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@ue-too/board / multiplyMatrix

Function: multiplyMatrix() ​

multiplyMatrix(m1, m2): object

Defined in: packages/board/src/camera/utils/matrix.ts:403

Multiplies two 2D transformation matrices. Order matters: M = m1 × m2 applies m2 first, then m1.

Parameters ​

m1 ​

TransformationMatrix

First transformation matrix (applied second)

m2 ​

TransformationMatrix

Second transformation matrix (applied first)

Returns ​

object

Combined transformation matrix

a ​

a: number

b ​

b: number

c ​

c: number

d ​

d: number

e ​

e: number

f ​

f: number

Remarks ​

Matrix multiplication is not commutative: m1 × m2 ≠ m2 × m1

The result applies transformations in right-to-left order:

  • Result = m1 × m2
  • Applying result to point P: (m1 × m2) × P = m1 × (m2 × P)
  • m2 is applied first, then m1

Common use: Building composite transformations

typescript
// Translate then rotate (rotate happens first!)
const translate = { a: 1, b: 0, c: 0, d: 1, e: 100, f: 0 };
const rotate = { a: 0, b: 1, c: -1, d: 0, e: 0, f: 0 }; // 90° ccw
const combined = multiplyMatrix(translate, rotate);
// Points are rotated, then translated

Example ​

typescript
// Combine scale and translation
const scale2x: TransformationMatrix = {
  a: 2, b: 0, c: 0, d: 2, e: 0, f: 0
};
const translate: TransformationMatrix = {
  a: 1, b: 0, c: 0, d: 1, e: 100, f: 50
};

// Scale then translate
const combined = multiplyMatrix(translate, scale2x);
// Points are scaled by 2, then translated by (100, 50)

// Chain multiple transformations
const m = multiplyMatrix(
  multiplyMatrix(translate, rotate),
  scale
);
// Equivalent to: scale → rotate → translate