summaryrefslogtreecommitdiff
path: root/2d/_collisions/rectangle_line.html
blob: e9720d1137f3cfb8215abdf1c958f983074f4703 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
<!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>&#127936;<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/circle_line.html" href="/2d/_collisions/circle_line.html">Circle-Line</a></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>&#127776;<span>3D</span></span>
				<ul class="inner-tree">
				</ul>
			</li>
			<li>
				<span>&#128295;<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>&#128712;<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>