在摄影测量学科中，国际摄影测量遵循OPK系统，即是xyz转角系统，而工业中往往使用zyx转角系统。

旋转矩阵的意义：描述相对地面的旋转情况，yaw-pitch-roll对应zyx对应k,p,w

#include <iostream>
#include<stdlib.h>
#include<eigen3/Eigen/Core>
#include<eigen3/Eigen/Dense>
#include<stdlib.h>
using namespace std;
Eigen::Matrix3d rotationVectorToMatrix(Eigen::Vector3d theta)
{
  Eigen::Matrix3d R_x=Eigen::AngleAxisd(theta(0),Eigen::Vector3d(1,0,0)).toRotationMatrix();
  Eigen::Matrix3d R_y=Eigen::AngleAxisd(theta(1),Eigen::Vector3d(0,1,0)).toRotationMatrix();
  Eigen::Matrix3d R_z=Eigen::AngleAxisd(theta(2),Eigen::Vector3d(0,0,1)).toRotationMatrix();
  return R_z*R_y*R_x;

}
bool isRotationMatirx(Eigen::Matrix3d R)
{
  int err=1e-6;//判断R是否奇异
  Eigen::Matrix3d shouldIdenity;
  shouldIdenity=R*R.transpose();
  Eigen::Matrix3d I=Eigen::Matrix3d::Identity();
  return (shouldIdenity-I).norm()<err?true:false;
}

int main(int argc, char *argv[])
{
  Eigen::Matrix3d R;
  Eigen::Vector3d theta(rand() % 360 - 180.0, rand() % 360 - 180.0, rand() % 360 - 180.0);
  theta=theta*M_PI/180;
  cout<<"旋转向量是：\n"<<theta.transpose()<<endl;
  R=rotationVectorToMatrix(theta);
  cout<<"旋转矩阵是：\n"<<R<<endl;
  if(! isRotationMatirx(R)){
   cout<<"旋转矩阵--->欧拉角\n"<<R.eulerAngles(2,1,0).transpose()<<endl;//z-y-x顺序，与theta顺序是x,y,z
  }
  else{
    assert(isRotationMatirx(R));
  }

  return 0;
}

#!/usr/bin/env python3
# -*- coding: utf-8 -*-

import cv2
import numpy as np
import math
import random

def isRotationMatrix(R) :
  Rt = np.transpose(R)
  shouldBeIdentity = np.dot(Rt, R)
  I = np.identity(3, dtype = R.dtype)
  n = np.linalg.norm(I - shouldBeIdentity)
  return n < 1e-6

def rotationMatrixToEulerAngles(R) :

  assert(isRotationMatrix(R))
  
  sy = math.sqrt(R[0,0] * R[0,0] + R[1,0] * R[1,0])
  
  singular = sy < 1e-6

  if not singular :
    x = math.atan2(R[2,1] , R[2,2])
    y = math.atan2(-R[2,0], sy)
    z = math.atan2(R[1,0], R[0,0])
  else :
    x = math.atan2(-R[1,2], R[1,1])
    y = math.atan2(-R[2,0], sy)
    z = 0

  return np.array([x, y, z])

def eulerAnglesToRotationMatrix(theta) :
  
  R_x = np.array([[1,     0,         0          ],
          [0,     math.cos(theta[0]), -math.sin(theta[0]) ],
          [0,     math.sin(theta[0]), math.cos(theta[0]) ]
          ])
    
    
          
  R_y = np.array([[math.cos(theta[1]),  0,   math.sin(theta[1]) ],
          [0,           1,   0          ],
          [-math.sin(theta[1]),  0,   math.cos(theta[1]) ]
          ])
        
  R_z = np.array([[math.cos(theta[2]),  -math.sin(theta[2]),  0],
          [math.sin(theta[2]),  math.cos(theta[2]),   0],
          [0,           0,           1]
          ])
          
          
  R = np.dot(R_z, np.dot( R_y, R_x ))

  return R


if __name__ == '__main__' :

  e = np.random.rand(3) * math.pi * 2 - math.pi
  
  R = eulerAnglesToRotationMatrix(e)
  e1 = rotationMatrixToEulerAngles(R)

  R1 = eulerAnglesToRotationMatrix(e1)
  print ("\nInput Euler angles :\n{0}".format(e))
  print ("\nR :\n{0}".format(R))
  print ("\nOutput Euler angles :\n{0}".format(e1))
  print ("\nR1 :\n{0}".format(R1))