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If you use the C++ way (cv::Rect), you can easily say

interesect  = r1 & r2;

for intersection calculation.

For CvRect:

CvRect intersect(CvRect r1, CvRect r2) 
{ 
    CvRect intersection; 

    // find overlapping region 
    intersection.x = (r1.x < r2.x) ? r2.x : r1.x; 
    intersection.y = (r1.y < r2.y) ? r2.y : r1.y; 
    intersection.width = (r1.x + r1.width < r2.x + r2.width) ? 
        r1.x + r1.width : r2.x + r2.width; 
    intersection.width -= intersection.x; 
    intersection.height = (r1.y + r1.height < r2.y + r2.height) ? 
        r1.y + r1.height : r2.y + r2.height; 
    intersection.height -= intersection.y; 

    // check for non-overlapping regions 
    if ((intersection.width <= 0) || (intersection.height <= 0)) { 
        intersection = cvRect(0, 0, 0, 0); 
    } 

    return intersection; 
}