三个欧拉角得到3x3旋转矩阵

Posted 2020-10-03

三维坐标系中，已知三个欧拉角alpha,beta,gamma，分别为绕x轴旋转alpha角度，绕y轴旋转beta角度，绕z轴旋转gamma角度。则旋转矩阵Rotation的求法如下：

Mat Rot=Mat::eye(3,3, CV_32FC1);

    Rot.at<float>(0, 0) = cos(beta) * cos(gamma);
    Rot.at<float>(0, 1) = cos(beta) * sin(gamma);
    Rot.at<float>(0, 2) = -sin(beta);
    Rot.at<float>(1, 0) = sin(alpha) * sin(beta) * cos(gamma) - cos(alpha) * sin(gamma);
    Rot.at<float>(1, 1) = sin(alpha) * sin(beta) * sin(gamma) + cos(alpha) * cos(gamma);
    Rot.at<float>(1, 2) = sin(alpha) * cos(beta);
    Rot.at<float>(2, 0) = cos(alpha) * sin(beta) * cos(gamma) + sin(alpha) * sin(gamma);
    Rot.at<float>(2, 1) = cos(alpha) * sin(beta) * sin(gamma) - sin(alpha) * cos(gamma);
    Rot.at<float>(2, 2) = cos(alpha) * cos(beta);

Rotation是3*3矩阵，用于三维空间坐标的旋转。