# Quartic curves

HTML: [altophp.com/bezier/curves/quartic](https://altophp.com/bezier/curves/quartic/)

A quartic Bézier curve has five control points and degree four. Use it when the
source data already has five points and reducing it to a cubic curve would
change the path.

<img src="../assets/quartic-curve.svg" alt="A quartic Bézier curve" width="240" height="200" />

## Create a curve

```php
<?php

require __DIR__.'/vendor/autoload.php';

use Alto\Bezier\Point;
use Alto\Bezier\QuarticCurve;

$curve = new QuarticCurve(
    new Point(10, 170),
    new Point(60, 10),
    new Point(120, 190),
    new Point(180, 20),
    new Point(230, 170),
);

echo $curve->pointAt(0.5).PHP_EOL;
```

The midpoint is:

```text
(120, 100)
```

The public properties `p0` through `p4` retain the original points. SVG has no
native quartic path command, so renderers must sample the curve or convert it
to supported segments.

See [Operations](https://altophp.com/bezier/operations.md) for sampling the curve with `points()`.

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Previous: [Cubic curves](https://altophp.com/bezier/curves/cubic.md)
Next: [Quintic curves](https://altophp.com/bezier/curves/quintic.md)

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ALTO\BEZIER: [altophp.com/bezier](https://altophp.com/bezier/)
ALTO(PHP): [altophp.com](https://altophp.com/)