LibXR::Quaternion< Scalar > Class Template Reference

四元数表示与运算，继承自 Eigen::Quaternion / Quaternion representation and operations, inheriting from Eigen::Quaternion More...

#include <transform.hpp>

Inheritance diagram for LibXR::Quaternion< Scalar >:

Collaboration diagram for LibXR::Quaternion< Scalar >:

Public Member Functions
	Quaternion ()
	默认构造函数，初始化为单位四元数 / Default constructor initializing to an identity quaternion
	Quaternion (Scalar w, Scalar x, Scalar y, Scalar z)
	通过四个分量初始化四元数 / Construct a quaternion using four components
	Quaternion (const Eigen::Quaternion< Scalar > &q)
	复制构造函数 / Copy constructor
	Quaternion (const RotationMatrix< Scalar > &R)
	通过旋转矩阵构造四元数 / Construct a quaternion from a rotation matrix
	Quaternion (const Eigen::Matrix< Scalar, 3, 3 > R)
	通过 3x3 旋转矩阵构造四元数 / Construct a quaternion from a 3x3 rotation matrix
template<typename T , std::enable_if_t< std::is_same< T, Scalar >::value||std::is_same< T, float >::value||std::is_same< T, double >::value, int > = 0>
	Quaternion (const T(&data)[4])
	通过四维数组初始化四元数 / Construct a quaternion from a 4-element array
Scalar	operator() (int i) const
	获取四元数的分量 / Retrieve a specific component of the quaternion
Quaternion &	operator= (const Eigen::Quaternion< Scalar > &q)
	赋值运算符 / Assignment operator
Quaternion	operator- () const
	取共轭四元数 / Get the conjugate quaternion
Quaternion	operator+ (const Quaternion &q) const
	四元数加法 / Quaternion addition
Quaternion	operator+ (const Eigen::Quaternion< Scalar > &q) const
Quaternion	operator- (const Quaternion &q) const
Quaternion	operator- (const Eigen::Quaternion< Scalar > &q) const
Quaternion	operator* (const Quaternion &q) const
	四元数乘法 / Quaternion multiplication
Quaternion	operator* (const Eigen::Quaternion< Scalar > &q) const
Quaternion	operator/ (const Quaternion &q) const
	四元数除法（即左乘其共轭） / Quaternion division (multiplication by its conjugate)
Quaternion	operator/ (const Eigen::Quaternion< Scalar > &q) const
template<typename Q , std::enable_if_t< std::is_same< Q, Quaternion >::value||std::is_same< Q, Eigen::Quaternion< Scalar > >::value, int > = 0>
const Quaternion &	operator+= (const Q &q)
template<typename Q , std::enable_if_t< std::is_same< Q, Quaternion >::value||std::is_same< Q, Eigen::Quaternion< Scalar > >::value, int > = 0>
const Quaternion &	operator-= (const Q &q)
Position< Scalar >	operator* (const Position< Scalar > &p) const
	旋转三维向量 / Rotate a 3D vector
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngle () const
	获取四元数的欧拉角表示（默认使用 ZYX 旋转顺序） Get the Euler angles representation of the quaternion (default ZYX order)
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngleYZX () const
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngleZYX () const
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngleYXZ () const
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngleZXY () const
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngleXZY () const
Eigen::Matrix< Scalar, 3, 1 >	ToEulerAngleXYZ () const
Eigen::Matrix< Scalar, 3, 3 >	ToRotationMatrix () const
	将四元数转换为 3x3 旋转矩阵 / Convert the quaternion to a 3x3 rotation matrix

Detailed Description

template<typename Scalar>
class LibXR::Quaternion< Scalar >

四元数表示与运算，继承自 Eigen::Quaternion / Quaternion representation and operations, inheriting from Eigen::Quaternion

该类提供了对四元数的基本运算，如加法、减法、乘法、除法，以及与旋转矩阵和欧拉角的转换等。 This class provides fundamental quaternion operations, such as addition, subtraction, multiplication, and division, along with conversions to rotation matrices and Euler angles.

Template Parameters

Scalar

数值类型（默认使用 DefaultScalar） / Numeric type (default: DefaultScalar)

Definition at line 809 of file transform.hpp.

Constructor & Destructor Documentation

Quaternion() [1/6]

template<typename Scalar >

LibXR::Quaternion< Scalar >::Quaternion ( )

inline

默认构造函数，初始化为单位四元数 / Default constructor initializing to an identity quaternion

Definition at line 816 of file transform.hpp.

: Eigen::Quaternion<Scalar>(1, 0, 0, 0) {}

Quaternion() [2/6]

template<typename Scalar >

LibXR::Quaternion< Scalar >::Quaternion ( Scalar  w, Scalar  x, Scalar  y, Scalar  z  )

inline

通过四个分量初始化四元数 / Construct a quaternion using four components

Parameters

w	实部 / Real part
x	i 分量 / i component
y	j 分量 / j component
z	k 分量 / k component

Definition at line 825 of file transform.hpp.

      : Eigen::Quaternion<Scalar>(w, x, y, z)
  {
  }

Quaternion() [3/6]

template<typename Scalar >

LibXR::Quaternion< Scalar >::Quaternion ( const Eigen::Quaternion< Scalar > &  q )

inline

复制构造函数 / Copy constructor

Parameters

q	另一个 Eigen::Quaternion 四元数 / Another Eigen::Quaternion

Definition at line 834 of file transform.hpp.

: Eigen::Quaternion<Scalar>(q) {}

Quaternion() [4/6]

template<typename Scalar >

LibXR::Quaternion< Scalar >::Quaternion ( const RotationMatrix< Scalar > &  R )

inline

通过旋转矩阵构造四元数 / Construct a quaternion from a rotation matrix

Parameters

R	旋转矩阵 / Rotation matrix

Definition at line 840 of file transform.hpp.

      : Eigen::Quaternion<Scalar>(
            Eigen::Quaternion<Scalar>(static_cast<Eigen::Matrix<Scalar, 3, 3>>(R)))
  {
  }

Quaternion() [5/6]

template<typename Scalar >

LibXR::Quaternion< Scalar >::Quaternion ( const Eigen::Matrix< Scalar, 3, 3 >  R )

inline

通过 3x3 旋转矩阵构造四元数 / Construct a quaternion from a 3x3 rotation matrix

Parameters

R	旋转矩阵 / Rotation matrix

Definition at line 851 of file transform.hpp.

      : Eigen::Quaternion<Scalar>(
            Eigen::Quaternion<Scalar>(static_cast<Eigen::Matrix<Scalar, 3, 3>>(R)))
  {
  }

Quaternion() [6/6]

template<typename Scalar >

template<typename T , std::enable_if_t< std::is_same< T, Scalar >::value||std::is_same< T, float >::value||std::is_same< T, double >::value, int > = 0>

LibXR::Quaternion< Scalar >::Quaternion ( const T(&)  data[4] )

inline

通过四维数组初始化四元数 / Construct a quaternion from a 4-element array

Parameters

data	4 维数组，表示 (w, x, y, z) / A 4-element array representing (w, x, y, z)

Definition at line 865 of file transform.hpp.

                                 : Eigen::Quaternion<Scalar>(data)
  {
  }

Member Function Documentation

operator()()

template<typename Scalar >

Scalar LibXR::Quaternion< Scalar >::operator() ( int  i ) const

inline

获取四元数的分量 / Retrieve a specific component of the quaternion

Parameters

i	分量索引 (0: x, 1: y, 2: z, 3: w) / Component index (0: x, 1: y, 2: z, 3: w)

Returns

该分量的值 / Value of the component

Definition at line 874 of file transform.hpp.

  {
    switch (i)
    {
      case 3:
        return this->w();
      case 0:
        return this->x();
      case 1:
        return this->y();
      case 2:
        return this->z();
      default:
        return 0;
    }
  }

operator*() [1/3]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator* ( const Eigen::Quaternion< Scalar > &  q ) const

inline

Definition at line 947 of file transform.hpp.

  {
    return Eigen::Quaternion<Scalar>(*this) * q;
  }

operator*() [2/3]

template<typename Scalar >

Position< Scalar > LibXR::Quaternion< Scalar >::operator* ( const Position< Scalar > &  p ) const

inline

旋转三维向量 / Rotate a 3D vector

Parameters

p	需要旋转的 Position 向量 / Position vector to be rotated

Returns

旋转后的 Position 向量 / Rotated Position vector

Definition at line 990 of file transform.hpp.

  {
    return Eigen::Quaternion<Scalar>(*this) * Eigen::Matrix<Scalar, 3, 1>(p);
  }

operator*() [3/3]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator* ( const Quaternion< Scalar > &  q ) const

inline

四元数乘法 / Quaternion multiplication

Parameters

q	另一个四元数 / Another quaternion

Returns

计算后的四元数 / Computed quaternion

Definition at line 942 of file transform.hpp.

  {
    return Eigen::Quaternion<Scalar>(*this) * Eigen::Quaternion<Scalar>(q);
  }

operator+() [1/2]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator+ ( const Eigen::Quaternion< Scalar > &  q ) const

inline

Definition at line 919 of file transform.hpp.

  {
    return Quaternion(this->w() + q.w(), this->x() + q.x(), this->y() + q.y(),
                      this->z() + q.z());
  }

operator+() [2/2]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator+ ( const Quaternion< Scalar > &  q ) const

inline

四元数加法 / Quaternion addition

Parameters

q	另一个四元数 / Another quaternion

Returns

计算后的四元数 / Computed quaternion

Definition at line 913 of file transform.hpp.

  {
    return Quaternion(this->w() + q.w(), this->x() + q.x(), this->y() + q.y(),
                      this->z() + q.z());
  }

operator+=()

template<typename Scalar >

template<typename Q , std::enable_if_t< std::is_same< Q, Quaternion >::value||std::is_same< Q, Eigen::Quaternion< Scalar > >::value, int > = 0>

const Quaternion & LibXR::Quaternion< Scalar >::operator+= ( const Q &  q )

inline

Definition at line 969 of file transform.hpp.

  {
    *this = *this + q;
    return *this;
  }

operator-() [1/3]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator- ( ) const

inline

取共轭四元数 / Get the conjugate quaternion

Returns

共轭四元数 / Conjugated quaternion

Definition at line 906 of file transform.hpp.

{ return Quaternion((*this).conjugate()); }

operator-() [2/3]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator- ( const Eigen::Quaternion< Scalar > &  q ) const

inline

Definition at line 931 of file transform.hpp.

  {
    return Quaternion(this->w() - q.w(), this->x() - q.x(), this->y() - q.y(),
                      this->z() - q.z());
  }

operator-() [3/3]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator- ( const Quaternion< Scalar > &  q ) const

inline

Definition at line 925 of file transform.hpp.

  {
    return Quaternion(this->w() - q.w(), this->x() - q.x(), this->y() - q.y(),
                      this->z() - q.z());
  }

operator-=()

template<typename Scalar >

template<typename Q , std::enable_if_t< std::is_same< Q, Quaternion >::value||std::is_same< Q, Eigen::Quaternion< Scalar > >::value, int > = 0>

const Quaternion & LibXR::Quaternion< Scalar >::operator-= ( const Q &  q )

inline

Definition at line 979 of file transform.hpp.

  {
    *this = *this - q;
    return *this;
  }

operator/() [1/2]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator/ ( const Eigen::Quaternion< Scalar > &  q ) const

inline

Definition at line 960 of file transform.hpp.

  {
    return (*this) * (-q);
  }

operator/() [2/2]

template<typename Scalar >

Quaternion LibXR::Quaternion< Scalar >::operator/ ( const Quaternion< Scalar > &  q ) const

inline

四元数除法（即左乘其共轭） / Quaternion division (multiplication by its conjugate)

Parameters

q	另一个四元数 / Another quaternion

Returns

计算后的四元数 / Computed quaternion

Definition at line 958 of file transform.hpp.

{ return (*this) * (-q); }

operator=()

template<typename Scalar >

Quaternion & LibXR::Quaternion< Scalar >::operator= ( const Eigen::Quaternion< Scalar > &  q )

inline

赋值运算符 / Assignment operator

Parameters

q	另一个四元数 / Another quaternion

Returns

赋值后的 Quaternion / Assigned Quaternion

Definition at line 896 of file transform.hpp.

  {
    *this = Quaternion(q);
    return *this;
  }

ToEulerAngle()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngle ( ) const

inline

获取四元数的欧拉角表示（默认使用 ZYX 旋转顺序） Get the Euler angles representation of the quaternion (default ZYX order)

该方法将四元数转换为欧拉角，表示旋转顺序为 ZYX（即先绕 Z 轴旋转，再绕 Y 轴，最后绕 X 轴）。 This method converts the quaternion into Euler angles using the ZYX rotation order (first rotate around the Z-axis, then Y-axis, and finally the X-axis).

Returns

计算得到的欧拉角向量 (roll, pitch, yaw) / Computed Euler angles vector (roll, pitch, yaw)

Definition at line 1006 of file transform.hpp.

{ return ToEulerAngleZYX(); }

ToEulerAngleXYZ()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngleXYZ ( ) const

inline

Definition at line 1058 of file transform.hpp.

  {
    Scalar yaw = std::atan2(-2 * (this->x() * this->y() - this->w() * this->z()),
                            1 - 2 * (this->z() * this->z() + this->y() * this->y()));
    Scalar pitch = std::asin(2 * (this->w() * this->y() + this->x() * this->z()));
    Scalar roll = std::atan2(-2 * (this->y() * this->z() - this->w() * this->x()),
                             1 - 2 * (this->y() * this->y() + this->x() * this->x()));
    return Eigen::Matrix<Scalar, 3, 1>(roll, pitch, yaw);
  }

ToEulerAngleXZY()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngleXZY ( ) const

inline

Definition at line 1048 of file transform.hpp.

  {
    Scalar pitch = std::atan2(2 * (this->w() * this->y() + this->x() * this->z()),
                              1 - 2 * (this->z() * this->z() + this->y() * this->y()));
    Scalar yaw = std::asin(2 * (this->w() * this->z() - this->x() * this->y()));
    Scalar roll = std::atan2(2 * (this->w() * this->x() + this->y() * this->z()),
                             1 - 2 * (this->z() * this->z() + this->x() * this->x()));
    return Eigen::Matrix<Scalar, 3, 1>(roll, pitch, yaw);
  }

ToEulerAngleYXZ()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngleYXZ ( ) const

inline

Definition at line 1028 of file transform.hpp.

  {
    Scalar roll = std::asin(2 * (this->w() * this->x() - this->y() * this->z()));
    Scalar yaw = std::atan2(2 * (this->w() * this->z() + this->x() * this->y()),
                            1 - 2 * (this->z() * this->z() + this->x() * this->x()));
    Scalar pitch = std::atan2(2 * (this->x() * this->z() + this->w() * this->y()),
                              1 - 2 * (this->y() * this->y() + this->x() * this->x()));
    return Eigen::Matrix<Scalar, 3, 1>(roll, pitch, yaw);
  }

ToEulerAngleYZX()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngleYZX ( ) const

inline

Definition at line 1008 of file transform.hpp.

  {
    Scalar roll = std::atan2(2 * this->w() * this->x() - 2 * this->y() * this->z(),
                             1 - 2 * (this->x() * this->x() + this->z() * this->z()));
    Scalar pitch = std::atan2(2 * this->w() * this->y() - 2 * this->x() * this->z(),
                              1 - 2 * (this->y() * this->y() + this->z() * this->z()));
    Scalar yaw = std::asin(2 * (this->w() * this->z() + this->x() * this->y()));
    return Eigen::Matrix<Scalar, 3, 1>(roll, pitch, yaw);
  }

ToEulerAngleZXY()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngleZXY ( ) const

inline

Definition at line 1038 of file transform.hpp.

  {
    Scalar pitch = std::atan2(-2 * (this->x() * this->z() - this->w() * this->y()),
                              1 - 2 * (this->y() * this->y() + this->x() * this->x()));
    Scalar roll = std::asin(2 * (this->w() * this->x() + this->y() * this->z()));
    Scalar yaw = std::atan2(-2 * (this->x() * this->y() - this->w() * this->z()),
                            1 - 2 * (this->z() * this->z() + this->x() * this->x()));
    return Eigen::Matrix<Scalar, 3, 1>(roll, pitch, yaw);
  }

ToEulerAngleZYX()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 1 > LibXR::Quaternion< Scalar >::ToEulerAngleZYX ( ) const

inline

Definition at line 1018 of file transform.hpp.

  {
    Scalar yaw = std::atan2(2 * (this->w() * this->z() + this->x() * this->y()),
                            1 - 2 * (this->z() * this->z() + this->y() * this->y()));
    Scalar pitch = std::asin(2 * (this->w() * this->y() - this->x() * this->z()));
    Scalar roll = std::atan2(2 * (this->w() * this->x() + this->y() * this->z()),
                             1 - 2 * (this->y() * this->y() + this->x() * this->x()));
    return Eigen::Matrix<Scalar, 3, 1>(roll, pitch, yaw);
  }

ToRotationMatrix()

template<typename Scalar >

Eigen::Matrix< Scalar, 3, 3 > LibXR::Quaternion< Scalar >::ToRotationMatrix ( ) const

inline

将四元数转换为 3x3 旋转矩阵 / Convert the quaternion to a 3x3 rotation matrix

该方法使用四元数生成等效的 3x3 旋转矩阵，矩阵可用于坐标变换、姿态计算等。 This method generates an equivalent 3x3 rotation matrix from the quaternion. The resulting matrix can be used for coordinate transformations, attitude calculations, etc.

Returns

计算得到的 3x3 旋转矩阵 / Computed 3x3 rotation matrix

Definition at line 1078 of file transform.hpp.

  {
    return Eigen::Matrix<Scalar, 3, 3>(*this);
  }

---

The documentation for this class was generated from the following file:

• src/utils/transform.hpp