README

Alto\Bezier is a precision PHP toolkit for evaluating, splitting, and measuring quadratic, cubic, quintic, and N-order Bézier curves using immutable value objects and a numerically stable De Casteljau core.

Features

Quadratic, cubic, quartic, quintic, and arbitrary N-order curves that all share the same API
Point evaluation: pointAt(t) and constant-speed pointAtDistance(distance) helpers
Curve subdivision with split(t) for tessellation or editing workflows
Differential geometry helpers: derivatives, tangents, normals
Arc-length calculation and arc-length parameterization with configurable sampling
Intersection detection between any two curves
Bounding boxes and evenly spaced point generators for export to SVG, canvas, or WebGL
Immutable, readonly classes with no external dependencies

Installation

composer require alto/bezier

Usage

Create and inspect a cubic curve

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)
);

$mid = $curve->pointAt(0.5);
[$left, $right] = $curve->split(0.4);
$heading = $curve->tangent(0.5);

Instantiate quadratic and N-order curves

use Alto\Bezier\QuadraticCurve;
use Alto\Bezier\NOrderCurve;
use Alto\Bezier\Point;

$quadratic = new QuadraticCurve(
    new Point(0, 0),
    new Point(50, 120),
    new Point(120, 0)
);

$wave = new NOrderCurve(...array_map(
    fn(int $i) => new Point($i * 20, sin($i / 2) * 40 + 60),
    range(0, 7)
));

Exporting control points to SVG

$path = sprintf(
    'M %s C %s %s %s',
    ...array_map(fn(Point $p) => $p->x.' '.$p->y, $curve->toArray())
);

Advanced

Arc length & constant-speed motion: length($samples) returns the numerical arc length, while pointAtDistance($distance, $samples) maps real distances back to coordinates.
Intersections: $curveA->intersections($curveB, tolerance: 0.25, maxDepth: 18) delivers intersection points along with their t parameters on each curve.
Numeric tuning: increase sampling (default 100) for long or intricate paths to improve accuracy for arc-length and parameterization routines.
Bounding boxes and grids: boundingBox() exposes width/height/corners, and points($interval) streams evenly spaced points for tessellation or hit-testing.

Testing

composer install
vendor/bin/phpstan analyse
vendor/bin/phpunit

License

This project is licensed under the MIT License.

alto / bezier

Maintainers

Details