by interpolation.

When adding control points, you add new sections. Two control points define a section – i.e.
it’s not possible to define a spline without at least two control points. Every time you add a
new control point, a new section is created. Each section is assigned an interpolation mode that
is picked from its lower control point.

# Quickly create splines

```
use splines::{Interpolation, Key, Spline};

let start = Key::new(0., 0., Interpolation::Linear);
let end = Key::new(1., 10., Interpolation::default());
let spline = Spline::from_vec(vec![start, end]);
```

You will notice that we used `Interpolation::Linear` for the first key. The first key `start`’s
interpolation will be used for the whole segment defined by those two keys. The `end`’s
interpolation won’t be used. You can in theory use any [`Interpolation`] you want for the last
key. We use the default one because we don’t care.

# Interpolate values

The whole purpose of splines is to interpolate discrete values to yield continuous ones. This is
usually done with the [`Spline::sample`] method. This method expects the sampling parameter
(often, this will be the time of your simulation) as argument and will yield an interpolated
value.

If you try to sample in out-of-bounds sampling parameter, you’ll get no value.

```
assert_eq!(spline.sample(0.), Some(0.));
assert_eq!(spline.clamped_sample(1.), Some(10.));
assert_eq!(spline.sample(1.1), None);
```

It’s possible that you want to get a value even if you’re out-of-bounds. This is especially
important for simulations / animations. Feel free to use the `Spline::clamped_interpolation` for
that purpose.

```
assert_eq!(spline.clamped_sample(-0.9), Some(0.)); // clamped to the first key
assert_eq!(spline.clamped_sample(1.1), Some(10.)); // clamped to the last key
```

# Polymorphic sampling types

[`Spline`] curves are parametered both by the carried value (being interpolated) but also the
sampling type. It’s very typical to use `f32` or `f64` but really, you can in theory use any
kind of type; that type must, however, implement a contract defined by a set of traits to
implement. See [the documentation of this module](crate::interpolate) for further details.

# Features and customization

This crate was written with features baked in and hidden behind feature-gates. The idea is that
the default configuration (i.e. you just add `"splines = …"` to your `Cargo.toml`) will always
give you the minimal, core and raw concepts of what splines, keys / knots and interpolation
modes are. However, you might want more. Instead of letting other people do the extra work to
add implementations for very famous and useful traits – and do it in less efficient way, because
they wouldn’t have access to the internals of this crate, it’s possible to enable features in an
ad hoc way.

This mechanism is not final and this is currently an experiment to see how people like it or
not. It’s especially important to see how it copes with the documentation.

So here’s a list of currently supported features and how to enable them:

  - **Serialization / deserialization.**
    + This feature implements both the `Serialize` and `Deserialize` traits from `serde` for all
      types exported by this crate.
    + Enable with the `"serialization"` feature.
  - **[cgmath](https://crates.io/crates/cgmath) implementors.**
    + Adds some useful implementations of `Interpolate` for some cgmath types.
    + Enable with the `"impl-cgmath"` feature.
  - **[nalgebra](https://crates.io/crates/nalgebra) implementors.**
    + Adds some useful implementations of `Interpolate` for some nalgebra types.
    + Enable with the `"impl-nalgebra"` feature.
  - **Standard library / no standard library.**
    + It’s possible to compile against the standard library or go on your own without it.
    + Compiling with the standard library is enabled by default.
    + Use `default-features = []` in your `Cargo.toml` to disable.
    + Enable explicitly with the `"std"` feature.

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