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

7 files changed, 127 insertions, 22 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>
diff --git a/2d/_collisions/polygon_polygon.html.content b/2d/_collisions/polygon_polygon.html.content
index 7f29ae0..29c284d 100644
--- a/2d/_collisions/polygon_polygon.html.content
+++ b/2d/_collisions/polygon_polygon.html.content
@@ -107,13 +107,15 @@
         <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.
+      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:
+
+      #SNIPPET polygon_polygon/snippet1.cpp
     </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>
diff --git a/2d/_collisions/polygon_polygon/dist/output.wasm b/2d/_collisions/polygon_polygon/dist/output.wasm
index a30f0c4..8e0443b 100755
--- a/2d/_collisions/polygon_polygon/dist/output.wasm
+++ b/2d/_collisions/polygon_polygon/dist/output.wasm
diff --git a/2d/_collisions/polygon_polygon/main.cpp b/2d/_collisions/polygon_polygon/main.cpp
index c458299..348e8d2 100644
--- a/2d/_collisions/polygon_polygon/main.cpp
+++ b/2d/_collisions/polygon_polygon/main.cpp
@@ -34,6 +34,7 @@ struct Rigidbody {
     void reset() {
         numImpulses = 0;
         velocity = { 0, 0 };
+        rotationalVelocity = 0.f;
     }
 
     void setMomentOfInertia(float32 moi) {
@@ -158,7 +159,7 @@ struct ConvexPolygon {
         edges = new Edge[numVertices]; // This will be filled in later when we are doing our SAT calculation.
 
         // Calculate moment of inertia
-        body.setMomentOfInertia((PI * body.mass) / 2.f);
+        body.momentOfInertia = (PI * (width * height * body.mass)) / 4.f;
 	}
 
 	void update(float32 dtSeconds) {
@@ -223,31 +224,29 @@ void load() {
     renderer.load(&context);
 
 	for (int index = 0; index < 4; index++) {
-		polygons[index].width = 50.f;
-		polygons[index].height = 50.f;
+        polygons[index].body.reset();
 
 		if (index == 0) {
 			polygons[index].body.position = { context.width / 4.f, context.height / 4.f };
             polygons[index].body.velocity = { 100.f, 200.f };
             polygons[index].body.mass = 2.f;
-            polygons[index].body.rotationalVelocity = 0.2f;
 		} else if (index == 1) {
 			polygons[index].body.position = { context.width / 4.f, context.height * (3.f /4.f) };
             polygons[index].body.velocity = { 50.f, -50.f };
             polygons[index].body.mass = 4.f;
-            polygons[index].body.rotationalVelocity = -0.5f;
 		} else if (index == 2) {
 			polygons[index].body.position = { context.width * (3.f / 4.f), context.height * (3.f / 4.f) };
             polygons[index].body.velocity = { -100.f, -50.f };
             polygons[index].body.mass = 6.f;
-            polygons[index].body.rotationalVelocity = 0.9f;
 		} else if (index == 3) {
 			polygons[index].body.position = { context.width * (3.f / 4.f), context.height / 4.f };
             polygons[index].body.velocity = { -150.f, 50.f };
             polygons[index].body.mass = 8.f;
-            polygons[index].body.rotationalVelocity = 1.4f;
 		}
 
+        polygons[index].width = (polygons[index].body.mass / 2.f) * 20.f;
+		polygons[index].height = (polygons[index].body.mass / 2.f) * 20.f;
+
 		polygons[index].numVertices = (index + 1) * 3;
 		polygons[index].color = Vector4 {
 			index == 0 || index == 3 ? 255.f : 0.f,
@@ -284,9 +283,9 @@ bool projectionsOverlap(Vector2 first, Vector2 second) {
 }
 
 float32 getProjectionOverlap(Vector2 first, Vector2 second) {
-	float32 firstOverlap = fabs(first.x - second.y);
-	float32 secondOverlap = fabs(second.x - first.y);
-	return firstOverlap > secondOverlap ? secondOverlap : firstOverlap;
+	float32 e = MIN(first.y, second.y);
+    float32 f = MAX(first.x, second.x);
+	return e - f;
 }
 
 const float32 EPSILON = 1.f;
@@ -374,13 +373,12 @@ void resolveCollision(Rigidbody* first, Rigidbody* second, IntersectionResult* i
     float32 linearDenomPart = collisionNormal.dot(collisionNormal * (1.f / first->mass + 1.f / second->mass));
 	float32 rotationalDenomPart = (firstPerpNorm * firstPerpNorm) / first->momentOfInertia + (sndPerpNorm * sndPerpNorm) / second->momentOfInertia;
 
-    // @TODO: Most of my 2D rotational work is pretty broken. Let's ignore it for the time being;
-    float32 impulseMagnitude = numerator / (linearDenomPart);// + rotationalDenomPart);
+    float32 impulseMagnitude = numerator / (linearDenomPart + rotationalDenomPart);
     first->velocity = first->velocity + (collisionNormal * (impulseMagnitude / first->mass));
 	second->velocity = second->velocity - (collisionNormal * (impulseMagnitude / second->mass));
 
-    // first->rotationalVelocity = first->rotationalVelocity + firstPerp.dot(collisionNormal * impulseMagnitude) / first->momentOfInertia;
-    // second->rotationalVelocity = second->rotationalVelocity - secondPerp.dot(collisionNormal * impulseMagnitude) / second->momentOfInertia;
+    first->rotationalVelocity = first->rotationalVelocity + firstPerp.dot(collisionNormal * impulseMagnitude) / first->momentOfInertia;
+    second->rotationalVelocity = second->rotationalVelocity - secondPerp.dot(collisionNormal * impulseMagnitude) / second->momentOfInertia;
 }
 
 void update(float32 deltaTimeSeconds, void* userData) {
@@ -430,6 +428,7 @@ void update(float32 deltaTimeSeconds, void* userData) {
 
 			first->update(frameTimeRemaining);
 			second->update(frameTimeRemaining);
+            i = 0;
 		}
     }
 
diff --git a/2d/_collisions/polygon_polygon/snippet1.cpp b/2d/_collisions/polygon_polygon/snippet1.cpp
new file mode 100644
index 0000000..3277cf9
--- /dev/null
+++ b/2d/_collisions/polygon_polygon/snippet1.cpp
@@ -0,0 +1,52 @@
+
+Vector2 getProjection(Vector2* vertices, int numVertices, Vector2 axis) {
+    // Find the min and max vertex projections
+    float32 min = axis.dot(vertices[0]);
+    float32 max = min;
+
+    for (int v = 1; v < numVertices; v++) {
+        float32 d = axis.dot(vertices[v]);
+
+        if (d < min) {
+            min = d;
+        } else if (d > max) {
+            max = d;
+        }
+    }
+
+    return Vector2 { min, max };
+}
+
+bool projectionsOverlap(Vector2 first, Vector2 second) {
+    return first.x <= second.y && second.x <= first.y;
+}
+
+bool doIntersect(ConvexPolygon* first, ConvexPolygon* second) {
+    IntersectionResult ir;
+
+    // Check agaisnt the edges of the first polygon
+    for (int i = 0; i < first->numVertices; i++) {
+        Vector2 normal = first->edges[i].normal;
+
+        Vector2 firstProj = getProjection(first->transformedVertices, first->numVertices, normal);
+        Vector2 secondProj = getProjection(second->transformedVertices, second->numVertices, normal);
+
+        if (!projectionsOverlap(firstProj, secondProj)) {
+            return false;
+        }
+    }
+
+    // Check against the edges of the second polygon
+    for (int i = 0; i < second->numVertices; i++) {
+        Vector2 normal = second->edges[i].normal;
+
+        Vector2 firstProj = getProjection(first->transformedVertices, first->numVertices, normal);
+        Vector2 secondProj = getProjection(second->transformedVertices, second->numVertices, normal);
+
+        if (!projectionsOverlap(firstProj, secondProj)) {
+            return false;
+        }
+    }
+
+    return true;
+}
diff --git a/2d/_collisions/rectangle_line.html b/2d/_collisions/rectangle_line.html
index dbaac7c..2fa5e62 100644
--- a/2d/_collisions/rectangle_line.html
+++ b/2d/_collisions/rectangle_line.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>
diff --git a/2d/_collisions/rectangle_rectangle.html b/2d/_collisions/rectangle_rectangle.html
index fb741fc..2cd2511 100644
--- a/2d/_collisions/rectangle_rectangle.html
+++ b/2d/_collisions/rectangle_rectangle.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>