Pixijs Math

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

```ts
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.

```ts
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.

```ts
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.

```ts
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)

// 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` fo