#include "../../../shared_cpp/OrthographicRenderer.h" #include "../../../shared_cpp/types.h" #include "../../../shared_cpp/WebglContext.h" #include "../../../shared_cpp/mathlib.h" #include "../../../shared_cpp/MainLoop.h" #include #include #include #include #include #include #include struct Rigidbody { Vector2 linearForce = { 0, 0 }; Vector2 velocity = { 0, 0 }; Vector2 position = { 0, 0 }; float32 mass = 1.f; float32 torque = 0.f; float32 rotationalVelocity = 0.f; float32 rotation = 0.f; float32 momentOfInertia = 1.f; float32 cofOfRestitution = 1.f; void reset() { linearForce = { 0, 0 }; velocity = { 0, 0 }; rotationalVelocity = 0.f; rotation = 0.f; } void applyForce(Vector2 force, Vector2 pointOfApplication) { linearForce += force; torque += pointOfApplication.getPerp().dot(force); } void applyGravity() { applyForce(Vector2 { 0.f, -100.f }, Vector2 { 0.f, 0.f }); } void update(float32 deltaTimeSeconds) { applyGravity(); Vector2 acceleration = linearForce / mass; velocity += (acceleration * deltaTimeSeconds); position += (velocity * deltaTimeSeconds); linearForce = Vector2 { 0.f, 0.f }; // New: Update the rotational velocity as well float32 rotationalAcceleration = torque / momentOfInertia; rotationalVelocity += (rotationalAcceleration * deltaTimeSeconds); rotation += (rotationalVelocity * deltaTimeSeconds); torque = 0.f; } }; struct Edge { Vector2 normal; Vector2 start; Vector2 end; }; struct Rectangle { OrthographicShape shape; Rigidbody body; Rigidbody previousBody; Vector2 originalPoints[4]; Vector2 transformedPoints[4]; Edge edges[4]; void load(OrthographicRenderer* renderer, Vector4 color, float32 width, float32 height) { color = color.toNormalizedColor(); float32 halfWidth = width / 2.f; float32 halfHeight = height / 2.f; OrthographicVertex vertices[6]; vertices[0].position = Vector2 { -halfWidth, -halfHeight }; vertices[1].position = Vector2 { -halfWidth, halfHeight }; vertices[2].position = Vector2 { halfWidth, halfHeight }; vertices[3].position = Vector2 { -halfWidth, -halfHeight }; vertices[4].position = Vector2 { halfWidth, -halfHeight }; vertices[5].position = Vector2 { halfWidth, halfHeight }; for (int32 i = 0; i < 6; i++) { vertices[i].color = color; } originalPoints[0] = vertices[0].position; originalPoints[1] = vertices[1].position; originalPoints[2] = vertices[2].position; originalPoints[3] = vertices[4].position; shape.load(vertices, 6, renderer); body.reset(); body.momentOfInertia = (width * width + height * height) * (body.mass / 12.f); } void update(float32 dtSeconds) { previousBody = body; body.update(dtSeconds); shape.model = Mat4x4().translateByVec2(body.position).rotate2D(body.rotation); // Note: This helps us check rectangle collisions using SAT later on. // This is probably a slightly slow way of doing this, but we will ignore // that for now. for (int idx = 0; idx < 4; idx++) { transformedPoints[idx] = shape.model * originalPoints[idx]; } for (int eidx = 0; eidx < 4; eidx++) { edges[eidx].start = transformedPoints[eidx]; edges[eidx].end = transformedPoints[eidx == 3 ? 0 : eidx + 1]; edges[eidx].normal = (edges[eidx].end - edges[eidx].start).getPerp().normalize(); } } void restorePreviousBody() { body = previousBody; } void render(OrthographicRenderer* renderer) { shape.render(renderer); } void unload() { shape.unload(); } }; struct IntersectionResult { bool intersect = false; Vector2 collisionNormal; Vector2 relativeVelocity; Vector2 firstPointOfApplication; Vector2 secondPointOfApplication; }; EM_BOOL onPlayClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData); EM_BOOL onStopClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData); void load(); void update(float32 time, void* userData); void unload(); WebglContext context; OrthographicRenderer renderer; MainLoop mainLoop; Rectangle r1; Rectangle r2; int main() { context.init("#gl_canvas"); emscripten_set_click_callback("#gl_canvas_play", NULL, false, onPlayClicked); emscripten_set_click_callback("#gl_canvas_stop", NULL, false, onStopClicked); return 0; } void load() { renderer.load(&context); r1.load(&renderer, Vector4 { 55.f, 235.f, 35.f, 255.f }, 128.f, 64.f); r1.body.mass = 3.f; r1.body.position = Vector2 { context.width / 4.f, context.height / 4.f }; r1.body.velocity = Vector2 { 100.f, 250.f }; r2.load(&renderer, Vector4 { 235.f, 5.f, 35.f, 255.f }, 96.f, 64.f); 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 }; mainLoop.run(update); } void handleCollisionWithWall(Rectangle* r) { if (r->body.position.x <= 0.f) { r->body.position.x = 0.f; r->body.velocity = r->body.velocity - Vector2 { 1.f, 0.f } * (2 * (r->body.velocity.dot(Vector2 { 1.f, 0.f }))); } if (r->body.position.y <= 0.f) { r->body.position.y = 0.f; r->body.velocity = r->body.velocity - Vector2 { 0.f, 1.f } * (2 * (r->body.velocity.dot(Vector2 { 0.f, 1.f }))); } if (r->body.position.x >= 800.f) { r->body.position.x = 800.f; r->body.velocity = r->body.velocity - Vector2 { -1.f, 0.f } * (2 * (r->body.velocity.dot(Vector2{ -1.f, 0.f }))); } if (r->body.position.y >= 600.f) { r->body.position.y = 600.f; r->body.velocity = r->body.velocity - Vector2 { 0.f, -1.f } * (2 * (r->body.velocity.dot(Vector2 { 0.f, -1.f }))) ; } } Vector2 getProjection(Vector2* vertices, Vector2 axis) { float32 min = axis.dot(vertices[0]); float32 max = min; for (int v = 1; v < 4; 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; } 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; } 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; float32 minOverlap = FLT_MAX; Vector2 minOverlapAxis; Edge* minOverlapEdge = NULL; bool minOverlapWasFirstRect = false; for (int i = 0; i < 4; i++) { Vector2 normal = firstEdges[i].normal; Vector2 firstProj = getProjection(firstPoints, normal); Vector2 secondProj = getProjection(secondPoints, normal); if (!projectionsOverlap(firstProj, secondProj)) { return ir; } float32 overlap = getProjectionOverlap(firstProj, secondProj); if (overlap < minOverlap) { minOverlap = overlap; minOverlapAxis = normal; minOverlapEdge = &firstEdges[i]; minOverlapWasFirstRect = true; } } for (int i = 0; i < 4; i++) { Vector2 normal = secondEdges[i].normal; Vector2 firstProj = getProjection(firstPoints, normal); Vector2 secondProj = getProjection(secondPoints, normal); if (!projectionsOverlap(firstProj, secondProj)) { return ir; } float32 overlap = getProjectionOverlap(firstProj, secondProj); if (overlap < minOverlap) { minOverlap = overlap; minOverlapAxis = normal; minOverlapEdge = &secondEdges[i]; } } 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.firstPointOfApplication = closestPoint - first->body.position; ir.secondPointOfApplication = closestPoint - second->body.position;; return ir; } void resolveCollision(Rigidbody* first, Rigidbody* second, IntersectionResult* ir) { Vector2 relativeVelocity = ir->relativeVelocity; Vector2 collisionNormal = ir->collisionNormal; Vector2 firstPerp = ir->firstPointOfApplication.getPerp(); Vector2 secondPerp = ir->secondPointOfApplication.getPerp(); float32 firstPerpNorm = firstPerp.dot(collisionNormal); float32 sndPerpNorm = secondPerp.dot(collisionNormal); float32 cofOfRestitution = (first->cofOfRestitution + second->cofOfRestitution) / 2.f; float32 numerator = (relativeVelocity * (-1 * (1.f + cofOfRestitution))).dot(collisionNormal); float32 linearDenomPart = collisionNormal.dot(collisionNormal * (1.f / first->mass + 1.f / second->mass)); float32 rotationalDenomPart = (firstPerpNorm * firstPerpNorm) / first->momentOfInertia + (sndPerpNorm * sndPerpNorm) / second->momentOfInertia; 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; } void update(float32 deltaTimeSeconds, void* userData) { r1.update(deltaTimeSeconds); r2.update(deltaTimeSeconds); // Handle intersection between the two rectangles here IntersectionResult ir = getIntersection(&r1, &r2); if (ir.intersect) { IntersectionResult irCopy = ir; float32 copyDt = deltaTimeSeconds; do { r1.restorePreviousBody(); r2.restorePreviousBody(); ir = irCopy; copyDt = copyDt /= 2.f; r1.update(copyDt); r2.update(copyDt); irCopy = getIntersection(&r1, &r2); if (copyDt <= 0.f) { printf("Error: Should not be happening.\n"); break; } } while (irCopy.intersect); printf("Found intersection at timestamp: %f\n", copyDt); resolveCollision(&r1.body, &r2.body, &ir); float32 frameTimeRemaining = deltaTimeSeconds - copyDt; r1.update(frameTimeRemaining); r2.update(frameTimeRemaining); } // Keep within the bounds handleCollisionWithWall(&r1); handleCollisionWithWall(&r2); // Renderer renderer.render(); r1.render(&renderer); r2.render(&renderer); } void unload() { mainLoop.stop(); renderer.unload(); r1.unload(); r2.unload(); } // // Interactions with DOM handled below // EM_BOOL onPlayClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData) { printf("Play clicked\n"); load(); return true; } EM_BOOL onStopClicked(int eventType, const EmscriptenMouseEvent* mouseEvent, void* userData) { printf("Stop clicked\n"); unload(); return true; }