From 19b0a3cafe144e8e77974bb0c9c63141a812e30d Mon Sep 17 00:00:00 2001
From: Matthew Kosarek <mattkae@protonmail.com>
Date: Sun, 6 Jun 2021 20:24:55 -0400
Subject: Nearly working SAT collision here, but I think I am going to piviot
 to circles for sake of demonstration in this instance

---
 2d/rigidbody/rigidbody_3.html.content     |   2 +-
 2d/rigidbody/rigidbody_3/dist/output.wasm | Bin 53544 -> 52832 bytes
 2d/rigidbody/rigidbody_3/main.cpp         | 144 ++++++++++++++----------------
 3 files changed, 70 insertions(+), 76 deletions(-)

(limited to '2d')

diff --git a/2d/rigidbody/rigidbody_3.html.content b/2d/rigidbody/rigidbody_3.html.content
index f79db4f..8985532 100644
--- a/2d/rigidbody/rigidbody_3.html.content
+++ b/2d/rigidbody/rigidbody_3.html.content
@@ -1,4 +1,4 @@
-<script src="./rigidbody_3/dist/output.js"></script>
+3<script src="./rigidbody_3/dist/output.js"></script>
 <script>
   window.onload = function() {
       var lPlayElement = document.getElementById('gl_canvas_play'),
diff --git a/2d/rigidbody/rigidbody_3/dist/output.wasm b/2d/rigidbody/rigidbody_3/dist/output.wasm
index 5df757d..1a6e153 100755
Binary files a/2d/rigidbody/rigidbody_3/dist/output.wasm and b/2d/rigidbody/rigidbody_3/dist/output.wasm differ
diff --git a/2d/rigidbody/rigidbody_3/main.cpp b/2d/rigidbody/rigidbody_3/main.cpp
index 2063718..75379c4 100644
--- a/2d/rigidbody/rigidbody_3/main.cpp
+++ b/2d/rigidbody/rigidbody_3/main.cpp
@@ -170,6 +170,7 @@ void load() {
 	r2.body.mass = 1.f;
     r2.body.position = Vector2 { context.width * (3.f / 4.f), context.height * (3.f / 4.f) };
 	r2.body.velocity = Vector2 { -300.f, -150.f };
+	r2.body.rotationalVelocity = 0.9f;
 
     mainLoop.run(update);
 }
@@ -193,6 +194,11 @@ void handleCollisionWithWall(Rectangle* r) {
     }
 }
 
+/*
+  Do not worry about how w are exactly finding the intersection here, for now.
+  We are using the Separating Axis Theorem to do so here. In the 2D -> Collisions
+  section of the website, we describe this method at length.
+*/
 Vector2 getProjection(Vector2* vertices, Vector2 axis) {
 	float32 min = axis.dot(vertices[0]);
 	float32 max = min;
@@ -210,108 +216,90 @@ Vector2 getProjection(Vector2* vertices, Vector2 axis) {
 	return Vector2 { min, max };
 }
 
-bool projectionsOverlap(Vector2 first, Vector2 second) {
+inline bool projectionsOverlap(Vector2 first, Vector2 second) {
 	return first.x <= second.y && second.x <= first.y;
 }
 
-float32 getProjectionOverlap(Vector2 first, Vector2 second) {
-	float32 firstOverlap = fabs(first.x - second.y);
-	float32 secondOverlap = fabs(second.x - first.y);
+inline float32 getProjectionOverlap(Vector2 first, Vector2 second) {
+	float32 firstOverlap = (first.x - second.y);  // TODO: Does this need to be absolute value?
+	float32 secondOverlap = (second.x - first.y);
 	return firstOverlap > secondOverlap ? secondOverlap : firstOverlap;
 }
 
-const float32 EPSILON = 1.f;
-IntersectionResult getIntersection(Rectangle* first, Rectangle* second) {
-	IntersectionResult ir;
-
-	// For two rectangles to overlap, it means that at least one of the corners of one is inside of the other
-    Edge* firstEdges = first->edges;
-	Vector2* firstPoints = first->transformedPoints;
-
-    Edge* secondEdges = second->edges;
-	Vector2* secondPoints = second->transformedPoints;
-
+struct IntermediateIntersectionResult {
 	float32 minOverlap = FLT_MAX;
-	Vector2 minOverlapAxis;
-	Edge* minOverlapEdge = NULL;
-	bool minOverlapWasFirstRect = false;
-    
+	Edge* minOverlapEdge;
+	bool isOverlapOnFirstEdge = true;
+};
+
+bool checkEdgeOverlap(Edge* edges, Rectangle* first, Rectangle* second, IntermediateIntersectionResult* iir, bool isFirstEdge) {
+	// Returns true if SAT passes for the provided set of edges.
 	for (int i = 0; i < 4; i++) {
-		Vector2 normal = firstEdges[i].normal;
+		Vector2 normal = edges[i].normal;
 
-	    Vector2 firstProj = getProjection(firstPoints, normal);
-		Vector2 secondProj = getProjection(secondPoints, normal);
+	    Vector2 firstProj = getProjection(first->transformedPoints, normal);
+		Vector2 secondProj = getProjection(second->transformedPoints, normal);
 
 		if (!projectionsOverlap(firstProj, secondProj)) {
-			return ir;
+			return false;
 		}
 
 		float32 overlap = getProjectionOverlap(firstProj, secondProj);
-		if (overlap < minOverlap) {
-			minOverlap = overlap;
-			minOverlapAxis = normal;
-			minOverlapEdge = &firstEdges[i];
-			minOverlapWasFirstRect = true;
+		if (overlap < iir->minOverlap) {
+			iir->minOverlap = overlap;
+		    iir->minOverlapEdge = &edges[i];
+			iir->isOverlapOnFirstEdge = isFirstEdge;
 		}
 	}
 
-	for (int i = 0; i < 4; i++) {
-		Vector2 normal = secondEdges[i].normal;
-
-	    Vector2 firstProj = getProjection(firstPoints, normal);
-		Vector2 secondProj = getProjection(secondPoints, normal);
+	return true;
+}
 
-		if (!projectionsOverlap(firstProj, secondProj)) {
-			return ir;
-		}
+const float32 EPSILON = 1.f;
+IntersectionResult getIntersection(Rectangle* first, Rectangle* second) {
+	IntersectionResult ir;
 
-		float32 overlap = getProjectionOverlap(firstProj, secondProj);
-		if (overlap < minOverlap) {
-			minOverlap = overlap;
-			minOverlapAxis = normal;
-			minOverlapEdge = &secondEdges[i];
-		}
+    IntermediateIntersectionResult iir;
+	if (!checkEdgeOverlap(first->edges, first, second, &iir, true)) {
+		return ir;
 	}
 
+	if (!checkEdgeOverlap(second->edges, first, second, &iir, false)) {
+		return ir;
+	}
+	
 	ir.intersect = true;
 	ir.relativeVelocity = first->body.velocity - second->body.velocity;
-	ir.collisionNormal = minOverlapAxis;
-
-    // Find the point of collision, this is kind of tricky, and it is just an approximation for now.
-    // At this point, we know that we intersected along the minOverlapAxis, but we do not know where
-    // that exactly happened. To remedy this will, we create two parallel lines: one at the top of the
-    // normal area, and one at the bottom. For point on both of the Rectangles, we will check:
-    // (1) if it is between these two planes
-    // (2) if, for that rectangle, it is the closest point to the original normal vector
-    // (3) or if it is equally distant from normal vector as another point (then this is a "flat" collision)
-    //
-    // The collision point MUST be between these two planes. We can then say the corner/face of the non-monoverlapAxis 
-    // Rectangle is the collision point. This enables us to then solve for their respective points of application fairly
-    // easily. If the collision "point" is an entire face, we make the collision point be the center point.
-    //
-
-	Vector2 closestPoint;
-	float32 minDistance = FLT_MAX;
-
-    for (int p = 0; p < 4; p++) {
-		Vector2 point = minOverlapWasFirstRect ? secondPoints[p] : firstPoints[p];
-
-		float32 distFromPointToStart = (minOverlapEdge->start - point).length();
-		float32 distFromPointToEnd = (minOverlapEdge->end - point).length();
-		float32 potentialMin = MIN(distFromPointToStart, distFromPointToEnd);
-
-		if (potentialMin < minDistance) {
-			closestPoint = point;
-			minDistance = potentialMin; 
+	ir.collisionNormal = iir.minOverlapEdge->normal;
+
+	float32 minDistanceFromEdge = FLT_MAX;
+	Vector2 pointOfContact;
+	Vector2* pointsToCheck = iir.isOverlapOnFirstEdge ? second->transformedPoints : first->transformedPoints;
+	for (int p = 0; p < 4; p++) {
+		Vector2 point = pointsToCheck[p];
+
+		float32 distanceFromEdge = MIN((iir.minOverlapEdge->start - point).length(), (iir.minOverlapEdge->end - point).length());
+
+		if (distanceFromEdge < minDistanceFromEdge) {
+			minDistanceFromEdge = distanceFromEdge;
+			pointOfContact = point;
 		}
-    }
+	}
+
 
-    ir.firstPointOfApplication = closestPoint - first->body.position;
-    ir.secondPointOfApplication = closestPoint - second->body.position;;
+    ir.firstPointOfApplication = pointOfContact - first->body.position;
+    ir.secondPointOfApplication = pointOfContact - second->body.position;;
 
 	return ir;
 }
 
+/**
+In this method, we resolve the collision of two rigidbodies using the IntersectionResult
+that we gathered from the collision information. Note that this particular tutorial
+is not about how we find this collision, but rather how we use this collision. To see the
+variety of ways of how this IntersectionResult can be calculated go to the 2D->Collision
+section of the website.
+***/
 void resolveCollision(Rigidbody* first, Rigidbody* second, IntersectionResult* ir) {
     Vector2 relativeVelocity = ir->relativeVelocity;
     Vector2 collisionNormal  = ir->collisionNormal;
@@ -337,18 +325,21 @@ void update(float32 deltaTimeSeconds, void* userData) {
     r1.update(deltaTimeSeconds);
 	r2.update(deltaTimeSeconds);
 
-	// Handle intersection between the two rectangles here
+	// Let's backtrack the simulation to find the precise point at which we collided.
+	// There exists many ways to find this precise point. This is by far the most
+	// expensive, but it gets the job done.
 	IntersectionResult ir = getIntersection(&r1, &r2);
 	if (ir.intersect) {
 		IntersectionResult irCopy = ir;
 		float32 copyDt = deltaTimeSeconds;
+		float32 subdivisionAmountSeconds = deltaTimeSeconds / 16.f;
 		
 		do {
 		    r1.restorePreviousBody();
 			r2.restorePreviousBody();
 				
 			ir = irCopy;
-			copyDt = copyDt /= 2.f;
+			copyDt = copyDt - subdivisionAmountSeconds;
 
 			r1.update(copyDt);
 		    r2.update(copyDt);
@@ -364,6 +355,9 @@ void update(float32 deltaTimeSeconds, void* userData) {
 
 		printf("Found intersection at timestamp: %f\n", copyDt);
 
+		// The following function is the main one that we're talking about in this tutorial.
+		// This function will take the collision data, and repel the objects away from one
+		// another using what we know from physics.
 		resolveCollision(&r1.body, &r2.body, &ir);
 		float32 frameTimeRemaining = deltaTimeSeconds - copyDt;
 
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