Alto Bezier

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.