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jQuery/JavaScript collision detection

How to detect if two <div> elements have collided?

The two divs are simple coloured boxes travelling perpendicular to each other, so no complicated shapes or angles.

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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] );
    };
})();

$(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 );
});
body {
    padding: 30px;
    color: #444;
    font-family: Arial, sans-serif;
}

h1 {
    font-size: 24px;
    margin-bottom: 20px;
}

#area {
    border: 2px solid gray;
    width: 500px;
    height: 400px;
    position: relative;
}

#area > div {
    background-color: rgba(122, 122, 122, 0.3);
    position: absolute;
    text-align: center;
    font-size: 50px;
    width: 60px;
    height: 60px;
}

#box0 {
    background-color: rgba(255, 0, 0, 0.5) !important;
    top: 150px;
    left: 150px;
}

#box1 {
    top: 260px;
    left: 50px;
}

#box2 {
    top: 110px;
    left: 160px;
}

#box3 {
    top: 200px;
    left: 200px;
}

#box4 {
    top: 50px;
    left: 400px;
}

p {
    margin: 5px 0;
}
<script src="https://ajax.googleapis.com/ajax/libs/jquery/1.7.1/jquery.min.js"></script>
<h1>Detect overlapping with JavaScript</h1>
<div id="area">
    <div id="box0"></div>
    <div id="box1">1</div>
    <div id="box2">2</div>
    <div id="box3">3</div>
    <div id="box4">4</div>
</div>

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