Recipes

These recipes combine the shared curve operations into common application tasks.

Import an SVG segment

SVG quadratic and cubic path segments map directly to their dedicated curve classes. A cubic segment needs the current path position, two controls, and the segment end:

<?php
use Alto\Bezier\CubicCurve;
use Alto\Bezier\Point;

$curve = new CubicCurve(
    new Point($currentX, $currentY),
    new Point($control1X, $control1Y),
    new Point($control2X, $control2Y),
    new Point($endX, $endY),
);

SVG does not provide native quartic, quintic, or arbitrary-degree path commands. Sample those curves or convert them to segments supported by the target renderer.

Animate at constant speed

Equal steps in t do not usually represent equal distances. Calculate the length once, then request positions by distance:

<?php
$samples = 200;
$frameCount = 20;
$length = $curve->length($samples);
$frames = [];

for ($frame = 0; $frame <= $frameCount; ++$frame) {
    $distance = $length * $frame / $frameCount;
    $frames[] = $curve->pointAtDistance($distance, $samples);
}

The first and last entries are the curve endpoints. Intermediate entries are approximately equally spaced along the path.

Reject distant curves before intersecting

Intersection detection already checks bounds during subdivision. An application comparing many curves can reject non-overlapping pairs first:

<?php
$a = $curve->boundingBox();
$b = $otherCurve->boundingBox();

$separate = $a->maxX() < $b->minX()
    || $b->maxX() < $a->minX()
    || $a->maxY() < $b->minY()
    || $b->maxY() < $a->minY();

$hits = $separate ? [] : $curve->intersections($otherCurve);

Fit a curve into a viewport

Use the bounding box to derive a translation and scale for a renderer:

<?php
$box = $curve->boundingBox();
$scale = min(
    $viewportWidth / $box->width(),
    $viewportHeight / $box->height(),
);

$offsetX = -$box->minX() * $scale;
$offsetY = -$box->minY() * $scale;

Handle zero-width or zero-height boxes before dividing when a curve can be degenerate or perfectly horizontal or vertical.