Eigen库各种旋转的表示和转化

Eigen/Geometry 模块提供了各种旋转和平移的表示

一、表示：

旋转矩阵直接使用 Matrix3d 或 Matrix3f：

Eigen::Matrix3d rotationMatrix=Eigen::Matrix3d::Identity();//初始化为一个单位阵。

旋转向量使用 AngleAxis：

Eigen::AngleAxisd rotationVector(M_PI/4,Eigen::Vector3d(0,0,1)); //角+轴：沿 Z 轴旋转 45 度

欧拉角：

Eigen::Vector3d ea0(yaw,pitching,droll);

二、转化：

旋转向量->旋转矩阵：rotationMatrix=rotation_vector.toRotationMatrix();

旋转向量->四元数：Eigen::Quaterniond q = Eigen::Quaterniond ( rotation_vector );

旋转矩阵->四元数：Eigen::Quaterniond q = Eigen::Quaterniond ( rotation_matrix );

四元素->旋转矩阵：Eigen::Matrix3d Rx = q.toRotationMatrix();

旋转向量->欧拉角：Eigen::Vector3d eulerAngle=rotationVector.matrix().eulerAngles(0,1,2);

旋转矩阵->欧拉角：Eigen::Vector3d euler_angles = rotation_matrix.eulerAngles ( 2,1,0 ); // ZYX顺序，即roll pitch yaw顺序

三、C++代码

#include <iostream>  
#include <Eigen/Eigen>  
#include <stdlib.h>  
#include <Eigen/Geometry>  
#include <Eigen/Core>  
#include <vector>  
#include <math.h>  
  
using namespace std;  
using namespace Eigen;  
  
Eigen::Quaterniond euler2Quaternion(const double roll, const double pitch, const double yaw)  
{  
    Eigen::AngleAxisd rollAngle(roll, Eigen::Vector3d::UnitZ());  
    Eigen::AngleAxisd yawAngle(yaw, Eigen::Vector3d::UnitY());  
    Eigen::AngleAxisd pitchAngle(pitch, Eigen::Vector3d::UnitX());  
  
    Eigen::Quaterniond q = rollAngle  yawAngle  pitchAngle;  
    cout << “Euler2Quaternion result is:” <<endl;  
    cout << ”x = ” << q.x() <<endl;  
    cout << ”y = ” << q.y() <<endl;  
    cout << ”z = ” << q.z() <<endl;  
    cout << ”w = ” << q.w() <<endl<<endl;  
    return q;  
}  
  
Eigen::Vector3d Quaterniond2Euler(const double x,const double y,const double z,const double w)  
{  
    Eigen::Quaterniond q;  
    q.x() = x;  
    q.y() = y;  
    q.z() = z;  
    q.w() = w;  
  
    Eigen::Vector3d euler = q.toRotationMatrix().eulerAngles(2, 1, 0);  
    cout << “Quaterniond2Euler result is:” <<endl;  
    cout << ”x = ”<< euler[2] << endl ;  
    cout << ”y = ”<< euler[1] << endl ;  
    cout << ”z = ”<< euler[0] << endl << endl;  
}  
  
Eigen::Matrix3d Quaternion2RotationMatrix(const double x,const double y,const double z,const double w)  
{  
    Eigen::Quaterniond q;  
    q.x() = x;  
    q.y() = y;  
    q.z() = z;  
    q.w() = w;  
  
    Eigen::Matrix3d R = q.normalized().toRotationMatrix();  
    cout << “Quaternion2RotationMatrix result is:” <<endl;  
    cout << ”R = ” << endl << R << endl<< endl;  
    return R;  
}  
  
  
Eigen::Quaterniond rotationMatrix2Quaterniond(Eigen::Matrix3d R)  
{  
    Eigen::Quaterniond q = Eigen::Quaterniond(R);  
    q.normalize();  
    cout << “RotationMatrix2Quaterniond result is:” <<endl;  
    cout << ”x = ” << q.x() <<endl;  
    cout << ”y = ” << q.y() <<endl;  
    cout << ”z = ” << q.z() <<endl;  
    cout << ”w = ” << q.w() <<endl<<endl;  
    return q;  
}  
  
Eigen::Matrix3d euler2RotationMatrix(const double roll, const double pitch, const double yaw)  
{  
    Eigen::AngleAxisd rollAngle(roll, Eigen::Vector3d::UnitZ());  
    Eigen::AngleAxisd yawAngle(yaw, Eigen::Vector3d::UnitY());  
    Eigen::AngleAxisd pitchAngle(pitch, Eigen::Vector3d::UnitX());  
  
    Eigen::Quaterniond q = rollAngle  yawAngle  pitchAngle;  
    Eigen::Matrix3d R = q.matrix();  
    cout << “Euler2RotationMatrix result is:” <<endl;  
    cout << ”R = ” << endl << R << endl<<endl;  
    return R;  
}  
  
Eigen::Vector3d RotationMatrix2euler(Eigen::Matrix3d R)  
{  
    Eigen::Matrix3d m;  
    m = R;  
    Eigen::Vector3d euler = m.eulerAngles(0, 1, 2);  
    cout << “RotationMatrix2euler result is:” << endl;  
    cout << ”x = ”<< euler[2] << endl ;  
    cout << ”y = ”<< euler[1] << endl ;  
    cout << ”z = ”<< euler[0] << endl << endl;  
    return euler;  
}  
  
  
int main(int argc, char **argv)  
{  
  
//this is euler2Quaternion transform function,please input your euler angle//  
  euler2Quaternion(0,0,0);  
  
//this is Quaternion2Euler transform function,please input your euler angle//  
  Quaterniond2Euler(0,0,0,1);  
  
//this is Quaternion2RotationMatrix transform function,please input your Quaternion parameter//  
  Quaternion2RotationMatrix(0,0,0,1);  
  
//this is rotationMatrix2Euler transform function,please input your RotationMatrix parameter like following//  
  Eigen::Vector3d x_axiz,y_axiz,z_axiz;  
  x_axiz << 1,0,0;  
  y_axiz << 0,1,0;  
  z_axiz << 0,0,1;  
  Eigen::Matrix3d R;  
  R << x_axiz,y_axiz,z_axiz;  
  rotationMatrix2Quaterniond(R);  
  
//this is euler2RotationMatrix transform function,please input your euler angle for the function parameter//  
  euler2RotationMatrix(0,0,0);  
  
//this is RotationMatrix2euler transform function,please input your euler angle for the function parameter//  
  RotationMatrix2euler(R);  
  
  cout << “All transform is done!” << endl;  
}

测试结果

参考：

https://blog.csdn.net/zhuoyueljl/article/details/70789472