Mat4x3

A 4×3 affine transform for 3D — rotation, scale, and translation, but no projection — stored in a 4×4 Float32Array.

Hierarchical 3D affine transforms composed with Mat4x3.multiply(). The 12-element affine matrix handles rotation, scale, and translation without the overhead of perspective rows.

Reach for it when a transform will never need perspective: object placement, node hierarchies, and camera views. Leaving out the projection row makes inversion cheaper and keeps the last column fixed at (0, 0, 0, 1).

Because the matrix is affine by construction, the linear-only operations are named for it: transposeLinear(), determinantLinear(), and invertAffine(). Use Mat4 instead when you need perspective() or orthographic().

import { Mat4x3, Vec3 } from '@1pizzateam/spock';

const view = new Mat4x3().lookAtRH(
  new Vec3(0, 2, 6), // eye
  new Vec3(0, 0, 0), // target
  new Vec3(0, 1, 0)  // up
);

const model = new Mat4x3()
  .translate(new Vec3(1, 0, 0))
  .rotateY(Math.PI / 4);

Constructor

Identity if no arguments; otherwise the given affine entries.

No arguments gives the identity transform. Pass the twelve affine entries to set them; the last column stays (0, 0, 0, 1) because this type cannot hold a projection.

new Mat4x3(x1?:number, x2?:number, x3?:number, y1?:number, y2?:number, y3?:number, z1?:number, z2?:number, z3?:number, t1?:number, t2?:number, t3?:number)

Parameters

• x1 — number. Optional.
• x2 — number. Optional.
• x3 — number. Optional.
• y1 — number. Optional.
• y2 — number. Optional.
• y3 — number. Optional.
• z1 — number. Optional.
• z2 — number. Optional.
• z3 — number. Optional.
• t1 — number. Optional.
• t2 — number. Optional.
• t3 — number. Optional.

Returns

Mat4x3

Example

import { Mat4x3 } from '@1pizzateam/spock';

const value = new Mat4x3(1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1);

Mat4x3.copy()

Copy another matrix into this one.

Overwrites this transform from another one, reusing the buffer.

copy(matrix4x3: Mat4x3): Mat4x3

Parameters

• matrix4x3 — Mat4x3.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().copy(new Mat4x3());

Mat4x3.toArray()

Live buffer, or a copy into target.

Returns the live 4×4 Float32Array behind the transform, padded so it uploads to WebGL as a mat4. Pass a target array to copy instead.

toArray(target?: Float32Array): Float32Array

Parameters

• target — Float32Array. Optional.

Returns

Float32Array — the Mat4x3 as an array

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().toArray(new Float32Array(16));

Mat4x3.toString()

Human-readable row string.

A readable dump of the entries for debugging.

toString(): string

Parameters

None.

Returns

string — the Mat4x3 as a string

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().toString();

Mat4x3.identity()

Set this matrix to identity.

Resets to the identity transform.

identity(): Mat4x3

Parameters

None.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().identity();

Mat4x3.scale()

Compose a 3D scale onto this matrix.

Composes a scale onto the current transform rather than replacing it.

scale(vector3: Vec3): Mat4x3

Parameters

• vector3 — Vec3.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3, Vec3 } from '@1pizzateam/spock';


const result = new Mat4x3().scale(new Vec3(1, 2, 3));

Mat4x3.rotateX()

Compose a rotation about X (radians).

Composes a rotation about the X axis, in radians, onto the current transform.

rotateX(angle: number): Mat4x3

Parameters

• angle — number.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().rotateX(Math.PI / 4);

Mat4x3.rotateY()

Compose a rotation about Y (radians).

Composes a rotation about the Y axis onto the current transform.

rotateY(angle: number): Mat4x3

Parameters

• angle — number.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().rotateY(Math.PI / 4);

Mat4x3.rotateZ()

Compose a rotation about Z (radians).

Composes a rotation about the Z axis onto the current transform.

rotateZ(angle: number): Mat4x3

Parameters

• angle — number.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().rotateZ(Math.PI / 4);

Mat4x3.translate()

Compose a 3D translation onto this matrix.

Composes a translation onto the current transform, so any rotation already applied also rotates this movement.

translate(vector3: Vec3): Mat4x3

Parameters

• vector3 — Vec3.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3, Vec3 } from '@1pizzateam/spock';


const result = new Mat4x3().translate(new Vec3(1, 2, 3));

Mat4x3.multiply()

Multiply by another affine 4×3 matrix.

Multiplies this transform by another in place. Order matters, and the affine last column is preserved.

multiply(matrix4x3: Mat4x3): Mat4x3

Parameters

• matrix4x3 — Mat4x3.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().multiply(new Mat4x3());

Mat4x3.lookAtRH()

Right-handed look-at view matrix; identity if eye equals target.

Builds a right-handed view transform placing the camera at eye looking toward target. If up is parallel to the view direction a fallback axis is used, and when eye equals target the result is identity, so neither case produces NaN.

lookAtRH(eye: Vec3, target: Vec3, up: Vec3): Mat4x3

Parameters

• eye — Vec3.
• target — Vec3.
• up — Vec3.

Returns

Mat4x3 — the Mat4x3 with its new values

Example

import { Mat4x3, Vec3 } from '@1pizzateam/spock';


const result = new Mat4x3().lookAtRH(new Vec3(1, 2, 3), new Vec3(1, 2, 3), new Vec3(1, 2, 3));

Mat4x3.transposeLinear()

Transpose the linear 3×3 part.

Transposes only the 3×3 rotation and scale part, leaving the translation column alone. For a pure rotation that transpose is also its inverse.

transposeLinear(): Mat4x3

Parameters

None.

Returns

Mat4x3

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().transposeLinear();

Mat4x3.determinantLinear()

Determinant of the linear 3×3 part.

Determinant of the 3×3 linear part, describing how the transform scales volume. Zero means it cannot be inverted.

determinantLinear(): number

Parameters

None.

Returns

number

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().determinantLinear();

Mat4x3.invertAffine()

Invert as an affine transform; unchanged if the linear part is singular.

Inverts using the fact that the transform is affine, which is cheaper than a general 4×4 inversion. A singular matrix is left unchanged.

invertAffine(): Mat4x3

Parameters

None.

Returns

Mat4x3

Example

import { Mat4x3 } from '@1pizzateam/spock';


const result = new Mat4x3().invertAffine();