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    <p>I would recommend simply doing a line-segment-line-segment intersection check on each line segment (edge) that makes up the rectangle. Here is a line segment intersection detection algorithm I wrote ages ago, dredged up from one of my old XNA projects:</p> <pre><code>// a1 is line1 start, a2 is line1 end, b1 is line2 start, b2 is line2 end static bool Intersects(Vector2 a1, Vector2 a2, Vector2 b1, Vector2 b2, out Vector2 intersection) { intersection = Vector2.Zero; Vector2 b = a2 - a1; Vector2 d = b2 - b1; float bDotDPerp = b.X * d.Y - b.Y * d.X; // if b dot d == 0, it means the lines are parallel so have infinite intersection points if (bDotDPerp == 0) return false; Vector2 c = b1 - a1; float t = (c.X * d.Y - c.Y * d.X) / bDotDPerp; if (t &lt; 0 || t &gt; 1) return false; float u = (c.X * b.Y - c.Y * b.X) / bDotDPerp; if (u &lt; 0 || u &gt; 1) return false; intersection = a1 + t * b; return true; } </code></pre> <p>I will leave inputting each edge into the above method and collecting the results as an exercise to the reader :)</p> <hr> <h2>Edit 1 year later now I've gone to university and done a Graphics course:</h2> <p>Take a look at the <a href="http://en.wikipedia.org/wiki/Cohen%E2%80%93Sutherland_algorithm" rel="noreferrer">Cohen–Sutherland algorithm</a> to do this efficiently when you have a large set of lines where most do not intersect the rectangle. It uses a 9 segment grid and you place each endpoint of the line in a region of said grid:</p> <p><img src="https://i.stack.imgur.com/YcU1P.gif" alt="grid"></p> <p>Using this we can tell if there will not be any line intersections:</p> <p><img src="https://i.stack.imgur.com/JXMEh.jpg" alt="grid with lines"></p> <p>For example here <code>CD</code> will not intersect the rectangle (shown in red in the first image) as both <code>C</code> and <code>D</code> are in the top row and neither will <code>AB</code>. For the ones where the line may intersect the the rectangle we have to try the line-line intersections.</p> <p>They way the sections are numbered/labelled allows us to simply do <code>x AND y != 0</code> (where <code>x</code> and <code>y</code> are the labels of the sections for each of the line's endpoints) to determine if there will not be an intersection.</p> <p>Using this method means we have to many, many fewer line-line intersections which speeds up the whole thing massively.</p>
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    1. COThat'll be easy enough to do. Thank you very much.
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      1. USSteffan Donal
    2. COIn the above code example, those are actually cross products, not dot products.
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      1. USNathanael Weiss
 

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