The perplexity about the formula derivation of camera calibration on the source code and tutorial documents

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the interpretation of initundistortRectify map in OpenCv tutorial

the sourcecode in undistort.cpp

void cv::initUndistortRectifyMap( InputArray _cameraMatrix, InputArray _distCoeffs,
                              InputArray _matR, InputArray _newCameraMatrix,
                              Size size, int m1type, OutputArray _map1, OutputArray _map2 )
{
      ...........
    for( int i = 0; i < size.height; i++ )
    {
        float* m1f = (float*)(map1.data + map1.step*i);
        float* m2f = (float*)(map2.data + map2.step*i);
        short* m1 = (short*)m1f;
        ushort* m2 = (ushort*)m2f;
        double _x = i*ir[1] + ir[2], _y = i*ir[4] + ir[5], _w = i*ir[7] + ir[8];

        for( int j = 0; j < size.width; j++, _x += ir[0], _y += ir[3], _w += ir[6] )
        {
            double w = 1./_w, x = _x*w, y = _y*w;
            double x2 = x*x, y2 = y*y;
            double r2 = x2 + y2, _2xy = 2*x*y;
            double kr = (1 + ((k3*r2 + k2)*r2 + k1)*r2)/(1 + ((k6*r2 + k5)*r2 + k4)*r2);
            double u = fx*(x*kr + p1*_2xy + p2*(r2 + 2*x2)) + u0;
            double v = fy*(y*kr + p1*(r2 + 2*y2) + p2*_2xy) + v0;
            if( m1type == CV_16SC2 )
            {
                int iu = saturate_cast<int>(u*INTER_TAB_SIZE);
                int iv = saturate_cast<int>(v*INTER_TAB_SIZE);
                m1[j*2] = (short)(iu >> INTER_BITS);
                m1[j*2+1] = (short)(iv >> INTER_BITS);
                m2[j] = (ushort)((iv & (INTER_TAB_SIZE-1))*INTER_TAB_SIZE + (iu & (INTER_TAB_SIZE-1)));
            }
            else if( m1type == CV_32FC1 )
            {
                m1f[j] = (float)u;
                m2f[j] = (float)v;
            }
            else
            {
                m1f[j*2] = (float)u;
                m1f[j*2+1] = (float)v;
            }
        }
    }
}

Something puzzle me between source code and tutorial

1.[u,v] in the tutorial is the point in the undistort image coordinates,but in source code is the point in the distort image.

2.the radial distort happens in converting the world coordinate to the camera coordinate or the camera coordinate to the image coordinate.In the source code [_x,_y,_w] is the world coordinate, which is nomalized into [x,y] as camera coordinate,that is true?

3.The R (rotation matrix) is assumed as identity,why?