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<article>
<h1>Rectangle intersection with a Line Segment</h1>
<section>
<h2>Algorithm</h2>
<p>
For each line segment that your rectangle could be intersecting with,
do the following:
<ol>
<li>
For each corner of your rectangle, check if the distance from that point to the line is less than some <i>epsilon</i>, where <i>epsilon</i> is a reasonable small number (usually a 1 or 2 units, depending on the size of your lines).
</li>
<li>
To check each point, use the "distance from point to line segment" formula, which can be found <a href="https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line">here</a> (I will not derive it just yet)
</li>
<li>
If a collision is found, we have all of the information required to solve the collision:
<ul>
<li>
<b>Collision Normal</b>: This is the perpendicular to the line segment, which can be found by:
<code>
<pre>
Vector2 getNormalToLineSegment(LineSegment* segment) {
Vector2 direction = segment->end - segment->start;
return *Vector2 { -direction.y, direction.x }).normalize();
}
</pre>
</code>
</li>
<li>
<b>First Point of Application</b>: Get the vector from the center of the rectangle (most like your position) to the corner which intersected.
</li>
<li>
<b>Second Point of Application</b>: Get vector from center of line to the corner which intersected.
</li>
</ul>
</li>
</ol>
</p>
</section>
<section>
<h2>
Live Example
</h2>
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<footer id="references">
<h2>References</h2>
<ul>
<li><a href="https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line">Distance from Point to Line</a></li>
</ul>
</footer>
</section>
</article>
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