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    <p>Here is an code example in python:</p> <pre><code>def extend(xmin, ymin, xmax, ymax, x1, y1, x2, y2): if y1 == y2: return (xmin, y1, xmax, y1) if x1 == x2: return (x1, ymin, x1, ymax) # based on (y - y1) / (x - x1) == (y2 - y1) / (x2 - x1) # =&gt; (y - y1) * (x2 - x1) == (y2 - y1) * (x - x1) y_for_xmin = y1 + (y2 - y1) * (xmin - x1) / (x2 - x1) y_for_xmax = y1 + (y2 - y1) * (xmax - x1) / (x2 - x1) x_for_ymin = x1 + (x2 - x1) * (ymin - y1) / (y2 - y1) x_for_ymax = x1 + (x2 - x1) * (ymax - y1) / (y2 - y1) if ymin &lt;= y_for_xmin &lt;= ymax: if xmin &lt;= x_for_ymax &lt;= xmax: return (xmin, y_for_xmin, x_for_ymax, ymax) if xmin &lt;= x_for_ymin &lt;= xmax: return (xmin, y_for_xmin, x_for_ymin, ymin) if ymin &lt;= y_for_xmax &lt;= ymax: if xmin &lt;= x_for_ymin &lt;= xmax: return (x_for_ymin, ymin, xmax, y_for_xmax) if xmin &lt;= x_for_ymax &lt;= xmax: return (x_for_ymax, ymax, xmax, y_for_xmax) def test(): assert (2, 1, 2, 5) == extend(1, 1, 5, 5, 2, 3, 2, 4) assert (1, 2, 4, 5) == extend(1, 1, 5, 5, 2, 3, 3, 4) assert (1, 3, 5, 3) == extend(1, 1, 5, 5, 3, 3, 4, 3) assert (1, 1, 5, 5) == extend(1, 1, 5, 5, 2, 2, 3, 3) assert (3, 1, 5, 5) == extend(1, 1, 5, 5, 3.5, 2, 4, 3) if __name__ == '__main__': test() </code></pre> <p>It doesn't check that the segment is contained in the rectangle and should work also if it is exterior to it (returns None -implicit- if there is no actual segment intersection).</p> <p>It is based on the assumption that the rectangle has the segments parallel with the axes.</p>
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    1. COthanks for this helpful code ,
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    2. COthis assert (3, 1, 5, 5) == extend(1, 1, 5, 5, 3.5, 2, 4, 3) return false
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    3. COThe last assert might fail because of a rounding problem (it works fine on my python 2.7.1), extend(1, 1, 5, 5, 3.5, 2, 4, 3) actually returns (3.0, 1, 5, 5.0).
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