问题
1. 旋转矩阵的定义;
2. 欧拉角的定义;
3. 旋转矩阵和欧拉角之间的关系;
4. 旋转矩阵和欧拉角之间的转换及其代码;
5. decomposeProjectionMatrix函数中的欧拉角的单位是弧度还是角度,pitch/yaw/roll三者的顺序以及方向性又是如何对应的?
6. 已知欧拉角,如何计算得到变换后的3D坐标。
pitch = eulerAngles[0];
yaw = eulerAngles[1];
roll = eulerAngles[2];
不知道上边的赋值是否正确;
欧拉角和旋转矩阵之间的转换:
/*
* Copyright (c) 2016 Satya Mallick <spmallick@learnopencv.com>
* All rights reserved. No warranty, explicit or implicit, provided.
*/
#include "opencv2/opencv.hpp"
#include <stdlib.h> /* srand, rand */
#include <time.h> /* time */
using namespace cv;
using namespace std;
// Checks if a matrix is a valid rotation matrix.
bool isRotationMatrix(Mat &R)
{
Mat Rt;
transpose(R, Rt);
Mat shouldBeIdentity = Rt * R;
Mat I = Mat::eye(3,3, shouldBeIdentity.type());
return norm(I, shouldBeIdentity) < 1e-6;
}
// Calculates rotation matrix to euler angles
// The result is the same as MATLAB except the order
// of the euler angles ( x and z are swapped ).
Vec3f rotationMatrixToEulerAngles(Mat &R)
{
assert(isRotationMatrix(R));
float sy = sqrt(R.at<double>(0,0) * R.at<double>(0,0) + R.at<double>(1,0) * R.at<double>(1,0) );
bool singular = sy < 1e-6; // If
float x, y, z;
if (!singular)
{
x = atan2(R.at<double>(2,1) , R.at<double>(2,2));
y = atan2(-R.at<double>(2,0), sy);
z = atan2(R.at<double>(1,0), R.at<double>(0,0));
}
else
{
x = atan2(-R.at<double>(1,2), R.at<double>(1,1));
y = atan2(-R.at<double>(2,0), sy);
z = 0;
}
return Vec3f(x, y, z);
}
// Calculates rotation matrix given euler angles.
Mat eulerAnglesToRotationMatrix(Vec3f &theta)
{
// Calculate rotation about x axis
Mat R_x = (Mat_<double>(3,3) <<
1, 0, 0,
0, cos(theta[0]), -sin(theta[0]),
0, sin(theta[0]), cos(theta[0])
);
// Calculate rotation about y axis
Mat R_y = (Mat_<double>(3,3) <<
cos(theta[1]), 0, sin(theta[1]),
0, 1, 0,
-sin(theta[1]), 0, cos(theta[1])
);
// Calculate rotation about z axis
Mat R_z = (Mat_<double>(3,3) <<
cos(theta[2]), -sin(theta[2]), 0,
sin(theta[2]), cos(theta[2]), 0,
0, 0, 1);
// Combined rotation matrix
Mat R = R_z * R_y * R_x;
return R;
}
int main(int argc, char** argv)
{
// Initialize random number generator
srand (time(NULL));
// Randomly generate Euler angles in Degrees.
Vec3f eDegrees(rand() % 360 - 180.0, rand() % 360 - 180.0, rand() % 360 - 180.0);
// Convert angles to radians
Vec3f e = eDegrees * M_PI / 180.0;
// Calculate rotation matrix
Mat R = eulerAnglesToRotationMatrix(e);
// Calculate Euler angles from rotation matrix
Vec3f e1 = rotationMatrixToEulerAngles(R);
// Calculate rotation matrix
Mat R1 = eulerAnglesToRotationMatrix(e1);
// Note e and e1 will be the same a lot of times
// but not always. R and R1 should be the same always.
cout << endl << "Input Angles" << endl << e << endl;
cout << endl << "R : " << endl << R << endl;
cout << endl << "Output Angles" << endl << e1 << endl;
cout << endl << "R1 : " << endl << R1 << endl;
}
View Code
参考
1. learnopencv_Rotation Matrix To Euler Angles;
2. http://answers.opencv.org/question/16796/computing-attituderoll-pitch-yaw-from-solvepnp/?answer=52913#post-id-52913;
3. https://github.com/lincolnhard/head-pose-estimation/issues/17;
完