jQuery/JavaScript を使用して長方形要素間の衝突検出を行うにはどうすればよいでしょうか?

var overlaps = (function () {
    function getPositions( elem ) {
        var pos, width, height;
        pos = $( elem ).position();
        width = $( elem ).width();
        height = $( elem ).height();
        return [ [ pos.left, pos.left + width ], [ pos.top, pos.top + height ] ];
    }

    function comparePositions( p1, p2 ) {
        var r1, r2;
        r1 = p1[0] < p2[0] ? p1 : p2;
        r2 = p1[0] < p2[0] ? p2 : p1;
        return r1[1] > r2[0] || r1[0] === r2[0];
    }

    return function ( a, b ) {
        var pos1 = getPositions( a ),
            pos2 = getPositions( b );
        return comparePositions( pos1[0], pos2[0] ) && comparePositions( pos1[1], pos2[1] );
    };
})();

<div>

$(function () {
    var area = $( '#area' )[0],
        box = $( '#box0' )[0],
        html;
    
    html = $( area ).children().not( box ).map( function ( i ) {
        return '<p>Red box + Box ' + ( i + 1 ) + ' = ' + overlaps( box, this ) + '</p>';
    }).get().join( '' );

    $( 'body' ).append( html );
});