Some minor updates to SAT explanation, and made icons work everywhere

1 files changed, 56 insertions, 4 deletions

diff --git a/2d/_collisions/polygon_polygon.html b/2d/_collisions/polygon_polygon.html
index 5d360af..4c4698a 100644
--- a/2d/_collisions/polygon_polygon.html
+++ b/2d/_collisions/polygon_polygon.html
@@ -4,7 +4,7 @@
 		<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">
+		<link rel="shortcut icon" href="/favicon/favicon.ico" type="image/x-icon">
 		<meta name="description" content="A place to learn all about real-time physics simulations through descriptions, code snippets, and example programs all written in C++ and OpenGL.">
 		<meta name="og:description" content="A place to learn all about real-time physics simulations through descriptions, code snippets, and example programs all written in C++ and OpenGL.">
 	</head>
@@ -159,13 +159,65 @@
         <li>If the projections overlap for each edge of both shapes, the shapes are intersecting. Return true.</li>
       </ol>
 
-      And that is all there is to <i>finding</i> the intersection between two convex polygons.
-    </p>
+      And that is all there is to <i>finding</i> the intersection between two convex polygons. Here is the code snippet that does this if you are interested:
+
+      <pre><code><span class="code_keyword">Vector2</span> getProjection(Vector2* vertices, <span class="code_keyword">int</span> numVertices, <span class="code_keyword">Vector2</span> axis) {
+    <span class="code_comment">// Find the min and max vertex projections</span>
+    <span class="code_keyword">float32</span> min = axis.dot(vertices[0]);
+    <span class="code_keyword">float32</span> max = min;
+
+    for (int v = 1; v < numVertices; v++) {
+        <span class="code_keyword">float32</span> d = axis.dot(vertices[v]);
+
+        if (d < min) {
+            min = d;
+        } else if (d > max) {
+            max = d;
+        }
+    }
+
+    <span class="code_keyword">return</span> <span class="code_keyword">Vector2</span> { min, max };
+}
+
+<span class="code_keyword">bool</span> projectionsOverlap(Vector2 first, <span class="code_keyword">Vector2</span> second) {
+    <span class="code_keyword">return</span> first.x <= second.y && second.x <= first.y;
+}
+
+<span class="code_keyword">bool</span> doIntersect(ConvexPolygon* first, ConvexPolygon* second) {
+    IntersectionResult ir;
+
+    <span class="code_comment">// Check agaisnt the edges of the first polygon</span>
+    for (int i = 0; i < first->numVertices; i++) {
+        <span class="code_keyword">Vector2</span> normal = first->edges[i].normal;
+
+        <span class="code_keyword">Vector2</span> firstProj = getProjection(first->transformedVertices, first->numVertices, normal);
+        <span class="code_keyword">Vector2</span> secondProj = getProjection(second->transformedVertices, second->numVertices, normal);
+
+        if (!projectionsOverlap(firstProj, secondProj)) {
+            <span class="code_keyword">return</span> false;
+        }
+    }
+
+    <span class="code_comment">// Check against the edges of the second polygon</span>
+    for (int i = 0; i < second->numVertices; i++) {
+        <span class="code_keyword">Vector2</span> normal = second->edges[i].normal;
+
+        <span class="code_keyword">Vector2</span> firstProj = getProjection(first->transformedVertices, first->numVertices, normal);
+        <span class="code_keyword">Vector2</span> secondProj = getProjection(second->transformedVertices, second->numVertices, normal);
+
+        if (!projectionsOverlap(firstProj, secondProj)) {
+            <span class="code_keyword">return</span> false;
+        }
+    }
+
+    <span class="code_keyword">return</span> true;
+}
+</code></pre>    </p>
   </section>
   <section>
     <h2>SAT Collision Resolution</h2>
     <p>
-      Now that we know our objects have intersecting, we want to be able to send them tumbling away from each other to simulate a collision. To do this, we will need to find the following things:
+      Now that we know our objects have intersected, we want to be able to send them tumbling away from each other to simulate a collision. To do this, we will need to find the following things:
       <ul>
         <li><b>Collision Normal</b>: in what direction, point towards object <b>A</b>, did the polygons intersect</li>
         <li><b>Point of Application</b>: at what point on each object did the objects first intersect</li>