Class Quaternion

constructor

• new Quaternion(x?: number, y?: number, z?: number, w?: number): Quaternion

  Parameters

  • x: number = 0
  • y: number = 0
  • z: number = 0
  • w: number = 1

  Returns Quaternion

x

y

z

w

Staticidentity

• identity(): Quaternion

  Returns the identity quaternion (0, 0, 0, 1).

  Returns Quaternion

StaticfromAxisAngle

• fromAxisAngle(axis: Vec3, rad: number): Quaternion

  Builds a quaternion representing a rotation of rad radians around axis (axis is normalized internally).

  Parameters

  • axis: Vec3
  • rad: number

  Returns Quaternion

StaticfromEuler

• fromEuler(x: number, y: number, z: number): Quaternion

  Builds a quaternion from intrinsic Euler angles (radians) applied in XYZ order.

  Parameters

  • x: number

    rotation around the X axis (pitch)

  • y: number

    rotation around the Y axis (yaw)

  • z: number

    rotation around the Z axis (roll)

  Returns Quaternion

StaticfromRotationMatrix

• fromRotationMatrix(m: Mat4): Quaternion

  Extracts the rotation of a matrix as a unit quaternion. Only the upper-left 3×3 (the rotation/basis part) is read, so a TRS or look-at matrix works directly provided its basis is orthonormal (no non-uniform scale). Uses the numerically-stable branch-by-largest-diagonal method.

  Handy for deriving an orientation from a constructed basis — e.g. a chase camera does Quaternion.fromRotationMatrix(Mat4.lookAt(eye, target, up).invert()).

  Parameters

  • m: Mat4

    Column-major matrix whose 3×3 rotation part is orthonormal.

  Returns Quaternion

StaticfromForward

• fromForward(forward: Vec3, up?: Vec3): Quaternion

  Builds the rotation that aims an object's local forward axis (Vec3.FORWARD, i.e. -Z) along forward in world space. The inverse of Vec3.FORWARD-relative worldDirection() readers like DirectionalLight / SpotLight: set go.rotation = Quaternion.fromForward(dir) and the light then shines down dir.

  up only resolves the roll about forward (irrelevant for a directional or spot light); it defaults to world up, swapping to world right when forward is nearly vertical so the basis stays well-conditioned.

  Parameters

  • forward: Vec3

    Desired world-space forward direction (normalized internally).

  • Optionalup: Vec3

    Optional reference up; defaults to Vec3.UP (or Vec3.RIGHT near-vertical).

  Returns Quaternion

clone

• clone(): Quaternion

  Returns a copy of this quaternion.

  Returns Quaternion

setAxisAngle

• setAxisAngle(axis: Vec3, rad: number): void

  Sets this quaternion to represent a rotation of rad radians around axis (axis is normalized internally).

  Parameters

  • axis: Vec3

    The axis of rotation.

  • rad: number

    The angle of rotation in radians.

  Returns void

setEuler

• setEuler(x: number, y: number, z: number): void

  Sets this quaternion from intrinsic Euler angles (radians) applied in XYZ order.

  Parameters

  • x: number

    rotation around the X axis (pitch)

  • y: number

    rotation around the Y axis (yaw)

  • z: number

    rotation around the Z axis (roll)

  Returns void

toEuler

• toEuler(): Vec3

  Decomposes this quaternion into intrinsic Euler angles (radians) in XYZ order, matching the convention used by fromEuler and setEuler.

  At the gimbal-lock poles (|pitch| ≈ π/2), roll is fixed at 0 and yaw absorbs the combined rotation.

  Returns Vec3

setIdentity

• setIdentity(): void

  Sets this quaternion to the identity rotation (0, 0, 0, 1). Useful for reusing an existing quaternion instance instead of creating a new one.

  Returns void

lengthSq

• lengthSq(): number

  Returns the squared length.

  Returns number

length

• length(): number

  Returns the Euclidean length.

  Returns number

normalize

• normalize(): Quaternion

  Returns a unit-length copy, or the identity quaternion if length is 0.

  Returns Quaternion

conjugate

• conjugate(): Quaternion

  Returns the conjugate (-x, -y, -z, w), which is the inverse for unit quaternions.

  Returns Quaternion

multiply

• multiply(b: Quaternion): Quaternion

  Returns the Hamilton product this * b, which composes rotations (this applied after b).

  Parameters

  • b: Quaternion

  Returns Quaternion

rotateVec3

• rotateVec3(v: Vec3): Vec3

  Rotates vector v by this quaternion and returns the result.

  Parameters

  • v: Vec3

  Returns Vec3

toMat4

• toMat4(): Mat4

  Converts this quaternion to its equivalent column-major 4x4 rotation matrix.

  Returns Mat4

slerp

• slerp(b: Quaternion, t: number): Quaternion

  Spherical linear interpolation from this to b at parameter t in [0, 1].

  Picks the shorter arc (negates b if the dot product is negative) and falls back to normalized linear interpolation when the angle between the quaternions is tiny.

  Parameters

  • b: Quaternion
  • t: number

  Returns Quaternion