GLM_GTC_quaternion
Stable extensions

Include <glm/gtc/quaternion.hpp> to use the features of this extension. More...

## Functions

template<typename T , qualifier Q>
GLM_FUNC_DECL T | angle (tquat< T, Q > const &x)
| Returns the quaternion rotation angle. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | angleAxis (T const &angle, vec< 3, T, Q > const &axis)
| Build a quaternion from an angle and a normalized axis. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 3, T, Q > | axis (tquat< T, Q > const &x)
| Returns the q rotation axis. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | conjugate (tquat< T, Q > const &q)
| Returns the q conjugate. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL T | dot (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns dot product of q1 and q2, i.e., q1[0] * q2[0] + q1[1] * q2[1] + ... More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | equal (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns the component-wise comparison of result x == y. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 3, T, Q > | eulerAngles (tquat< T, Q > const &x)
| Returns euler angles, pitch as x, yaw as y, roll as z. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | greaterThan (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns the component-wise comparison of result x > y. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | greaterThanEqual (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns the component-wise comparison of result x >= y. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | inverse (tquat< T, Q > const &q)
| Returns the q inverse. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | isinf (tquat< T, Q > const &x)
| Returns true if x holds a positive infinity or negative infinity representation in the underlying implementation's set of floating point representations. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | isnan (tquat< T, Q > const &x)
| Returns true if x holds a NaN (not a number) representation in the underlying implementation's set of floating point representations. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL T | length (tquat< T, Q > const &q)
| Returns the length of the quaternion. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | lerp (tquat< T, Q > const &x, tquat< T, Q > const &y, T a)
| Linear interpolation of two quaternions. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | lessThan (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns the component-wise comparison result of x < y. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | lessThanEqual (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns the component-wise comparison of result x <= y. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL mat< 3, 3, T, Q > | mat3_cast (tquat< T, Q > const &x)
| Converts a quaternion to a 3 * 3 matrix. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL mat< 4, 4, T, Q > | mat4_cast (tquat< T, Q > const &x)
| Converts a quaternion to a 4 * 4 matrix. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | mix (tquat< T, Q > const &x, tquat< T, Q > const &y, T a)
| Spherical linear interpolation of two quaternions. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | normalize (tquat< T, Q > const &q)
| Returns the normalized quaternion. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL vec< 4, bool, Q > | notEqual (tquat< T, Q > const &x, tquat< T, Q > const &y)
| Returns the component-wise comparison of result x != y. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL T | pitch (tquat< T, Q > const &x)
| Returns pitch value of euler angles expressed in radians. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | quat_cast (mat< 3, 3, T, Q > const &x)
| Converts a 3 * 3 matrix to a quaternion. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | quat_cast (mat< 4, 4, T, Q > const &x)
| Converts a 4 * 4 matrix to a quaternion. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL T | roll (tquat< T, Q > const &x)
| Returns roll value of euler angles expressed in radians. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | rotate (tquat< T, Q > const &q, T const &angle, vec< 3, T, Q > const &axis)
| Rotates a quaternion from a vector of 3 components axis and an angle. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL tquat< T, Q > | slerp (tquat< T, Q > const &x, tquat< T, Q > const &y, T a)
| Spherical linear interpolation of two quaternions. More...
template<typename T , qualifier Q>
GLM_FUNC_DECL T | yaw (tquat< T, Q > const &x)
| Returns yaw value of euler angles expressed in radians. More...

## Detailed Description

Include <glm/gtc/quaternion.hpp> to use the features of this extension.

Defines a templated quaternion type and several quaternion operations.

## Function Documentation

GLM_FUNC_DECL T glm::angle | ( | tquat< T, Q > const & | x | ) |

Returns the quaternion rotation angle.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::angleAxis | ( | T const & | angle,
|  | vec< 3, T, Q > const & | axis
| ) |  |

Build a quaternion from an angle and a normalized axis.

Parameters

  angle | Angle expressed in radians.
  axis | Axis of the quaternion, must be normalized.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<3, T, Q> glm::axis | ( | tquat< T, Q > const & | x | ) |

Returns the q rotation axis.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::conjugate | ( | tquat< T, Q > const & | q | ) |

Returns the q conjugate.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL T glm::dot | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns dot product of q1 and q2, i.e., q1[0] * q2[0] + q1[1] * q2[1] + ...

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::equal | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns the component-wise comparison of result x == y.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<3, T, Q> glm::eulerAngles | ( | tquat< T, Q > const & | x | ) |

Returns euler angles, pitch as x, yaw as y, roll as z.

The result is expressed in radians.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::greaterThan | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns the component-wise comparison of result x > y.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::greaterThanEqual | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns the component-wise comparison of result x >= y.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::inverse | ( | tquat< T, Q > const & | q | ) |

Returns the q inverse.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::isinf | ( | tquat< T, Q > const & | x | ) |

Returns true if x holds a positive infinity or negative infinity representation in the underlying implementation's set of floating point representations.

Returns false otherwise, including for implementations with no infinity representations.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::isnan | ( | tquat< T, Q > const & | x | ) |

Returns true if x holds a NaN (not a number) representation in the underlying implementation's set of floating point representations.

Returns false otherwise, including for implementations with no NaN representations.

/!\ When using compiler fast math, this function may fail.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL T glm::length | ( | tquat< T, Q > const & | q | ) |

Returns the length of the quaternion.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::lerp | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y,
|  | T | a
| ) |  |

Linear interpolation of two quaternions.

The interpolation is oriented.

Parameters

  x | A quaternion
  y | A quaternion
  a | Interpolation factor. The interpolation is defined in the range [0, 1].

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::lessThan | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns the component-wise comparison result of x < y.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::lessThanEqual | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns the component-wise comparison of result x <= y.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL mat<3, 3, T, Q> glm::mat3_cast | ( | tquat< T, Q > const & | x | ) |

Converts a quaternion to a 3 * 3 matrix.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

Referenced by glm::toMat3().

GLM_FUNC_DECL mat<4, 4, T, Q> glm::mat4_cast | ( | tquat< T, Q > const & | x | ) |

Converts a quaternion to a 4 * 4 matrix.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

Referenced by glm::toMat4().

GLM_FUNC_DECL tquat<T, Q> glm::mix | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y,
|  | T | a
| ) |  |

Spherical linear interpolation of two quaternions.

The interpolation is oriented and the rotation is performed at constant speed. For short path spherical linear interpolation, use the slerp function.

Parameters

  x | A quaternion
  y | A quaternion
  a | Interpolation factor. The interpolation is defined beyond the range [0, 1].

Template Parameters

  T | Floating-point scalar types.

See also
  - slerp(tquat<T, Q> const& x, tquat<T, Q> const& y, T const& a)
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::normalize | ( | tquat< T, Q > const & | q | ) |

Returns the normalized quaternion.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL vec<4, bool, Q> glm::notEqual | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y
| ) |  |

Returns the component-wise comparison of result x != y.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL T glm::pitch | ( | tquat< T, Q > const & | x | ) |

Returns pitch value of euler angles expressed in radians.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::quat_cast | ( | mat< 3, 3, T, Q > const & | x | ) |

Converts a 3 * 3 matrix to a quaternion.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

Referenced by glm::toQuat().

GLM_FUNC_DECL tquat<T, Q> glm::quat_cast | ( | mat< 4, 4, T, Q > const & | x | ) |

Converts a 4 * 4 matrix to a quaternion.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL T glm::roll | ( | tquat< T, Q > const & | x | ) |

Returns roll value of euler angles expressed in radians.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::rotate | ( | tquat< T, Q > const & | q,
|  | T const & | angle,
|  | vec< 3, T, Q > const & | axis
| ) |  |

Rotates a quaternion from a vector of 3 components axis and an angle.

Parameters

  q | Source orientation
  angle | Angle expressed in radians.
  axis | Axis of the rotation

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL tquat<T, Q> glm::slerp | ( | tquat< T, Q > const & | x,
|  | tquat< T, Q > const & | y,
|  | T | a
| ) |  |

Spherical linear interpolation of two quaternions.

The interpolation always take the short path and the rotation is performed at constant speed.

Parameters

  x | A quaternion
  y | A quaternion
  a | Interpolation factor. The interpolation is defined beyond the range [0, 1].

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion

GLM_FUNC_DECL T glm::yaw | ( | tquat< T, Q > const & | x | ) |

Returns yaw value of euler angles expressed in radians.

Template Parameters

  T | Floating-point scalar types.

See also
  GLM_GTC_quaternion