Operations

Every curve class extends Curve and supports the same operations. The methods return new values and never mutate the curve or its points.

Evaluate and sample

pointAt() evaluates one parameter. Values from 0 to 1 cover the curve from its start point to its end point.

<?php
$point = $curve->pointAt(0.25);

foreach ($curve->points(0.1) as $sample) {
    // Use each Point instance.
}

points() accepts an interval greater than 0 and no greater than 1. It returns a generator, so samples do not need to be stored together.

Split

<?php
[$left, $right] = $curve->split(0.5);

The result contains two curves of the same concrete type. The end of $left and the start of $right are the point at the split parameter.

Direction

<?php
$velocity = $curve->derivative(0.5);
$tangent = $curve->tangent(0.5);
$normal = $curve->normal(0.5);

derivative() returns the velocity vector. tangent() normalizes that vector, and normal() rotates the tangent 90 degrees counterclockwise. A stationary point produces zero tangent and normal vectors.

Length and distance

Curve length is approximated numerically:

<?php
$length = $curve->length(samples: 200);
$quarterT = $curve->parameterAtDistance($length / 4, samples: 200);
$quarterPoint = $curve->pointAtDistance($length / 4, samples: 200);

Use the same sample count when relating a length to a distance parameter. Higher values improve the approximation and require more calculations. length() requires at least two samples. Distance methods reject negative distances and distances beyond the calculated curve length.

Intersections

<?php
$hits = $curve->intersections(
    $otherCurve,
    tolerance: 0.25,
    maxDepth: 18,
);

foreach ($hits as $hit) {
    $point = $hit['point'];
    $tOnFirst = $hit['t1'];
    $tOnSecond = $hit['t2'];
}

Intersection detection uses recursive subdivision and returns approximate points. A smaller tolerance can refine the result but increases the work. The maximum depth limits the subdivision search.

Bounds

<?php
$box = $curve->boundingBox();

$width = $box->width();
$height = $box->height();
$topLeft = $box->getTopLeft();

Quadratic and cubic curves calculate their extrema analytically. Higher-degree curves return a conservative box derived from their control points and sampled curve positions. The coordinate helpers minX(), maxX(), minY(), and maxY() are useful for fast rejection tests.

Export control points

<?php
$coordinates = $curve->toArray();

toArray() returns the control points as [x, y] pairs. It does not sample or flatten the curve.