# GLKQuaternion ## Overview The `GLKQuaternion` type defines a structure that represents a quaternion. A quaternion is defined by a scalar component `s` and an XYZ vector `v`. Quaternions are often used in graphics programming as a compact representation of a rotation of an object in three dimensions. The functions that manipulate `GLKQuaternion` structures treat the inputs as immutable, instead returning a new quaternion that represent the results of the operation. ## Topics ### Creating Quaternions [`GLKQuaternionMake`](/documentation/GLKit/GLKQuaternionMake(_:_:_:_:)) Returns a quaternion created from its separate components. [`GLKQuaternionMakeWithArray`](/documentation/GLKit/GLKQuaternionMakeWithArray(_:)) Returns a quaternion created from an array of components. [`GLKQuaternionMakeWithVector3`](/documentation/GLKit/GLKQuaternionMakeWithVector3(_:_:)) Returns a quaternion created from a vector and a scalar. [`GLKQuaternionMakeWithAngleAndAxis`](/documentation/GLKit/GLKQuaternionMakeWithAngleAndAxis(_:_:_:_:)) Creates a quaternion that represents a rotation around an axis. [`GLKQuaternionMakeWithAngleAndVector3Axis`](/documentation/GLKit/GLKQuaternionMakeWithAngleAndVector3Axis(_:_:)) Creates a quaternion that represents a rotation around an axis. [`GLKQuaternionMakeWithMatrix3`](/documentation/GLKit/GLKQuaternionMakeWithMatrix3(_:)) Creates a quaternion from a rotation matrix. [`GLKQuaternionMakeWithMatrix4`](/documentation/GLKit/GLKQuaternionMakeWithMatrix4(_:)) Creates a quaternion from a rotation matrix. ### Retrieving Information About a Quaternion [`GLKQuaternionLength`](/documentation/GLKit/GLKQuaternionLength(_:)) Returns the length of a quaternion. [`GLKQuaternionAxis`](/documentation/GLKit/GLKQuaternionAxis(_:)) Returns the axis of rotation of a quaternion. [`GLKQuaternionAngle`](/documentation/GLKit/GLKQuaternionAngle(_:)) Returns the rotation angle of a quaternion. ### Performing Mathematical Operations on Quaternions [`GLKQuaternionNormalize`](/documentation/GLKit/GLKQuaternionNormalize(_:)) Returns a normalized version of a quaternion. [`GLKQuaternionInvert`](/documentation/GLKit/GLKQuaternionInvert(_:)) Returns an inverse of a quaternion. [`GLKQuaternionConjugate`](/documentation/GLKit/GLKQuaternionConjugate(_:)) Returns the conjugate of a quaternion. [`GLKQuaternionAdd`](/documentation/GLKit/GLKQuaternionAdd(_:_:)) Returns the sum of two quaternions. [`GLKQuaternionSubtract`](/documentation/GLKit/GLKQuaternionSubtract(_:_:)) Returns the difference between two quaternions. [`GLKQuaternionMultiply`](/documentation/GLKit/GLKQuaternionMultiply(_:_:)) Returns the product of two quaternions. [`GLKQuaternionSlerp`](/documentation/GLKit/GLKQuaternionSlerp(_:_:_:)) Returns the spherical linear interpolation of two quaternions. ### Applying Quaternions to Vectors [`GLKQuaternionRotateVector3`](/documentation/GLKit/GLKQuaternionRotateVector3(_:_:)) Returns a new vector that is calculated by applying a quaternion rotation to a vector. [`GLKQuaternionRotateVector3Array`](/documentation/GLKit/GLKQuaternionRotateVector3Array(_:_:_:)) Applies a quaternion rotation to an array of vectors. [`GLKQuaternionRotateVector4`](/documentation/GLKit/GLKQuaternionRotateVector4(_:_:)) Returns a new vector calculated by applying a quaternion rotation to a vector. [`GLKQuaternionRotateVector4Array`](/documentation/GLKit/GLKQuaternionRotateVector4Array(_:_:_:)) Applies a quaternion rotation to an array of vectors. ### Data Types [`GLKQuaternion`](/documentation/GLKit/GLKQuaternion) A representation of a quaternion. ### Constants [`GLKQuaternionIdentity`](/documentation/GLKit/GLKQuaternionIdentity) An identity quaternion. --- Copyright © 2026 Apple Inc. All rights reserved. | [Terms of Use](https://www.apple.com/legal/internet-services/terms/site.html) | [Privacy Policy](https://www.apple.com/privacy/privacy-policy)