Rotation in 3D using OpenCV's warpPerspective

In order to easily rotate an image in 3D space, I have written a simple method that will do just that. It accepts rotations (in degrees) along each of the three axis (x, y and z), with 90 degrees being the "normal" position.
It also supports translations along each of the axis, and a variable focal distance (you would usually want the focal distance to be the same as your dz).

The parameters are:
input: the image that you want rotated.
output: the Mat object to put the resulting file in.
alpha: the rotation around the x axis
beta: the rotation around the y axis
gamma: the rotation around the z axis (basically a 2D rotation)
dx: translation along the x axis
dy: translation along the y axis
dz: translation along the z axis (distance to the image)
f: focal distance (distance between camera and image, a smaller number exaggerates the effect)

The method is defined as:



  void rotateImage(const Mat &input, Mat &output, double alpha, double beta, double gamma, double dx, double dy, double dz, double f)

  {

    alpha = (alpha - 90.)*CV_PI/180.;

    beta = (beta - 90.)*CV_PI/180.;

    gamma = (gamma - 90.)*CV_PI/180.;

    // get width and height for ease of use in matrices

    double w = (double)input.cols;

    double h = (double)input.rows;

    // Projection 2D -> 3D matrix

    Mat A1 = (Mat_<double>(4,3) <<

              1, 0, -w/2,

              0, 1, -h/2,

              0, 0,    0,

              0, 0,    1);

    // Rotation matrices around the X, Y, and Z axis

    Mat RX = (Mat_<double>(4, 4) <<

              1,          0,           0, 0,

              0, cos(alpha), -sin(alpha), 0,

              0, sin(alpha),  cos(alpha), 0,

              0,          0,           0, 1);

    Mat RY = (Mat_<double>(4, 4) <<

              cos(beta), 0, -sin(beta), 0,

              0, 1,          0, 0,

              sin(beta), 0,  cos(beta), 0,

              0, 0,          0, 1);

    Mat RZ = (Mat_<double>(4, 4) <<

              cos(gamma), -sin(gamma), 0, 0,

              sin(gamma),  cos(gamma), 0, 0,

              0,          0,           1, 0,

              0,          0,           0, 1);

    // Composed rotation matrix with (RX, RY, RZ)

    Mat R = RX * RY * RZ;

    // Translation matrix

    Mat T = (Mat_<double>(4, 4) <<

             1, 0, 0, dx,

             0, 1, 0, dy,

             0, 0, 1, dz,

             0, 0, 0, 1);

    // 3D -> 2D matrix

    Mat A2 = (Mat_<double>(3,4) <<

              f, 0, w/2, 0,

              0, f, h/2, 0,

              0, 0,   1, 0);

    // Final transformation matrix

    Mat trans = A2 * (T * (R * A1));

    // Apply matrix transformation

    warpPerspective(input, output, trans, input.size(), INTER_LANCZOS4);

  }

Example usage to rotate an image 45° around the y-axis:

rotateImage(orignalImage, outputImage, 90, 135, 90, 0, 0, 200, 200);