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 856 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 863 of file transform.hpp.

863: 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 872 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 881 of file transform.hpp.

881: 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 887 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 898 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 912 of file transform.hpp.

      : Eigen::Quaternion<Scalar>(
            static_cast<Scalar>(data[0]), static_cast<Scalar>(data[1]),
            static_cast<Scalar>(data[2]), static_cast<Scalar>(data[3]))
  {
  }

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 924 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 997 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 1040 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 992 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 969 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 963 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 1019 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 956 of file transform.hpp.

956{ 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 981 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 975 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 1029 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 1010 of file transform.hpp.

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

◆ 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 1008 of file transform.hpp.

1008{ 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 946 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 1056 of file transform.hpp.

1056{ return ToEulerAngleZYX(); }

◆ ToEulerAngleXYZ()

template<typename Scalar >

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

inline

Definition at line 1108 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 1098 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 1078 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 1058 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 1088 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 1068 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 1128 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

Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/6]

◆ Quaternion() [2/6]

◆ Quaternion() [3/6]

◆ Quaternion() [4/6]

◆ Quaternion() [5/6]

◆ Quaternion() [6/6]

Member Function Documentation

◆ operator()()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+() [1/2]

◆ operator+() [2/2]

◆ operator+=()

◆ operator-() [1/3]

◆ operator-() [2/3]

◆ operator-() [3/3]

◆ operator-=()

◆ operator/() [1/2]

◆ operator/() [2/2]

◆ operator=()

◆ ToEulerAngle()

◆ ToEulerAngleXYZ()

◆ ToEulerAngleXZY()

◆ ToEulerAngleYXZ()

◆ ToEulerAngleYZX()

◆ ToEulerAngleZXY()

◆ ToEulerAngleZYX()

◆ ToRotationMatrix()