/pixijs-math

name: pixijs-math
description: "Use this skill when working with coordinates, vectors, matrices, shapes, hit testing, or layout rectangles in PixiJS v8. Covers Point/ObservablePoint, Matrix (2D affine, decompose (including mirrored/negative-scale matrices), apply, applyInverse), shapes (Rectangle, Circle, Ellipse, Polygon, RoundedRectangle, Triangle), Rectangle layout helpers (pad, fit, enlarge, ceil, scale, getBounds), strokeContains hit tests, Polygon isClockwise/containsPolygon, toGlobal/toLocal, PointData/PointLike/Size types, DEG_TO_RAD, and pixi.js/math-extras vector and intersection helpers. Triggers on: Point, ObservablePoint, Matrix, Rectangle, Circle, Polygon, Triangle, RoundedRectangle, toGlobal, toLocal, hitArea, strokeContains, pad, fit, enlarge, ceil, getBounds, containsRect, intersects, isClockwise, math-extras, lineIntersection, segmentIntersection, DEG_TO_RAD, PointData, decompose, mirror, flip, negative scale, setFromMatrix."
license: MIT

PixiJS exposes lightweight math primitives (Point, Matrix, shape classes) used throughout the library for transforms, hit testing, and coordinate conversion. Import `pixi.js/math-extras` to add vector operations (add, dot, magnitude, reflect) and Rectangle intersection/union helpers.

Quick Start

const parent = new Container();
parent.position.set(100, 100);
parent.scale.set(2);
app.stage.addChild(parent);

const child = new Container();
child.position.set(50, 50);
parent.addChild(child);

const globalPt = child.toGlobal(new Point(0, 0));

const m = new Matrix()
  .translate(100, 50)
  .rotate(Math.PI / 4)
  .scale(2, 2);
const world = m.apply(new Point(10, 20));

const hitArea = new Rectangle(0, 0, 200, 100);
console.log(hitArea.contains(50, 50));

**Related skills:** `pixijs-scene-container` (transform properties), `pixijs-events` (hitArea usage), `pixijs-scene-core-concepts` (culling with Rectangle).

Core Patterns

Point and ObservablePoint

Point is a simple {x, y} value type. ObservablePoint fires a callback when x or y changes; it is used internally by Container's position, scale, pivot, origin, and skew.

import { Point } from "pixi.js";

const p = new Point(10, 20);
p.set(30, 40); // set both
p.set(50); // x=50, y=50

const clone = p.clone();
console.log(p.equals(clone)); // true

p.copyFrom({ x: 1, y: 2 }); // accepts any PointData

// Point.shared: temporary point, reset to (0,0) on each access
const temp = Point.shared;
temp.set(100, 200);
// do not store a reference to Point.shared

Container properties like `position`, `scale`, `pivot`, `origin`, and `skew` are ObservablePoints. Setting `.x` or `.y` on them triggers transform recalculation automatically.

import { Container } from "pixi.js";

const obj = new Container();
obj.position.set(100, 200); // triggers observer -> marks transform dirty
obj.position.x = 150; // also triggers observer

Matrix (2D affine transform)

Matrix represents a 3x3 affine transform: `| a c tx | b d ty | 0 0 1 |`. It supports translate, scale, rotate, append, prepend, invert, and decompose.

import { Matrix, Point } from "pixi.js";

// Build a transform
const m = new Matrix()
  .translate(100, 50)
  .rotate(Math.PI / 4)
  .scale(2, 2);

// Transform a point (local -> parent space)
const local = new Point(10, 20);
const world = m.apply(local);

// Inverse transform (parent -> local space)
const backToLocal = m.applyInverse(world);

// Combine matrices
const a = new Matrix().translate(50, 0);
const b = new Matrix().rotate(Math.PI / 2);
a.append(b); // a = a * b

// Decompose into position/scale/rotation/skew
const transform = {
  position: new Point(),
  scale: new Point(),
  pivot: new Point(),
  skew: new Point(),
  rotation: 0,
};
m.decompose(transform);
console.log(transform.rotation); // ~0.785 (PI/4)

// A mirrored matrix (one axis flipped, axes still perpendicular) decomposes into
// rotation + negative scale.x with zero skew. scale.y is never negative: a y-axis
// flip comes back as scale.x = -1 plus a half turn. Either way the parts rebuild the matrix.
const mirrored = new Matrix().rotate(Math.PI / 6).scale(-1, 1);
mirrored.decompose(transform);
transform.scale.x; // -1
transform.skew.x; // 0

// Shared temporary matrix (reset on each access)
const temp = Matrix.shared;
// IDENTITY is read-only reference
const isDefault = m.equals(Matrix.IDENTITY);

Coordinate transforms via Container

Containers provide `toGlobal`, `toLocal`, and `getGlobalPosition` for coordinate conversion.

import { Container, Point } from "pixi.js";

const parent = new Container();
parent.position.set(100, 100);
parent.scale.set(2);

const child = new Container();
child.position.set(50, 50);
parent.addChild(child);

// Local point in child's space -> global (world) space
const globalPt = child.toGlobal(new Point(0, 0));
// globalPt = { x: 200, y: 200 } (100 + 50*2, 100 + 50*2)

// Global point -> child's local space
const localPt = child.toLocal(new Point(200, 200));
// localPt = { x: 0, y: 0 }

// Convert between two containers
const other = new Container();
other.position.set(300, 300);
const ptInOther = child.toLocal(new Point(10, 10), other);

Shapes and hit testing

Rectangle, Circle, Ellipse, Polygon, RoundedRectangle, and Triangle all implement `contains(x, y)` for point-in-shape tests, plus `getBounds(out?)` and `strokeContains(x, y, width, alignment?)` (`Triangle` ignores `alignment` and always tests a centered stroke). They can be used as `hitArea` on containers for custom interaction regions.

import { Rectangle, Circle, Ellipse, Polygon, Container } from "pixi.js";

const rect = new Rectangle(0, 0, 200, 100);
rect.contains(50, 50); // true
rect.contains(300, 50); // false
rect.left; // 0
rect.right; // 200
rect.top; // 0
rect.bottom; // 100
rect.isEmpty(); // false (Rectangle.EMPTY returns a fresh empty rect)

// Native Rectangle-to-Rectangle methods (no math-extras needed)
const other = new Rectangle(50, 50, 100, 10