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-rw-r--r--2d/rigidbody/rigidbody_3.html.content2
-rwxr-xr-x2d/rigidbody/rigidbody_3/dist/output.wasmbin53544 -> 52832 bytes
-rw-r--r--2d/rigidbody/rigidbody_3/main.cpp144
3 files changed, 70 insertions, 76 deletions
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
--- a/2d/rigidbody/rigidbody_3/dist/output.wasm
+++ b/2d/rigidbody/rigidbody_3/dist/output.wasm
Binary files 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;