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cv::Rect has union('|') and intersection('&') operators. you could use them like this:

Rect r1(5,5,10,10);       //[10 x 10 from (5, 5)]
Rect r2(16,16,10,10);     //[10 x 10 from (16, 16)]
Rect r3 = r1 | r2;        //[21 x 21 from (5, 5)]