int k = 0;
for (int x = 0; x < N; ++x)
    pts[k++] = Point2d((double)x*(imgSize.width-1)/(N-1), 0);
for (int x = 0; x < N; ++x)
    pts[k++] = Point2d( (double)x*(imgSize.width-1)/(N-1), imgSize.height - 1);
for (int y = 1; y < N - 1; ++y)
    pts[k++] = Point2d(0, (double)y*(imgSize.height-1)/(N-1));
for (int y = 1; y < N - 1; ++y)
    pts[k++] = Point2d(imgSize.width - 1, (double)y*(imgSize.height-1)/(N-1);

undistortPoints(_pts, _pts, _cameraMatrix, _distCoeffs, R, newCameraMatrix);

double iX0=-FLT_MAX, iX1=FLT_MAX, iY0=-FLT_MAX, iY1=FLT_MAX;
double oX0=FLT_MAX, oX1=-FLT_MAX, oY0=FLT_MAX, oY1=-FLT_MAX;
// find the inscribed rectangle.
// the code will likely not work with extreme rotation matrices (R) (>45%)
k = 0;
for (int x = 0; x < N; ++x) {
    Point2d p = pts[k++];
    oX0 = MIN(oX0, p.x);  
    oX1 = MAX(oX1, p.x);
    oY0 = MIN(oY0, p.y);  
    oY1 = MAX(oY1, p.y);
    iY0 = MAX(iY0, p.y);
}
for (int x = 0; x < N; ++x) {
    Point2d p = pts[k++];
    oX0 = MIN(oX0, p.x);  
    oX1 = MAX(oX1, p.x);
    oY0 = MIN(oY0, p.y);  
    oY1 = MAX(oY1, p.y);
    iY1 = MIN(iY1, p.y); 
}
for (int y = 1; y < N - 1; ++y) {
    Point2d p = pts[k++];
    oX0 = MIN(oX0, p.x); 
    oX1 = MAX(oX1, p.x);
    oY0 = MIN(oY0, p.y); 
    oY1 = MAX(oY1, p.y);
    iX0 = MAX(iX0, p.x);
}
for (int y = 1; y < N - 1; ++y) {
    Point2d p = pts[k++];
    oX0 = MIN(oX0, p.x);
    oX1 = MAX(oX1, p.x);
    oY0 = MIN(oY0, p.y);
    oY1 = MAX(oY1, p.y);
    iX1 = MIN(iX1, p.x);
}