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Quat< T > Class Template Reference

`#include <openvdb/math/Quat.h>`

## Public Types

using | value_type = T
using | ValueType = T

## Public Member Functions

| Quat ()=default
| Quat (T x, T y, T z, T w)
| Constructor with four arguments, e.g. Quatf q(1,2,3,4);.
| Quat (T *a)
| Constructor with array argument, e.g. float a[4]; Quatf q(a);.
| Quat (const Vec3< T > &axis, T angle)
| Quat (math::Axis axis, T angle)
| Constructor given rotation as axis and angle.
template<typename T1>
| Quat (const Mat3< T1 > &rot)
| Constructor given a rotation matrix.
T & | x ()
| Reference to the component, e.g. q.x() = 4.5f;.
T & | y ()
T & | z ()
T & | w ()
T | x () const
| Get the component, e.g. float f = q.w();.
T | y () const
T | z () const
T | w () const
T & | operator[] (int i)
| Array style reference to the components, e.g. q[3] = 1.34f;.
T | operator[] (int i) const
| Array style constant reference to the components, e.g. float f = q[1];.
| operator T* ()
| Cast to T*.
| operator const T * () const
T & | operator() (int i)
| Alternative indexed reference to the elements.
T | operator() (int i) const
| Alternative indexed constant reference to the elements,.
T | angle () const
| Return angle of rotation.
Vec3< T > | axis () const
| Return axis of rotation.
Quat & | init (T x, T y, T z, T w)
| "this" quaternion gets initialized to [x, y, z, w]
Quat & | init ()
| "this" quaternion gets initialized to identity, same as setIdentity()
Quat & | setAxisAngle (const Vec3< T > &axis, T angle)
Quat & | setZero ()
| Set "this" vector to zero.
Quat & | setIdentity ()
| Set "this" vector to identity.
Vec3< T > | eulerAngles (RotationOrder rotationOrder) const
| Returns vector of x,y,z rotational components.
bool | operator== (const Quat &q) const
| Equality operator, does exact floating point comparisons.
bool | eq (const Quat &q, T eps=1.0e-7) const
| Test if "this" is equivalent to q with tolerance of eps value.
Quat & | operator+= (const Quat &q)
| Add quaternion q to "this" quaternion, e.g. q += q1;.
Quat & | operator-= (const Quat &q)
| Subtract quaternion q from "this" quaternion, e.g. q -= q1;.
Quat & | operator*= (T scalar)
| Scale "this" quaternion by scalar, e.g. q *= scalar;.
Quat | operator+ (const Quat &q) const
| Return (this+q), e.g. q = q1 + q2;.
Quat | operator- (const Quat &q) const
| Return (this-q), e.g. q = q1 - q2;.
Quat | operator* (const Quat &q) const
| Return (this*q), e.g. q = q1 * q2;.
Quat | operator*= (const Quat &q)
| Assigns this to (this*q), e.g. q *= q1;.
Quat | operator* (T scalar) const
| Return (this*scalar), e.g. q = q1 * scalar;.
Quat | operator/ (T scalar) const
| Return (this/scalar), e.g. q = q1 / scalar;.
Quat | operator- () const
| Negation operator, e.g. q = -q;.
Quat & | add (const Quat &q1, const Quat &q2)
Quat & | sub (const Quat &q1, const Quat &q2)
Quat & | mult (const Quat &q1, const Quat &q2)
Quat & | scale (T scale, const Quat &q)
T | dot (const Quat &q) const
| Dot product.
Quat | derivative (const Vec3< T > &omega) const
bool | normalize (T eps=T(1.0e-8))
| this = normalized this
Quat | unit () const
| this = normalized this
Quat | inverse (T tolerance=T(0)) const
| returns inverse of this
Quat | conjugate () const
Vec3< T > | rotateVector (const Vec3< T > &v) const
| Return rotated vector by "this" quaternion.
std::string | str () const
void | write (std::ostream &os) const
void | read (std::istream &is)

## Static Public Member Functions

static unsigned | numElements ()
static Quat | zero ()
| Predefined constants, e.g. Quat q = Quat::identity();.
static Quat | identity ()

## Static Public Attributes

static const int | size = 4

## Protected Attributes

T | mm [4]

## Friends

std::ostream & | operator<< (std::ostream &stream, const Quat &q)
| Output to the stream, e.g. std::cout << q << std::endl;.
Quat | slerp (const Quat &q1, const Quat &q2, T t, T tolerance)

## Member Typedef Documentation

## value_type

template<typename T>

using value_type = T

## ValueType

template<typename T>

using ValueType = T

## Constructor & Destructor Documentation

## Quat() [1/6]

template<typename T>

Quat | ( |  | ) |

default

Trivial constructor, the quaternion is NOT initialized

Note
  destructor, copy constructor, assignment operator and move constructor are left to be defined by the compiler (default)

## Quat() [2/6]

template<typename T>

Quat | ( | T | x,
|  | T | y,
|  | T | z,
|  | T | w )

inline

Constructor with four arguments, e.g. Quatf q(1,2,3,4);.

## Quat() [3/6]

template<typename T>

Quat | ( | T * | a | ) |

inline

Constructor with array argument, e.g. float a[4]; Quatf q(a);.

## Quat() [4/6]

template<typename T>

Quat | ( | const Vec3< T > & | axis,
|  | T | angle )

inline

Constructor given rotation as axis and angle, the axis must be unit vector

## Quat() [5/6]

template<typename T>

Quat | ( | math::Axis | axis,
|  | T | angle )

inline

Constructor given rotation as axis and angle.

## Quat() [6/6]

template<typename T>
template<typename T1>

Quat | ( | const Mat3< T1 > & | rot | ) |

inline

Constructor given a rotation matrix.

## Member Function Documentation

## add()

template<typename T>

Quat & add | ( | const Quat< T > & | q1,
|  | const Quat< T > & | q2 )

inline

this = q1 + q2 "this", q1 and q2 need not be distinct objects, e.g. q.add(q1,q);

## angle()

template<typename T>

T angle | ( |  | ) | const

inline

Return angle of rotation.

## axis()

template<typename T>

Vec3< T > axis | ( |  | ) | const

inline

Return axis of rotation.

## conjugate()

template<typename T>

Quat conjugate | ( |  | ) | const

inline

Return the conjugate of "this", same as invert without unit quaternion test

## derivative()

template<typename T>

Quat derivative | ( | const Vec3< T > & | omega | ) | const

inline

Return the quaternion rate corrsponding to the angular velocity omega and "this" current rotation

## dot()

template<typename T>

T dot | ( | const Quat< T > & | q | ) | const

inline

Dot product.

## eq()

template<typename T>

bool eq | ( | const Quat< T > & | q,
|  | T | eps = 1.0e-7 ) const

inline

Test if "this" is equivalent to q with tolerance of eps value.

## eulerAngles()

template<typename T>

Vec3< T > eulerAngles | ( | RotationOrder | rotationOrder | ) | const

inline

Returns vector of x,y,z rotational components.

## identity()

template<typename T>

Quat identity | ( |  | ) |

inlinestatic

## init() [1/2]

template<typename T>

Quat & init | ( |  | ) |

inline

"this" quaternion gets initialized to identity, same as setIdentity()

## init() [2/2]

template<typename T>

Quat & init | ( | T | x,
|  | T | y,
|  | T | z,
|  | T | w )

inline

"this" quaternion gets initialized to [x, y, z, w]

## inverse()

template<typename T>

Quat inverse | ( | T | tolerance = T(0) | ) | const

inline

returns inverse of this

## mult()

template<typename T>

Quat & mult | ( | const Quat< T > & | q1,
|  | const Quat< T > & | q2 )

inline

this = q1 * q2 q1 and q2 must be distinct objects than "this", e.g. q.mult(q1,q2);

## normalize()

template<typename T>

bool normalize | ( | T | eps = T(1.0e-8) | ) |

inline

this = normalized this

## numElements()

template<typename T>

unsigned numElements | ( |  | ) |

inlinestatic

## operator const T *()

template<typename T>

operator const T * | ( |  | ) | const

inline

## operator T*()

template<typename T>

operator T* | ( |  | ) |

inline

Cast to T*.

## operator()() [1/2]

template<typename T>

T & operator() | ( | int | i | ) |

inline

Alternative indexed reference to the elements.

## operator()() [2/2]

template<typename T>

T operator() | ( | int | i | ) | const

inline

Alternative indexed constant reference to the elements,.

## operator*() [1/2]

template<typename T>

Quat operator* | ( | const Quat< T > & | q | ) | const

inline

Return (this*q), e.g. q = q1 * q2;.

## operator*() [2/2]

template<typename T>

Quat operator* | ( | T | scalar | ) | const

inline

Return (this*scalar), e.g. q = q1 * scalar;.

## operator*=() [1/2]

template<typename T>

Quat operator*= | ( | const Quat< T > & | q | ) |

inline

Assigns this to (this*q), e.g. q *= q1;.

## operator*=() [2/2]

template<typename T>

Quat & operator*= | ( | T | scalar | ) |

inline

Scale "this" quaternion by scalar, e.g. q *= scalar;.

## operator+()

template<typename T>

Quat operator+ | ( | const Quat< T > & | q | ) | const

inline

Return (this+q), e.g. q = q1 + q2;.

## operator+=()

template<typename T>

Quat & operator+= | ( | const Quat< T > & | q | ) |

inline

Add quaternion q to "this" quaternion, e.g. q += q1;.

## operator-() [1/2]

template<typename T>

Quat operator- | ( |  | ) | const

inline

Negation operator, e.g. q = -q;.

## operator-() [2/2]

template<typename T>

Quat operator- | ( | const Quat< T > & | q | ) | const

inline

Return (this-q), e.g. q = q1 - q2;.

## operator-=()

template<typename T>

Quat & operator-= | ( | const Quat< T > & | q | ) |

inline

Subtract quaternion q from "this" quaternion, e.g. q -= q1;.

## operator/()

template<typename T>

Quat operator/ | ( | T | scalar | ) | const

inline

Return (this/scalar), e.g. q = q1 / scalar;.

## operator==()

template<typename T>

bool operator== | ( | const Quat< T > & | q | ) | const

inline

Equality operator, does exact floating point comparisons.

## operator[]() [1/2]

template<typename T>

T & operator[] | ( | int | i | ) |

inline

Array style reference to the components, e.g. q[3] = 1.34f;.

## operator[]() [2/2]

template<typename T>

T operator[] | ( | int | i | ) | const

inline

Array style constant reference to the components, e.g. float f = q[1];.

## read()

template<typename T>

void read | ( | std::istream & | is | ) |

inline

## rotateVector()

template<typename T>

Vec3< T > rotateVector | ( | const Vec3< T > & | v | ) | const

inline

Return rotated vector by "this" quaternion.

## scale()

template<typename T>

Quat & scale | ( | T | scale,
|  | const Quat< T > & | q )

inline

this = scalar*q, q need not be distinct object than "this", e.g. q.scale(1.5,q1);

## setAxisAngle()

template<typename T>

Quat & setAxisAngle | ( | const Vec3< T > & | axis,
|  | T | angle )

inline

Set "this" quaternion to rotation specified by axis and angle, the axis must be unit vector

## setIdentity()

template<typename T>

Quat & setIdentity | ( |  | ) |

inline

Set "this" vector to identity.

## setZero()

template<typename T>

Quat & setZero | ( |  | ) |

inline

Set "this" vector to zero.

## str()

template<typename T>

std::string str | ( |  | ) | const

inline

Returns
  string representation of Classname

## sub()

template<typename T>

Quat & sub | ( | const Quat< T > & | q1,
|  | const Quat< T > & | q2 )

inline

this = q1 - q2 "this", q1 and q2 need not be distinct objects, e.g. q.sub(q1,q);

## unit()

template<typename T>

Quat unit | ( |  | ) | const

inline

this = normalized this

## w() [1/2]

template<typename T>

T & w | ( |  | ) |

inline

## w() [2/2]

template<typename T>

T w | ( |  | ) | const

inline

## write()

template<typename T>

void write | ( | std::ostream & | os | ) | const

inline

## x() [1/2]

template<typename T>

T & x | ( |  | ) |

inline

Reference to the component, e.g. q.x() = 4.5f;.

## x() [2/2]

template<typename T>

T x | ( |  | ) | const

inline

Get the component, e.g. float f = q.w();.

## y() [1/2]

template<typename T>

T & y | ( |  | ) |

inline

## y() [2/2]

template<typename T>

T y | ( |  | ) | const

inline

## z() [1/2]

template<typename T>

T & z | ( |  | ) |

inline

## z() [2/2]

template<typename T>

T z | ( |  | ) | const

inline

## zero()

template<typename T>

Quat zero | ( |  | ) |

inlinestatic

Predefined constants, e.g. Quat q = Quat::identity();.

## Friends And Related Symbol Documentation

## operator<<

template<typename T>

std::ostream & operator<< | ( | std::ostream & | stream,
|  | const Quat< T > & | q )

friend

Output to the stream, e.g. std::cout << q << std::endl;.

## slerp

template<typename T>

Quat slerp | ( | const Quat< T > & | q1,
|  | const Quat< T > & | q2,
|  | T | t,
|  | T | tolerance )

friend

## Member Data Documentation

## mm

template<typename T>

T mm[4]

protected

## size

template<typename T>

const int size = 4

static