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  5. QQuaternion

QQuaternion 類

QQuaternion 類錶示由嚮量和標量組成的四元數。 更多...

頭： #include <QQuaternion>
CMake: find_package(Qt6 REQUIRED COMPONENTS Gui)
target_link_libraries(mytarget PRIVATE Qt6::Gui)
qmake: QT += gui

公共函數

QQuaternion ()
QQuaternion (const QVector4D & vector )
QQuaternion (float scalar , const QVector3D & vector )
QQuaternion (float scalar , float xpos , float ypos , float zpos )
QQuaternion conjugated () const
void getAxes (QVector3D * xAxis , QVector3D * yAxis , QVector3D * zAxis ) const
void getAxisAndAngle (float * x , float * y , float * z , float * angle ) const
void getAxisAndAngle (QVector3D * axis , float * angle ) const
void getEulerAngles (float * pitch , float * yaw , float * roll ) const
QQuaternion inverted () const
bool isIdentity () const
bool isNull () const
float length () const
float lengthSquared () const
void normalize ()
QQuaternion normalized () const
QVector3D rotatedVector (const QVector3D & vector ) const
float scalar () const
void setScalar (float scalar )
void setVector (const QVector3D & vector )
void setVector (float x , float y , float z )
void setX (float x )
void setY (float y )
void setZ (float z )
QVector3D toEulerAngles () const
QMatrix3x3 toRotationMatrix () const
QVector4D toVector4D () const
QVector3D vector () const
float x () const
float y () const
float z () const
QVariant operator QVariant () const
QQuaternion & operator*= (const QQuaternion & quaternion )
QQuaternion & operator*= (float factor )
QQuaternion & operator+= (const QQuaternion & quaternion )
QQuaternion & operator-= (const QQuaternion & quaternion )
QQuaternion & operator/= (float divisor )

靜態公共成員

float dotProduct (const QQuaternion & q1 , const QQuaternion & q2 )
QQuaternion fromAxes (const QVector3D & xAxis , const QVector3D & yAxis , const QVector3D & zAxis )
QQuaternion fromAxisAndAngle (const QVector3D & axis , float angle )
QQuaternion fromAxisAndAngle (float x , float y , float z , float angle )
QQuaternion fromDirection (const QVector3D & direction , const QVector3D & up )
QQuaternion fromEulerAngles (float pitch , float yaw , float roll )
QQuaternion fromEulerAngles (const QVector3D & angles )
QQuaternion fromRotationMatrix (const QMatrix3x3 & rot3x3 )
QQuaternion nlerp (const QQuaternion & q1 , const QQuaternion & q2 , float t )
QQuaternion rotationTo (const QVector3D & from , const QVector3D & to )
QQuaternion slerp (const QQuaternion & q1 , const QQuaternion & q2 , float t )
bool qFuzzyCompare (const QQuaternion & q1 , const QQuaternion & q2 )
bool operator!= (const QQuaternion & q1 , const QQuaternion & q2 )
QQuaternion operator* (const QQuaternion & q1 , const QQuaternion & q2 )
QVector3D operator* (const QQuaternion & quaternion , const QVector3D & vec )
QQuaternion operator* (const QQuaternion & quaternion , float factor )
QQuaternion operator* (float factor , const QQuaternion & quaternion )
QQuaternion operator+ (const QQuaternion & q1 , const QQuaternion & q2 )
QQuaternion operator- (const QQuaternion & quaternion )
QQuaternion operator- (const QQuaternion & q1 , const QQuaternion & q2 )
QQuaternion operator/ (const QQuaternion & quaternion , float divisor )
QDataStream & operator<< (QDataStream & stream , const QQuaternion & quaternion )
bool operator== (const QQuaternion & q1 , const QQuaternion & q2 )
QDataStream & operator>> (QDataStream & stream , QQuaternion & quaternion )

詳細描述

Quaternions are used to represent rotations in 3D space, and consist of a 3D rotation axis specified by the x, y, and z coordinates, and a scalar representing the rotation angle.

成員函數文檔編製

[constexpr noexcept] QQuaternion:: QQuaternion ()

Constructs an identity quaternion (1, 0, 0, 0), i.e. with the vector (0, 0, 0) and scalar 1.

[explicit constexpr noexcept] QQuaternion:: QQuaternion (const QVector4D & vector )

構造四元數從分量為 vector .

[constexpr noexcept] QQuaternion:: QQuaternion ( float scalar , const QVector3D & vector )

Constructs a quaternion vector from the specified vector and scalar .

另請參閱 vector () 和 scalar ().

[constexpr noexcept] QQuaternion:: QQuaternion ( float scalar , float xpos , float ypos , float zpos )

Constructs a quaternion with the vector ( xpos , ypos , zpos ) 和 scalar .

[constexpr noexcept] QQuaternion QQuaternion:: conjugated () const

Returns the conjugate of this quaternion, which is (-x, -y, -z, scalar).

[static constexpr noexcept] float QQuaternion:: dotProduct (const QQuaternion & q1 , const QQuaternion & q2 )

返迴點積為 q1 and q2 .

另請參閱 length ().

[static] QQuaternion QQuaternion:: fromAxes (const QVector3D & xAxis , const QVector3D & yAxis , const QVector3D & zAxis )

Constructs the quaternion using 3 axes ( xAxis , yAxis , zAxis ).

注意： The axes are assumed to be orthonormal.

另請參閱 getAxes () 和 fromRotationMatrix ().

[static] QQuaternion QQuaternion:: fromAxisAndAngle (const QVector3D & axis , float angle )

Creates a normalized quaternion that corresponds to rotating through angle degrees about the specified 3D axis .

另請參閱 getAxisAndAngle ().

[static] QQuaternion QQuaternion:: fromAxisAndAngle ( float x , float y , float z , float angle )

Creates a normalized quaternion that corresponds to rotating through angle degrees about the 3D axis ( x , y , z ).

另請參閱 getAxisAndAngle ().

[static] QQuaternion QQuaternion:: fromDirection (const QVector3D & direction , const QVector3D & up )

Constructs the quaternion using specified forward direction direction and upward direction up . If the upward direction was not specified or the forward and upward vectors are collinear, a new orthonormal upward direction will be generated.

另請參閱 fromAxes () 和 rotationTo ().

[static] QQuaternion QQuaternion:: fromEulerAngles ( float pitch , float yaw , float roll )

Creates a quaternion that corresponds to a rotation of roll degrees around the z axis, pitch degrees around the x axis, and yaw degrees around the y axis (in that order).

另請參閱 getEulerAngles ().

[static] QQuaternion QQuaternion:: fromEulerAngles (const QVector3D & angles )

這是重載函數。

Creates a quaternion that corresponds to a rotation of angles : angles. z () degrees around the z axis, angles. x () degrees around the x axis, and angles. y () degrees around the y axis (in that order).

另請參閱 toEulerAngles ().

[static] QQuaternion QQuaternion:: fromRotationMatrix (const QMatrix3x3 & rot3x3 )

Creates a quaternion that corresponds to the rotation matrix rot3x3 .

注意： If the given rotation matrix is not normalized, the resulting quaternion will contain scaling information.

另請參閱 toRotationMatrix () 和 fromAxes ().

void QQuaternion:: getAxes ( QVector3D * xAxis , QVector3D * yAxis , QVector3D * zAxis ) const

Returns the 3 orthonormal axes ( xAxis , yAxis , zAxis ) defining the quaternion.

所有的 xAxis , yAxis ，和 zAxis must be valid, non- nullptr pointers, otherwise the behavior is undefined.

另請參閱 fromAxes () 和 toRotationMatrix ().

void QQuaternion:: getAxisAndAngle ( float * x , float * y , float * z , float * angle ) const

Extracts a 3D axis ( x , y , z ) and a rotating angle angle (in degrees) that corresponds to this quaternion.

所有的 x , y , z ，和 angle must be valid, non- nullptr pointers, otherwise the behavior is undefined.

另請參閱 fromAxisAndAngle ().

void QQuaternion:: getAxisAndAngle ( QVector3D * axis , float * angle ) const

這是重載函數。

Extracts a 3D axis axis and a rotating angle angle (in degrees) that corresponds to this quaternion.

Both axis and angle must be valid, non- nullptr pointers, otherwise the behavior is undefined.

另請參閱 fromAxisAndAngle ().

void QQuaternion:: getEulerAngles ( float * pitch , float * yaw , float * roll ) const

計算 roll , pitch ，和 yaw Euler angles (in degrees) that corresponds to this quaternion.

所有的 pitch , yaw ，和 roll must be valid, non- nullptr pointers, otherwise the behavior is undefined.

另請參閱 fromEulerAngles ().

[constexpr noexcept] QQuaternion QQuaternion:: inverted () const

Returns the inverse of this quaternion. If this quaternion is null, then a null quaternion is returned.

另請參閱 isNull () 和 length ().

[constexpr noexcept] bool QQuaternion:: isIdentity () const

返迴 true if the x, y, and z components of this quaternion are set to 0.0, and the scalar component is set to 1.0; otherwise returns false .

[constexpr noexcept] bool QQuaternion:: isNull () const

返迴 true if the x, y, z, and scalar components of this quaternion are set to 0.0; otherwise returns false .

float QQuaternion:: length () const

Returns the length of the quaternion. This is also called the "norm".

另請參閱 lengthSquared (), normalized ()，和 dotProduct ().

float QQuaternion:: lengthSquared () const

Returns the squared length of the quaternion.

注意： Though cheap to compute, this is susceptible to overflow and underflow that length () avoids in many cases.

另請參閱 length () 和 dotProduct ().

[static] QQuaternion QQuaternion:: nlerp (const QQuaternion & q1 , const QQuaternion & q2 , float t )

Interpolates along the shortest linear path between the rotational positions q1 and q2 。值 t should be between 0 and 1, indicating the distance to travel between q1 and q2 . The result will be normalized ().

若 t is less than or equal to 0, then q1 will be returned. If t is greater than or equal to 1, then q2 將被返迴。

The nlerp() function is typically faster than slerp () and will give approximate results to spherical interpolation that are good enough for some applications.

另請參閱 slerp ().

void QQuaternion:: normalize ()

Normalizes the current quaternion in place. Nothing happens if this is a null quaternion or the length of the quaternion is very close to 1.

另請參閱 length () 和 normalized ().

QQuaternion QQuaternion:: normalized () const

Returns the normalized unit form of this quaternion.

If this quaternion is null, then a null quaternion is returned. If the length of the quaternion is very close to 1, then the quaternion will be returned as-is. Otherwise the normalized form of the quaternion of length 1 will be returned.

另請參閱 normalize (), length ()，和 dotProduct ().

QVector3D QQuaternion:: rotatedVector (const QVector3D & vector ) const

Rotates vector with this quaternion to produce a new vector in 3D space. The following code: 

QVector3D result = q.rotatedVector(vector);

相當於以下： 

QVector3D result = (q * QQuaternion(0, vector) * q.conjugated()).vector();

[static] QQuaternion QQuaternion:: rotationTo (const QVector3D & from , const QVector3D & to )

Returns the shortest arc quaternion to rotate from the direction described by the vector from to the direction described by the vector to .

另請參閱 fromDirection ().

[constexpr noexcept] float QQuaternion:: scalar () const

Returns the scalar component of this quaternion.

另請參閱 setScalar (), x (), y ()，和 z ().

[constexpr noexcept] void QQuaternion:: setScalar ( float scalar )

Sets the scalar component of this quaternion to scalar .

另請參閱 scalar (), setX (), setY ()，和 setZ ().

[constexpr noexcept] void QQuaternion:: setVector (const QVector3D & vector )

Sets the vector component of this quaternion to vector .

另請參閱 vector () 和 setScalar ().

[constexpr noexcept] void QQuaternion:: setVector ( float x , float y , float z )

Sets the vector component of this quaternion to ( x , y , z ).

另請參閱 vector () 和 setScalar ().

[constexpr noexcept] void QQuaternion:: setX ( float x )

Sets the x coordinate of this quaternion's vector to the given x 坐標。

另請參閱 x (), setY (), setZ ()，和 setScalar ().

[constexpr noexcept] void QQuaternion:: setY ( float y )

Sets the y coordinate of this quaternion's vector to the given y 坐標。

另請參閱 y (), setX (), setZ ()，和 setScalar ().

[constexpr noexcept] void QQuaternion:: setZ ( float z )

Sets the z coordinate of this quaternion's vector to the given z 坐標。

另請參閱 z (), setX (), setY ()，和 setScalar ().

[static] QQuaternion QQuaternion:: slerp (const QQuaternion & q1 , const QQuaternion & q2 , float t )

Interpolates along the shortest spherical path between the rotational positions q1 and q2 。值 t should be between 0 and 1, indicating the spherical distance to travel between q1 and q2 .

若 t is less than or equal to 0, then q1 will be returned. If t is greater than or equal to 1, then q2 將被返迴。

另請參閱 nlerp ().

QVector3D QQuaternion:: toEulerAngles () const

Calculates roll, pitch, and yaw Euler angles (in degrees) that correspond to this quaternion.

另請參閱 fromEulerAngles ().

QMatrix3x3 QQuaternion:: toRotationMatrix () const

Creates a rotation matrix that corresponds to this quaternion.

注意： If this quaternion is not normalized, the resulting rotation matrix will contain scaling information.

另請參閱 fromRotationMatrix () 和 getAxes ().

[constexpr noexcept] QVector4D QQuaternion:: toVector4D () const

Returns this quaternion as a 4D vector.

[constexpr noexcept] QVector3D QQuaternion:: vector () const

Returns the vector component of this quaternion.

另請參閱 setVector () 和 scalar ().

[constexpr noexcept] float QQuaternion:: x () const

Returns the x coordinate of this quaternion's vector.

另請參閱 setX (), y (), z ()，和 scalar ().

[constexpr noexcept] float QQuaternion:: y () const

Returns the y coordinate of this quaternion's vector.

另請參閱 setY (), x (), z ()，和 scalar ().

[constexpr noexcept] float QQuaternion:: z () const

Returns the z coordinate of this quaternion's vector.

另請參閱 setZ (), x (), y ()，和 scalar ().

QVariant QQuaternion:: operator QVariant () const

Returns the quaternion as a QVariant .

[constexpr noexcept] QQuaternion &QQuaternion:: operator*= (const QQuaternion & quaternion )

Multiplies this quaternion by quaternion and returns a reference to this quaternion.

[constexpr noexcept] QQuaternion &QQuaternion:: operator*= ( float factor )

Multiplies this quaternion's components by the given factor , and returns a reference to this quaternion.

另請參閱 operator/= ().

[constexpr noexcept] QQuaternion &QQuaternion:: operator+= (const QQuaternion & quaternion )

添加給定 quaternion to this quaternion and returns a reference to this quaternion.

另請參閱 operator-= ().

[constexpr noexcept] QQuaternion &QQuaternion:: operator-= (const QQuaternion & quaternion )

減去給定 quaternion from this quaternion and returns a reference to this quaternion.

另請參閱 operator+= ().

[constexpr] QQuaternion &QQuaternion:: operator/= ( float divisor )

Divides this quaternion's components by the given divisor , and returns a reference to this quaternion.

另請參閱 operator*= ().

相關非成員

[constexpr noexcept] bool qFuzzyCompare (const QQuaternion & q1 , const QQuaternion & q2 )

返迴 true if q1 and q2 are equal, allowing for a small fuzziness factor for floating-point comparisons; false otherwise.

[constexpr noexcept] bool operator!= (const QQuaternion & q1 , const QQuaternion & q2 )

返迴 true if q1 不等於 q2 ；否則返迴 false 。此運算符使用精確浮點比較。

[constexpr noexcept] QQuaternion operator* (const QQuaternion & q1 , const QQuaternion & q2 )

Multiplies q1 and q2 using quaternion multiplication. The result corresponds to applying both of the rotations specified by q1 and q2 .

另請參閱 QQuaternion::operator*= ().

QVector3D operator* (const QQuaternion & quaternion , const QVector3D & vec )

Rotates a vector vec with a quaternion quaternion to produce a new vector in 3D space.

[constexpr noexcept] QQuaternion operator* (const QQuaternion & quaternion , float factor )

返迴副本為給定 quaternion ，乘以給定 factor .

另請參閱 QQuaternion::operator*= ().

[constexpr noexcept] QQuaternion operator* ( float factor , const QQuaternion & quaternion )

返迴副本為給定 quaternion ，乘以給定 factor .

另請參閱 QQuaternion::operator*= ().

[constexpr noexcept] QQuaternion operator+ (const QQuaternion & q1 , const QQuaternion & q2 )

返迴 QQuaternion object that is the sum of the given quaternions, q1 and q2 ；各分量分彆相加。

另請參閱 QQuaternion::operator+= ().

[constexpr noexcept] QQuaternion operator- (const QQuaternion & quaternion )

這是重載函數。

返迴 QQuaternion object that is formed by changing the sign of all three components of the given quaternion .

相當於 QQuaternion(0,0,0,0) - quaternion .

[constexpr noexcept] QQuaternion operator- (const QQuaternion & q1 , const QQuaternion & q2 )

返迴 QQuaternion 對象的形成是通過減去 q2 from q1 ；分彆減去各分量。

另請參閱 QQuaternion::operator-= ().

[constexpr] QQuaternion operator/ (const QQuaternion & quaternion , float divisor )

返迴 QQuaternion object formed by dividing all components of the given quaternion 通過給定 divisor .

另請參閱 QQuaternion::operator/= ().

QDataStream & operator<< ( QDataStream & stream , const QQuaternion & quaternion )

寫入給定 quaternion 到給定 stream 並返迴流引用。

另請參閱 序列化 Qt 數據類型 .

[constexpr noexcept] bool operator== (const QQuaternion & q1 , const QQuaternion & q2 )

返迴 true if q1 等於 q2 ；否則返迴 false 。此運算符使用精確浮點比較。

QDataStream & operator>> ( QDataStream & stream , QQuaternion & quaternion )

讀取四元數從給定 stream 進給定 quaternion 並返迴流引用。

另請參閱 序列化 Qt 數據類型 .

內容

  1. 公共函數

  2. 靜態公共成員

  3. 相關非成員

  4. 詳細描述