How do I find out if two shapes drawn in svg overlap each other?

I'm building a svg graph by using php.

I cannot find out how to determine if two elements intersect, for instance a line (path) and rectangle (rect)

    <rect
       style="opacity:0.5;fill:#ff0000;fill-opacity:1;stroke:#808080;stroke-width:1px"
       id="rectangle"
       width="40"
       height="35"
       x="57"
       y="50" />
    <path
       style="fill:none;stroke:#000000;stroke-width:1px;stroke-linecap:butt;stroke-linejoin:miter;stroke-opacity:1"
       d="M 114,50 C 65,99 65,99 65,99"
       id="line" />

or two rectangles

    <rect
       y="50"
       x="57"
       height="35"
       width="40"
       id="rectangle"
       style="opacity:0.5;fill:#ff0000;fill-opacity:1;stroke:#808080;stroke-width:1px" />
    <rect
       y="58.92128"
       x="72.528419"
       height="39"
       width="39"
       id="rect2879"
       style="opacity:0.5;fill:#00ff00;fill-opacity:1;stroke:#808080;stroke-width:1px" />

I'm looking for a mathematical formula or code example in any language.