euler2rotation_eigen.cpp

#include <Eigen/Dense>
#include <Eigen/Core>
#include <iostream>

using namespace std;

const double ARC_TO_DEG = 57.29577951308238;
const double DEG_TO_ARC = 0.0174532925199433;

Eigen::Matrix3d eulerAnglesToRotationMatrix(Eigen::Vector3d &theta);
bool isRotationMatrix(Eigen::Matrix3d R);
Eigen::Vector3d rotationMatrixToEulerAngles(Eigen::Matrix3d &R);

int main()
{
	double roll_deg = 0.5;      // 绕X轴
	double pitch_deg = 0.8;     // 绕Y轴
	double yaw_deg = 108.5;     // 绕Z轴

	// 转化为弧度
	double roll_arc = roll_deg * DEG_TO_ARC;    // 绕X轴
	double pitch_arc = pitch_deg * DEG_TO_ARC;  // 绕Y轴
	double yaw_arc = yaw_deg * DEG_TO_ARC;      // 绕Z轴

	cout << endl;
	cout << "roll_arc = " << roll_arc << endl;
	cout << "pitch_arc = " << pitch_arc << endl;
	cout << "yaw_arc = " << yaw_arc << endl;

	// 初始化欧拉角（rpy）,对应绕x轴，绕y轴，绕z轴的旋转角度
	Eigen::Vector3d euler_angle(roll_arc, pitch_arc, yaw_arc);

	// 使用Eigen库将欧拉角转换为旋转矩阵
	Eigen::Matrix3d rotation_matrix1, rotation_matrix2;
	rotation_matrix1 = Eigen::AngleAxisd(euler_angle[2], Eigen::Vector3d::UnitZ()) *
		Eigen::AngleAxisd(euler_angle[1], Eigen::Vector3d::UnitY()) *
		Eigen::AngleAxisd(euler_angle[0], Eigen::Vector3d::UnitX());
	cout << "\nrotation matrix1 =\n" << rotation_matrix1 << endl << endl;

	// 使用自定义函数将欧拉角转换为旋转矩阵
	rotation_matrix2 = eulerAnglesToRotationMatrix(euler_angle);
	cout << "rotation matrix2 =\n" << rotation_matrix2 << endl << endl;

	// 使用Eigen将旋转矩阵转换为欧拉角
	Eigen::Vector3d eulerAngle1 = rotation_matrix1.eulerAngles(2, 1, 0); // ZYX顺序，yaw,pitch,roll
	cout << "roll_1 pitch_1 yaw_1 = " << eulerAngle1[2] << " " << eulerAngle1[1]
		<< " " << eulerAngle1[0] << endl << endl;

	// 使用自定义函数将旋转矩阵转换为欧拉角
	Eigen::Vector3d eulerAngle2 = rotationMatrixToEulerAngles(rotation_matrix1); // roll,pitch,yaw
	cout << "roll_2 pitch_2 yaw_2 = " << eulerAngle2[0] << " " << eulerAngle2[1]
		<< " " << eulerAngle2[2] << endl << endl;

	system("pause");
	return 0;
}

// 欧拉角转旋转矩阵
Eigen::Matrix3d eulerAnglesToRotationMatrix(Eigen::Vector3d &theta) {
	Eigen::Matrix3d R_x;	//计算旋转矩阵的x分量
	R_x <<
		1, 0, 0,
		0, cos(theta[0]), -sin(theta[0]),
		0, sin(theta[0]), cos(theta[0]);

	Eigen::Matrix3d R_y;	//计算旋转矩阵的Y分量
	R_y <<
		cos(theta[1]), 0, sin(theta[1]),
		0, 1, 0,
		-sin(theta[1]), 0, cos(theta[1]);

	Eigen::Matrix3d R_z;	//计算旋转矩阵的Z分量
	R_z <<
		cos(theta[2]), -sin(theta[2]), 0,
		sin(theta[2]), cos(theta[2]), 0,
		0, 0, 1;

	Eigen::Matrix3d R = R_z * R_y*R_x;

	return R;
}

bool isRotationMatrix(Eigen::Matrix3d R)
{
	double err = 1e-6;
	Eigen::Matrix3d shouldIdenity;
	shouldIdenity = R * R.transpose();
	Eigen::Matrix3d I = Eigen::Matrix3d::Identity();

	return (shouldIdenity - I).norm() < err;
}

Eigen::Vector3d rotationMatrixToEulerAngles(Eigen::Matrix3d &R)
{
	assert(isRotationMatrix(R));

	double sy = sqrt(R(0, 0)*R(0, 0) + R(1, 0)*R(1, 0));

	bool singular = sy < 1e-6;
	double x, y, z;
	if (!singular)
	{
		x = atan2(R(2, 1), R(2, 2));
		y = atan2(-R(2, 0), sy);
		z = atan2(R(1, 0), R(0, 0));
	}
	else
	{
		x = atan2(-R(1, 2), R(1, 1));
		y = atan2(-R(2, 0), sy);
		z = 0;
	}
	return { x,y,z };
}