Triangles

Triangles cuts the surface into equilateral triangles, one orientation inked over the field of the other. Take it for a faceted ground, a backdrop under a chart, or any surface that should read as cut rather than woven.

Three regular polygons tile the plane on their own: the square, the hexagon and the triangle. grid draws the first and honeycomb the second, and this is the third. A strip alternates a triangle standing on its base with one hanging from the line above, and the strip below repeats it half a side across, because the vertices of the two strips have to meet.

Example

<?php

declare(strict_types=1);

use Atelier\Pattern\Pattern;
use Atelier\Pattern\PatternRegistry;
use Atelier\Svg\Document;
use Atelier\Svg\Dumper\CompactXmlDumper;
use Atelier\Svg\Element\Shape\RectElement;

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

$triangles = Pattern::triangles(size: 24, up: 1.0, down: 0.3);

$document = Document::create(360, 200);

(new PatternRegistry($triangles))->attachTo($document);

$surface = new RectElement();
$surface->setX('0')->setY('0')->setWidth('360')->setHeight('200');
$surface->setAttribute('fill', $triangles->fill());

$document->getRootElement()?->appendChild($surface);

echo (new CompactXmlDumper())->dump($document);

Options

The settings control two paint layers, not independent final face opacities. Away from antialiased edges, the standing faces have alpha up + down * (1 - up) and the hanging faces have alpha down, before withOpacity() applies to the group. With both set to 0.5, those values are 0.75 and 0.5: equal intermediate settings do not produce a flat tone. A down of 0 leaves the hanging faces transparent. down: 1 gives one opaque tone.

The hanging triangles are not drawn as shapes. The tile is painted with down from edge to edge and the standing triangles go on top at up. This avoids separate adjacent face fills. Two fills that share an edge leave a hairline between them, because a renderer antialiases each one against what was already there, and a lattice of those hairlines reads as a ruled pattern nobody asked for. One field has no interior edge to show.

How the tile closes

The tile is one side wide and two strip heights tall, a strip standing size * sqrt(3) / 2.

Each strip contributes one standing triangle. The one in the lower strip has its apex on the left edge, so half of it hangs outside the tile and it is drawn again a period to the right. The field underneath is the tile itself and needs no copy.