#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 force = { 0, 0 }; Vector2 velocity = { 0, 0 }; Vector2 position = { 0, 0 }; float32 rotationalVelocity = 0.f; float32 rotation = 0.f; float32 mass = 1.f; float32 cofOfRestition = 1.f; float32 momentOfInertia = 1.f; void reset() { force = { 0, 0 }; velocity = { 0, 0 }; rotationalVelocity = 0.f; rotation = 0.f; } void applyForce(Vector2 f) { force += f; } void applyGravity(float32 deltaTimeSeconds) { velocity += (Vector2 { 0.f, -50.f } * deltaTimeSeconds); } void update(float32 deltaTimeSeconds) { applyGravity(deltaTimeSeconds); Vector2 acceleration = force / mass; velocity += (acceleration * deltaTimeSeconds); position += (velocity * deltaTimeSeconds); force = Vector2 { 0.f, 0.f }; rotation += (rotationalVelocity * deltaTimeSeconds); } void setMomentOfInertia(float32 moi) { momentOfInertia = moi; } }; struct IntersectionResult { bool intersect = false; Vector2 collisionNormal; Vector2 relativeVelocity; Vector2 firstPointOfApplication; Vector2 secondPointOfApplication; }; struct Edge { Vector2 normal; Vector2 start; Vector2 end; }; struct ConvexPolygon { OrthographicShape shape; Rigidbody body; Rigidbody previousBody; Vector4 color; int32 numVertices = 3; float32 width = 0.f; float32 height = 0.f; Vector2* originalVertices; Vector2* transformedVertices; Edge* edges; void load(OrthographicRenderer* renderer) { transformedVertices = new Vector2[numVertices]; // This will be used for SAT calculations later originalVertices = new Vector2[numVertices]; // Generate the shape with numVertices many sides in a "fan" shape (i.e. 3 vertices per vertex) // The shape will have all equal sides, just to make it easier on me. Therefore, it will fit inside // the conditions of a circle, which is fun. Before anyone gets mad: I know I can avoid recalculating // a lot of these cosines and sines. I will be okay; I will live. The bigger problem with this demo // is the 2k lines of JavaScript that are required to display it. int32 verticesNeeded = numVertices * 3; float32 angleIncrements = (2.f * PI) / static_cast(numVertices); OrthographicVertex* shaderVertices = new OrthographicVertex[verticesNeeded]; for (int32 vidx = 0; vidx < numVertices; vidx++) { int32 indexPosition = vidx * 3; float32 firstAngle = angleIncrements * vidx; shaderVertices[indexPosition].position = { cosf(firstAngle) * width, sinf(firstAngle) * height }; originalVertices[vidx] = shaderVertices[indexPosition].position; shaderVertices[indexPosition + 1].position = { 0.f, 0.f }; float32 secondAngle = angleIncrements * (vidx + 1); shaderVertices[indexPosition + 2].position = { cosf(secondAngle) * width, sinf(secondAngle) * height }; // Apply some global stylings for (int subIdx = 0; subIdx < 3; subIdx++) { shaderVertices[indexPosition + subIdx].color = color.toNormalizedColor(); } } shape.load(shaderVertices, verticesNeeded, renderer); delete[] shaderVertices; 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); } void update(float32 dtSeconds) { previousBody = body; body.update(dtSeconds); shape.model = Mat4x4().translateByVec2(body.position).rotate2D(body.rotation); // Populate the current position of our edges for (int vidx = 0; vidx < numVertices; vidx++) { Vector2 start = shape.model * originalVertices[vidx]; transformedVertices[vidx] = start; Vector2 end = shape.model * originalVertices[vidx == numVertices - 1 ? 0 : vidx + 1]; edges[vidx] = { (end - start).getPerp().normalize(), start, end }; } } void restorePreviousBody() { body = previousBody; } void render(OrthographicRenderer* renderer) { shape.render(renderer); } void unload() { shape.unload(); delete[] originalVertices; originalVertices = NULL; delete[] transformedVertices; transformedVertices = NULL; delete[] edges; edges = NULL; } }; 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; ConvexPolygon polygons[4]; 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); for (int index = 0; index < 4; index++) { polygons[index].width = 50.f; polygons[index].height = 50.f; 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].numVertices = (index + 1) * 3; polygons[index].color = Vector4 { index == 0 || index == 3 ? 255.f : 0.f, index == 1 || index == 3 ? 255.f : 0.f, index == 2 ? 255.f : 0.f, 255.f }; polygons[index].load(&renderer); } printf("Main loop beginning\n"); mainLoop.run(update); } Vector2 getProjection(Vector2* vertices, int numVertices, Vector2 axis) { 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; } 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(ConvexPolygon* first, ConvexPolygon* second) { IntersectionResult ir; // For two rectangles to overlap, it means that at least one of the corners of one is inside of the other float32 minOverlap = FLT_MAX; Edge* minOverlapEdge = NULL; bool minOverlapWasFirst = false; 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 ir; } float32 overlap = getProjectionOverlap(firstProj, secondProj); if (overlap < minOverlap) { minOverlap = overlap; minOverlapEdge = &first->edges[i]; minOverlapWasFirst = true; } } 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 ir; } float32 overlap = getProjectionOverlap(firstProj, secondProj); if (overlap < minOverlap) { minOverlap = overlap; minOverlapEdge = &second->edges[i]; } } ir.intersect = true; ir.relativeVelocity = first->body.velocity - second->body.velocity; ir.collisionNormal = minOverlapEdge->normal; // Time to find just where we intersected Vector2 closestPoint; float32 minDistance = FLT_MAX; for (int p = 0; p < (minOverlapWasFirst ? second->numVertices : first->numVertices); p++) { Vector2 point = minOverlapWasFirst ? second->transformedVertices[p] : first->transformedVertices[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 cofOfRestition = (first->cofOfRestition + second->cofOfRestition) / 2.f; float32 numerator = (relativeVelocity * (-1 * (1.f + cofOfRestition))).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; // @TODO: Most of my 2D rotational work is pretty broken. Let's ignore it for the time being; 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) { // Update for (int p = 0; p < 4; p++) { polygons[p].update(deltaTimeSeconds); } // Check collisions with other rectangles for (int i = 0; i < 4; i++) { ConvexPolygon* first = &polygons[i]; for (int j = i + 1; j < 4; j++) { ConvexPolygon* second = &polygons[j]; IntersectionResult ir = getIntersection(first, second); if (!ir.intersect) { continue; } // Handle collison here IntersectionResult irCopy = ir; float32 copyDt = deltaTimeSeconds; do { first->restorePreviousBody(); second->restorePreviousBody(); ir = irCopy; copyDt = copyDt /= 2.f; first->update(copyDt); second->update(copyDt); irCopy = getIntersection(first, second); if (copyDt <= 0.f) { printf("Error: Should not be happening.\n"); break; } } while (irCopy.intersect); printf("Found intersection at timestamp: %f\n", copyDt); resolveCollision(&first->body, &second->body, &ir); float32 frameTimeRemaining = deltaTimeSeconds - copyDt; first->update(frameTimeRemaining); second->update(frameTimeRemaining); } } // Check collisions with walls for (int p = 0; p < 4; p++) { ConvexPolygon* polygon = &polygons[p]; if (polygon->body.position.x <= 0.f) { polygon->body.position.x = 0.f; polygon->body.velocity = polygon->body.velocity - Vector2 { 1.f, 0.f } * (2 * (polygon->body.velocity.dot(Vector2 { 1.f, 0.f }))); } if (polygon->body.position.y <= 0.f) { polygon->body.position.y = 0.f; polygon->body.velocity = polygon->body.velocity - Vector2 { 0.f, 1.f } * (2 * (polygon->body.velocity.dot(Vector2 { 0.f, 1.f }))); } if (polygon->body.position.x >= 800.f) { polygon->body.position.x = 800.f; polygon->body.velocity = polygon->body.velocity - Vector2 { -1.f, 0.f } * (2 * (polygon->body.velocity.dot(Vector2{ -1.f, 0.f }))); } if (polygon->body.position.y >= 600.f) { polygon->body.position.y = 600.f; polygon->body.velocity = polygon->body.velocity - Vector2 { 0.f, -1.f } * (2 * (polygon->body.velocity.dot(Vector2 { 0.f, -1.f }))) ; } } // Renderer renderer.render(); for (int p = 0; p < 4; p++) { polygons[p].render(&renderer); } } void unload() { mainLoop.stop(); renderer.unload(); for (int p = 0; p < 4; p++) { polygons[p].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; }