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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<link rel="stylesheet" href="/index.css">
<title>Physics for Games</title>
<link rel="shortcut icon" href="favicon/favicon.ico" type="image/x-icon">
</head>
<body>
<header>
<h1><a title="physicsforgames.com" href="/">Physics for Games</a></h1>
</header>
<main>
<nav>
<ul class="outer-tree">
<li><a href="/">Introduction</a></li>
<li>
<span>🏀<span>2D</span></span>
<ul class="inner-tree">
<li><label>Rigidbody</label></li>
<li><a title="/2d/rigidbody/rigidbody_1.html" href="/2d/rigidbody/rigidbody_1.html">Linear Forces</a></li>
<li><label>Collisions</label></li>
<li><a title="/2d/_collisions/rectangle_line.html" href="/2d/_collisions/rectangle_line.html">Rectangle-Line</a></li>
<li><a title="/2d/_collisions/rectangle_rectangle.html" href="/2d/_collisions/rectangle_rectangle.html">Rectangle-Rectangle</a></li>
<li><a title="/2d/_collisions/pill_line.html" href="/2d/_collisions/pill_line.html">Pill-Line</a></li>
<li><a title="/2d/_collisions/pill_pill.html" href="/2d/_collisions/pill_pill.html">Pill-Pill</a></li>
<li><a title="/2d/_collisions/polygon_polygon.html" href="/2d/_collisions/polygon_polygon.html">Polygon-Polygon</a></li>
</ul>
</li>
<li>
<span>🌠<span>3D</span></span>
<ul class="inner-tree">
</ul>
</li>
<li>
<span>🔧<span>WebAssembly</span></span>
<ul class="inner-tree">
<li><a title="/intro/intro.html" href="/intro/intro.html">Introduction</a></li>
</ul>
</li>
<li>
<span>🛈<span>About</span></span>
<ul class="inner-tree">
<li><a title="/roadmap.html" href="/roadmap.html">Roadmap</a></li>
</ul>
</li>
</ul>
</nav>
<script src="./rectangle_line/dist/output.js"></script>
<script>
window.onload = function() {
var lPlayElement = document.getElementById('gl_canvas_play'),
lStopElement = document.getElementById('gl_canvas_stop');
lPlayElement.addEventListener('click', function() {
lPlayElement.style.display = 'none';
lStopElement.style.display = 'block';
});
lStopElement.addEventListener('click', function() {
lStopElement.style.display = 'none';
lPlayElement.style.display = 'block';
});
}
</script>
<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>
<div class="opengl_canvas_container">
<canvas id="gl_canvas" width="800" height="600"></canvas>
<button id="gl_canvas_play" class="play_button">
Play
</button>
<button id="gl_canvas_stop" class="stop_button">
Stop
</button>
</div>
<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>
</main>
</body>
</html>
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