pixi.js
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JavaScript
'use strict';
var _const = require('../misc/const.js');
var Point = require('../point/Point.js');
"use strict";
class Matrix {
/**
* @param a - x scale
* @param b - y skew
* @param c - x skew
* @param d - y scale
* @param tx - x translation
* @param ty - y translation
*/
constructor(a = 1, b = 0, c = 0, d = 1, tx = 0, ty = 0) {
/**
* Array representation of the matrix.
* Only populated when `toArray()` is called.
* @default null
* @see {@link Matrix.toArray} For filling this array
*/
this.array = null;
this.a = a;
this.b = b;
this.c = c;
this.d = d;
this.tx = tx;
this.ty = ty;
}
/**
* Creates a Matrix object based on the given array.
* Populates matrix components from a flat array in column-major order.
*
* > [!NOTE] Array mapping order:
* > ```
* > array[0] = a (x scale)
* > array[1] = b (y skew)
* > array[2] = tx (x translation)
* > array[3] = c (x skew)
* > array[4] = d (y scale)
* > array[5] = ty (y translation)
* > ```
* @example
* ```ts
* // Create matrix from array
* const matrix = new Matrix();
* matrix.fromArray([
* 2, 0, 100, // a, b, tx
* 0, 2, 100 // c, d, ty
* ]);
*
* // Create matrix from typed array
* const float32Array = new Float32Array([
* 1, 0, 0, // Scale x1, no skew
* 0, 1, 0 // No skew, scale x1
* ]);
* matrix.fromArray(float32Array);
* ```
* @param array - The array to populate the matrix from
* @see {@link Matrix.toArray} For converting matrix to array
* @see {@link Matrix.set} For setting values directly
*/
fromArray(array) {
this.a = array[0];
this.b = array[1];
this.c = array[3];
this.d = array[4];
this.tx = array[2];
this.ty = array[5];
}
/**
* Sets the matrix properties directly.
* All matrix components can be set in one call.
* @example
* ```ts
* // Set to identity matrix
* matrix.set(1, 0, 0, 1, 0, 0);
*
* // Set to scale matrix
* matrix.set(2, 0, 0, 2, 0, 0); // Scale 2x
*
* // Set to translation matrix
* matrix.set(1, 0, 0, 1, 100, 50); // Move 100,50
* ```
* @param a - Scale on x axis
* @param b - Shear on y axis
* @param c - Shear on x axis
* @param d - Scale on y axis
* @param tx - Translation on x axis
* @param ty - Translation on y axis
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.identity} For resetting to identity
* @see {@link Matrix.fromArray} For setting from array
*/
set(a, b, c, d, tx, ty) {
this.a = a;
this.b = b;
this.c = c;
this.d = d;
this.tx = tx;
this.ty = ty;
return this;
}
/**
* Creates an array from the current Matrix object.
*
* > [!NOTE] The array format is:
* > ```
* > Non-transposed:
* > [a, c, tx,
* > b, d, ty,
* > 0, 0, 1]
* >
* > Transposed:
* > [a, b, 0,
* > c, d, 0,
* > tx,ty,1]
* > ```
* @example
* ```ts
* // Basic array conversion
* const matrix = new Matrix(2, 0, 0, 2, 100, 100);
* const array = matrix.toArray();
*
* // Using existing array
* const float32Array = new Float32Array(9);
* matrix.toArray(false, float32Array);
*
* // Get transposed array
* const transposed = matrix.toArray(true);
* ```
* @param transpose - Whether to transpose the matrix
* @param out - Optional Float32Array to store the result
* @returns The array containing the matrix values
* @see {@link Matrix.fromArray} For creating matrix from array
* @see {@link Matrix.array} For cached array storage
*/
toArray(transpose, out) {
if (!this.array) {
this.array = new Float32Array(9);
}
const array = out || this.array;
if (transpose) {
array[0] = this.a;
array[1] = this.b;
array[2] = 0;
array[3] = this.c;
array[4] = this.d;
array[5] = 0;
array[6] = this.tx;
array[7] = this.ty;
array[8] = 1;
} else {
array[0] = this.a;
array[1] = this.c;
array[2] = this.tx;
array[3] = this.b;
array[4] = this.d;
array[5] = this.ty;
array[6] = 0;
array[7] = 0;
array[8] = 1;
}
return array;
}
/**
* Get a new position with the current transformation applied.
*
* Can be used to go from a child's coordinate space to the world coordinate space. (e.g. rendering)
* @example
* ```ts
* // Basic point transformation
* const matrix = new Matrix().translate(100, 50).rotate(Math.PI / 4);
* const point = new Point(10, 20);
* const transformed = matrix.apply(point);
*
* // Reuse existing point
* const output = new Point();
* matrix.apply(point, output);
* ```
* @param pos - The origin point to transform
* @param newPos - Optional point to store the result
* @returns The transformed point
* @see {@link Matrix.applyInverse} For inverse transformation
* @see {@link Point} For point operations
*/
apply(pos, newPos) {
newPos = newPos || new Point.Point();
const x = pos.x;
const y = pos.y;
newPos.x = this.a * x + this.c * y + this.tx;
newPos.y = this.b * x + this.d * y + this.ty;
return newPos;
}
/**
* Get a new position with the inverse of the current transformation applied.
*
* Can be used to go from the world coordinate space to a child's coordinate space. (e.g. input)
* @example
* ```ts
* // Basic inverse transformation
* const matrix = new Matrix().translate(100, 50).rotate(Math.PI / 4);
* const worldPoint = new Point(150, 100);
* const localPoint = matrix.applyInverse(worldPoint);
*
* // Reuse existing point
* const output = new Point();
* matrix.applyInverse(worldPoint, output);
*
* // Convert mouse position to local space
* const mousePoint = new Point(mouseX, mouseY);
* const localMouse = matrix.applyInverse(mousePoint);
* ```
* @param pos - The origin point to inverse-transform
* @param newPos - Optional point to store the result
* @returns The inverse-transformed point
* @see {@link Matrix.apply} For forward transformation
* @see {@link Matrix.invert} For getting inverse matrix
*/
applyInverse(pos, newPos) {
newPos = newPos || new Point.Point();
const a = this.a;
const b = this.b;
const c = this.c;
const d = this.d;
const tx = this.tx;
const ty = this.ty;
const id = 1 / (a * d + c * -b);
const x = pos.x;
const y = pos.y;
newPos.x = d * id * x + -c * id * y + (ty * c - tx * d) * id;
newPos.y = a * id * y + -b * id * x + (-ty * a + tx * b) * id;
return newPos;
}
/**
* Translates the matrix on the x and y axes.
* Adds to the position values while preserving scale, rotation and skew.
* @example
* ```ts
* // Basic translation
* const matrix = new Matrix();
* matrix.translate(100, 50); // Move right 100, down 50
*
* // Chain with other transformations
* matrix
* .scale(2, 2)
* .translate(100, 0)
* .rotate(Math.PI / 4);
* ```
* @param x - How much to translate on the x axis
* @param y - How much to translate on the y axis
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.set} For setting position directly
* @see {@link Matrix.setTransform} For complete transform setup
*/
translate(x, y) {
this.tx += x;
this.ty += y;
return this;
}
/**
* Applies a scale transformation to the matrix.
* Multiplies the scale values with existing matrix components.
* @example
* ```ts
* // Basic scaling
* const matrix = new Matrix();
* matrix.scale(2, 3); // Scale 2x horizontally, 3x vertically
*
* // Chain with other transformations
* matrix
* .translate(100, 100)
* .scale(2, 2) // Scales after translation
* .rotate(Math.PI / 4);
* ```
* @param x - The amount to scale horizontally
* @param y - The amount to scale vertically
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.setTransform} For setting scale directly
* @see {@link Matrix.append} For combining transformations
*/
scale(x, y) {
this.a *= x;
this.d *= y;
this.c *= x;
this.b *= y;
this.tx *= x;
this.ty *= y;
return this;
}
/**
* Applies a rotation transformation to the matrix.
*
* Rotates around the origin (0,0) by the given angle in radians.
* @example
* ```ts
* // Basic rotation
* const matrix = new Matrix();
* matrix.rotate(Math.PI / 4); // Rotate 45 degrees
*
* // Chain with other transformations
* matrix
* .translate(100, 100) // Move to rotation center
* .rotate(Math.PI) // Rotate 180 degrees
* .scale(2, 2); // Scale after rotation
*
* // Common angles
* matrix.rotate(Math.PI / 2); // 90 degrees
* matrix.rotate(Math.PI); // 180 degrees
* matrix.rotate(Math.PI * 2); // 360 degrees
* ```
* @remarks
* - Rotates around origin point (0,0)
* - Affects position if translation was set
* - Uses counter-clockwise rotation
* - Order of operations matters when chaining
* @param angle - The angle in radians
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.setTransform} For setting rotation directly
* @see {@link Matrix.append} For combining transformations
*/
rotate(angle) {
const cos = Math.cos(angle);
const sin = Math.sin(angle);
const a1 = this.a;
const c1 = this.c;
const tx1 = this.tx;
this.a = a1 * cos - this.b * sin;
this.b = a1 * sin + this.b * cos;
this.c = c1 * cos - this.d * sin;
this.d = c1 * sin + this.d * cos;
this.tx = tx1 * cos - this.ty * sin;
this.ty = tx1 * sin + this.ty * cos;
return this;
}
/**
* Appends the given Matrix to this Matrix.
* Combines two matrices by multiplying them together: this = this * matrix
* @example
* ```ts
* // Basic matrix combination
* const matrix = new Matrix();
* const other = new Matrix().translate(100, 0).rotate(Math.PI / 4);
* matrix.append(other);
* ```
* @remarks
* - Order matters: A.append(B) !== B.append(A)
* - Modifies current matrix
* - Preserves transformation order
* - Commonly used for combining transforms
* @param matrix - The matrix to append
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.prepend} For prepending transformations
* @see {@link Matrix.appendFrom} For appending two external matrices
*/
append(matrix) {
const a1 = this.a;
const b1 = this.b;
const c1 = this.c;
const d1 = this.d;
this.a = matrix.a * a1 + matrix.b * c1;
this.b = matrix.a * b1 + matrix.b * d1;
this.c = matrix.c * a1 + matrix.d * c1;
this.d = matrix.c * b1 + matrix.d * d1;
this.tx = matrix.tx * a1 + matrix.ty * c1 + this.tx;
this.ty = matrix.tx * b1 + matrix.ty * d1 + this.ty;
return this;
}
/**
* Appends two matrices and sets the result to this matrix.
* Performs matrix multiplication: this = A * B
* @example
* ```ts
* // Basic matrix multiplication
* const result = new Matrix();
* const matrixA = new Matrix().scale(2, 2);
* const matrixB = new Matrix().rotate(Math.PI / 4);
* result.appendFrom(matrixA, matrixB);
* ```
* @remarks
* - Order matters: A * B !== B * A
* - Creates a new transformation from two others
* - More efficient than append() for multiple operations
* - Does not modify input matrices
* @param a - The first matrix to multiply
* @param b - The second matrix to multiply
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.append} For single matrix combination
* @see {@link Matrix.prepend} For reverse order multiplication
*/
appendFrom(a, b) {
const a1 = a.a;
const b1 = a.b;
const c1 = a.c;
const d1 = a.d;
const tx = a.tx;
const ty = a.ty;
const a2 = b.a;
const b2 = b.b;
const c2 = b.c;
const d2 = b.d;
this.a = a1 * a2 + b1 * c2;
this.b = a1 * b2 + b1 * d2;
this.c = c1 * a2 + d1 * c2;
this.d = c1 * b2 + d1 * d2;
this.tx = tx * a2 + ty * c2 + b.tx;
this.ty = tx * b2 + ty * d2 + b.ty;
return this;
}
/**
* Sets the matrix based on all the available properties.
* Combines position, scale, rotation, skew and pivot in a single operation.
* @example
* ```ts
* // Basic transform setup
* const matrix = new Matrix();
* matrix.setTransform(
* 100, 100, // position
* 0, 0, // pivot
* 2, 2, // scale
* Math.PI / 4, // rotation (45 degrees)
* 0, 0 // skew
* );
* ```
* @remarks
* - Updates all matrix components at once
* - More efficient than separate transform calls
* - Uses radians for rotation and skew
* - Pivot affects rotation center
* @param x - Position on the x axis
* @param y - Position on the y axis
* @param pivotX - Pivot on the x axis
* @param pivotY - Pivot on the y axis
* @param scaleX - Scale on the x axis
* @param scaleY - Scale on the y axis
* @param rotation - Rotation in radians
* @param skewX - Skew on the x axis
* @param skewY - Skew on the y axis
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.decompose} For extracting transform properties
* @see {@link TransformableObject} For transform data structure
*/
setTransform(x, y, pivotX, pivotY, scaleX, scaleY, rotation, skewX, skewY) {
this.a = Math.cos(rotation + skewY) * scaleX;
this.b = Math.sin(rotation + skewY) * scaleX;
this.c = -Math.sin(rotation - skewX) * scaleY;
this.d = Math.cos(rotation - skewX) * scaleY;
this.tx = x - (pivotX * this.a + pivotY * this.c);
this.ty = y - (pivotX * this.b + pivotY * this.d);
return this;
}
/**
* Prepends the given Matrix to this Matrix.
* Combines two matrices by multiplying them together: this = matrix * this
* @example
* ```ts
* // Basic matrix prepend
* const matrix = new Matrix().scale(2, 2);
* const other = new Matrix().translate(100, 0);
* matrix.prepend(other); // Translation happens before scaling
* ```
* @remarks
* - Order matters: A.prepend(B) !== B.prepend(A)
* - Modifies current matrix
* - Reverses transformation order compared to append()
* @param matrix - The matrix to prepend
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.append} For appending transformations
* @see {@link Matrix.appendFrom} For combining external matrices
*/
prepend(matrix) {
const tx1 = this.tx;
if (matrix.a !== 1 || matrix.b !== 0 || matrix.c !== 0 || matrix.d !== 1) {
const a1 = this.a;
const c1 = this.c;
this.a = a1 * matrix.a + this.b * matrix.c;
this.b = a1 * matrix.b + this.b * matrix.d;
this.c = c1 * matrix.a + this.d * matrix.c;
this.d = c1 * matrix.b + this.d * matrix.d;
}
this.tx = tx1 * matrix.a + this.ty * matrix.c + matrix.tx;
this.ty = tx1 * matrix.b + this.ty * matrix.d + matrix.ty;
return this;
}
/**
* Decomposes the matrix into its individual transform components.
* Extracts position, scale, rotation and skew values from the matrix.
* @example
* ```ts
* // Basic decomposition
* const matrix = new Matrix()
* .translate(100, 100)
* .rotate(Math.PI / 4)
* .scale(2, 2);
*
* const transform = {
* position: new Point(),
* scale: new Point(),
* pivot: new Point(),
* skew: new Point(),
* rotation: 0
* };
*
* matrix.decompose(transform);
* console.log(transform.position); // Point(100, 100)
* console.log(transform.rotation); // ~0.785 (PI/4)
* console.log(transform.scale); // Point(2, 2)
* ```
* @remarks
* - Handles combined transformations
* - Accounts for pivot points
* - Chooses between rotation/skew based on transform type
* - Uses radians for rotation and skew
* @param transform - The transform object to store the decomposed values
* @returns The transform with the newly applied properties
* @see {@link Matrix.setTransform} For composing from components
* @see {@link TransformableObject} For transform structure
*/
decompose(transform) {
const a = this.a;
const b = this.b;
const c = this.c;
const d = this.d;
const pivot = transform.pivot;
const skewX = -Math.atan2(-c, d);
const skewY = Math.atan2(b, a);
const delta = Math.abs(skewX + skewY);
if (delta < 1e-5 || Math.abs(_const.PI_2 - delta) < 1e-5) {
transform.rotation = skewY;
transform.skew.x = transform.skew.y = 0;
} else {
transform.rotation = 0;
transform.skew.x = skewX;
transform.skew.y = skewY;
}
transform.scale.x = Math.sqrt(a * a + b * b);
transform.scale.y = Math.sqrt(c * c + d * d);
transform.position.x = this.tx + (pivot.x * a + pivot.y * c);
transform.position.y = this.ty + (pivot.x * b + pivot.y * d);
return transform;
}
/**
* Inverts this matrix.
* Creates the matrix that when multiplied with this matrix results in an identity matrix.
* @example
* ```ts
* // Basic matrix inversion
* const matrix = new Matrix()
* .translate(100, 50)
* .scale(2, 2);
*
* matrix.invert(); // Now transforms in opposite direction
*
* // Verify inversion
* const point = new Point(50, 50);
* const transformed = matrix.apply(point);
* const original = matrix.invert().apply(transformed);
* // original ≈ point
* ```
* @remarks
* - Modifies the current matrix
* - Useful for reversing transformations
* - Cannot invert matrices with zero determinant
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.identity} For resetting to identity
* @see {@link Matrix.applyInverse} For inverse transformations
*/
invert() {
const a1 = this.a;
const b1 = this.b;
const c1 = this.c;
const d1 = this.d;
const tx1 = this.tx;
const n = a1 * d1 - b1 * c1;
this.a = d1 / n;
this.b = -b1 / n;
this.c = -c1 / n;
this.d = a1 / n;
this.tx = (c1 * this.ty - d1 * tx1) / n;
this.ty = -(a1 * this.ty - b1 * tx1) / n;
return this;
}
/**
* Checks if this matrix is an identity matrix.
*
* An identity matrix has no transformations applied (default state).
* @example
* ```ts
* // Check if matrix is identity
* const matrix = new Matrix();
* console.log(matrix.isIdentity()); // true
*
* // Check after transformations
* matrix.translate(100, 0);
* console.log(matrix.isIdentity()); // false
*
* // Reset and verify
* matrix.identity();
* console.log(matrix.isIdentity()); // true
* ```
* @remarks
* - Verifies a = 1, d = 1 (no scale)
* - Verifies b = 0, c = 0 (no skew)
* - Verifies tx = 0, ty = 0 (no translation)
* @returns True if matrix has no transformations
* @see {@link Matrix.identity} For resetting to identity
* @see {@link Matrix.IDENTITY} For constant identity matrix
*/
isIdentity() {
return this.a === 1 && this.b === 0 && this.c === 0 && this.d === 1 && this.tx === 0 && this.ty === 0;
}
/**
* Resets this Matrix to an identity (default) matrix.
* Sets all components to their default values: scale=1, no skew, no translation.
* @example
* ```ts
* // Reset transformed matrix
* const matrix = new Matrix()
* .scale(2, 2)
* .rotate(Math.PI / 4);
* matrix.identity(); // Back to default state
*
* // Chain after reset
* matrix
* .identity()
* .translate(100, 100)
* .scale(2, 2);
*
* // Compare with identity constant
* const isDefault = matrix.equals(Matrix.IDENTITY);
* ```
* @remarks
* - Sets a=1, d=1 (default scale)
* - Sets b=0, c=0 (no skew)
* - Sets tx=0, ty=0 (no translation)
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.IDENTITY} For constant identity matrix
* @see {@link Matrix.isIdentity} For checking identity state
*/
identity() {
this.a = 1;
this.b = 0;
this.c = 0;
this.d = 1;
this.tx = 0;
this.ty = 0;
return this;
}
/**
* Creates a new Matrix object with the same values as this one.
* @returns A copy of this matrix. Good for chaining method calls.
*/
clone() {
const matrix = new Matrix();
matrix.a = this.a;
matrix.b = this.b;
matrix.c = this.c;
matrix.d = this.d;
matrix.tx = this.tx;
matrix.ty = this.ty;
return matrix;
}
/**
* Creates a new Matrix object with the same values as this one.
* @param matrix
* @example
* ```ts
* // Basic matrix cloning
* const matrix = new Matrix()
* .translate(100, 100)
* .rotate(Math.PI / 4);
* const copy = matrix.clone();
*
* // Clone and modify
* const modified = matrix.clone()
* .scale(2, 2);
*
* // Compare matrices
* console.log(matrix.equals(copy)); // true
* console.log(matrix.equals(modified)); // false
* ```
* @returns A copy of this matrix. Good for chaining method calls.
* @see {@link Matrix.copyTo} For copying to existing matrix
* @see {@link Matrix.copyFrom} For copying from another matrix
*/
copyTo(matrix) {
matrix.a = this.a;
matrix.b = this.b;
matrix.c = this.c;
matrix.d = this.d;
matrix.tx = this.tx;
matrix.ty = this.ty;
return matrix;
}
/**
* Changes the values of the matrix to be the same as the ones in given matrix.
* @example
* ```ts
* // Basic matrix copying
* const source = new Matrix()
* .translate(100, 100)
* .rotate(Math.PI / 4);
* const target = new Matrix();
* target.copyFrom(source);
* ```
* @param matrix - The matrix to copy from
* @returns This matrix. Good for chaining method calls.
* @see {@link Matrix.clone} For creating new matrix copy
* @see {@link Matrix.copyTo} For copying to another matrix
*/
copyFrom(matrix) {
this.a = matrix.a;
this.b = matrix.b;
this.c = matrix.c;
this.d = matrix.d;
this.tx = matrix.tx;
this.ty = matrix.ty;
return this;
}
/**
* Checks if this matrix equals another matrix.
* Compares all components for exact equality.
* @example
* ```ts
* // Basic equality check
* const m1 = new Matrix();
* const m2 = new Matrix();
* console.log(m1.equals(m2)); // true
*
* // Compare transformed matrices
* const transform = new Matrix()
* .translate(100, 100)
* const clone = new Matrix()
* .scale(2, 2);
* console.log(transform.equals(clone)); // false
* ```
* @param matrix - The matrix to compare to
* @returns True if matrices are identical
* @see {@link Matrix.copyFrom} For copying matrix values
* @see {@link Matrix.isIdentity} For identity comparison
*/
equals(matrix) {
return matrix.a === this.a && matrix.b === this.b && matrix.c === this.c && matrix.d === this.d && matrix.tx === this.tx && matrix.ty === this.ty;
}
toString() {
return `[pixi.js:Matrix a=${this.a} b=${this.b} c=${this.c} d=${this.d} tx=${this.tx} ty=${this.ty}]`;
}
/**
* A default (identity) matrix with no transformations applied.
*
* > [!IMPORTANT] This is a shared read-only object. Create a new Matrix if you need to modify it.
* @example
* ```ts
* // Get identity matrix reference
* const identity = Matrix.IDENTITY;
* console.log(identity.isIdentity()); // true
*
* // Compare with identity
* const matrix = new Matrix();
* console.log(matrix.equals(Matrix.IDENTITY)); // true
*
* // Create new matrix instead of modifying IDENTITY
* const transform = new Matrix()
* .copyFrom(Matrix.IDENTITY)
* .translate(100, 100);
* ```
* @readonly
* @returns A read-only identity matrix
* @see {@link Matrix.shared} For temporary calculations
* @see {@link Matrix.identity} For resetting matrices
*/
static get IDENTITY() {
return identityMatrix.identity();
}
/**
* A static Matrix that can be used to avoid creating new objects.
* Will always ensure the matrix is reset to identity when requested.
*
* > [!IMPORTANT] This matrix is shared and temporary. Do not store references to it.
* @example
* ```ts
* // Use for temporary calculations
* const tempMatrix = Matrix.shared;
* tempMatrix.translate(100, 100).rotate(Math.PI / 4);
* const point = tempMatrix.apply({ x: 10, y: 20 });
*
* // Will be reset to identity on next access
* const fresh = Matrix.shared; // Back to identity
* ```
* @remarks
* - Always returns identity matrix
* - Safe to modify temporarily
* - Not safe to store references
* - Useful for one-off calculations
* @readonly
* @returns A fresh identity matrix for temporary use
* @see {@link Matrix.IDENTITY} For immutable identity matrix
* @see {@link Matrix.identity} For resetting matrices
*/
static get shared() {
return tempMatrix.identity();
}
}
const tempMatrix = new Matrix();
const identityMatrix = new Matrix();
exports.Matrix = Matrix;
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