Getting started

A Bézier curve is defined by its control points. The parameter t identifies a position along the curve: 0 is the start and 1 is the end.

After installation, save this script as curve.php beside vendor/ and run php curve.php. It creates a cubic curve, evaluates its midpoint, measures its approximate length, and splits it into two curves:

<?php

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

use Alto\Bezier\CubicCurve;
use Alto\Bezier\Point;

$curve = new CubicCurve(
    new Point(0, 0),
    new Point(40, 160),
    new Point(160, -40),
    new Point(200, 120),
);

$midpoint = $curve->pointAt(0.5);
$length = $curve->length(samples: 200);
[$left, $right] = $curve->split(0.5);

echo "Midpoint: {$midpoint}".PHP_EOL;
echo 'Approximate length: '.round($length, 2).PHP_EOL;
echo 'Split joins at: '.$left->pointAt(1).PHP_EOL;

The script prints:

Midpoint: (100, 60)
Approximate length: 276.51
Split joins at: (100, 60)

The blue curve uses the example's control points; the dashed polygon joins those controls. The orange point is pointAt(0.5), not the halfway distance.

The split curves meet at the original midpoint. Increasing the sample count improves the numerical length approximation at the cost of more work.

Next, choose a curve type or explore the operations shared by every curve.