#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 // Side note: It is Eastertime, so I chose this easter color palette. Enjoy: https://htmlcolors.com/palette/144/easter 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 = 0.f; void reset() { force = { 0, 0 }; velocity = { 0, 0 }; rotationalVelocity = 0.f; rotation = 0.f; } void applyForce(Vector2 f) { force += f; } void applyGravity() { force += Vector2 { 0.f, -100.f }; } void update(float32 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 Pill { OrthographicShape shape; Rigidbody body; float32 a = 0; float32 b = 0; Pill copy() { Pill retval; retval.shape = shape; retval.body = body; retval.a = a; retval.b = b; return retval; } void load(OrthographicRenderer* renderer, float32 numSegments, float32 width, float32 height) { // Note that a so-called "pill" is simply an ellipse. // Equation of an ellipse is: // // x^2 / a^2 + y^2 / b^2 = 1 // // or, in parametric form: // // x = a * cos(t), y = b * sin(t) // float32 angleIncrements = (2.f * PI) / numSegments; uint32 numVertices = static_cast(numSegments * 3.f); OrthographicVertex* vertices = new OrthographicVertex[numVertices]; a = width / 2.f; b = height / 2.f; Vector4 color = Vector4().fromColor(243,166,207, 255); for (uint32 vertexIndex = 0; vertexIndex < numVertices; vertexIndex += 3) { // Create a single "slice" of the ellipse (like a pizza) float32 currAngle = (vertexIndex / 3.f) * angleIncrements; float32 nextAngle = (vertexIndex / 3.f + 1.f) * angleIncrements; vertices[vertexIndex].position = Vector2 { 0.f, 0.f }; vertices[vertexIndex].color = color; vertices[vertexIndex + 1].position = Vector2 { a * cosf(currAngle), b * sinf(currAngle) }; vertices[vertexIndex + 1].color = color; vertices[vertexIndex + 2].position = Vector2 { a * cosf(nextAngle), b * sinf(nextAngle) }; vertices[vertexIndex + 2].color = color; } shape.load(vertices, numVertices, renderer); body.reset(); // https://byjus.com/jee/moment-of-inertia-of-ellipse/ body.momentOfInertia = (body.mass * (a * a + b * b)) / 4.f; a = width / 2.f; b = height / 2.f; delete[] vertices; } void update(float32 deltaTimeSeconds) { body.update(deltaTimeSeconds); shape.model = Mat4x4().translateByVec2(body.position).rotate2D(body.rotation); } void render(OrthographicRenderer* renderer) { shape.render(renderer); } void unload() { shape.unload(); } float32 getArea() { return 0.f; } }; struct LineSegment { OrthographicShape shape; Rigidbody body; Vector2 start; Vector2 end; float32 length; Vector2 normal; OrthographicVertex vertices[2]; void load(OrthographicRenderer* renderer, Vector4 color, Vector2 inStart, Vector2 inEnd) { start = inStart; end = inEnd; length = (start - end).length(); vertices[0].position = start; vertices[0].color = color; vertices[1].position = end; vertices[1].color = color; normal = (end - start).getPerp().normalize(); shape.load(vertices, 2, renderer); body.reset(); body.mass = 1000000000.f; body.cofOfRestition = 1.f; body.rotationalVelocity = 0; body.velocity = Vector2(); body.momentOfInertia = body.mass * (length / 2.f); } void render(OrthographicRenderer* renderer) { shape.render(renderer, GL_LINES); } void unload() { shape.unload(); } Vector2 getPointOnLine(float32 t) { return { start.x + (end.x - start.x) * t, start.y + (end.y - start.y) * t, }; } Vector2 getNormal() { return (end - start).getPerp().normalize(); } }; 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(); IntersectionResult getIntersection(Pill* pill, LineSegment* segment); void resolveCollision(Rigidbody* first, Rigidbody* second, IntersectionResult* ir); // Global Variables WebglContext context; OrthographicRenderer renderer; Pill pill; MainLoop mainLoop; LineSegment segmentList[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); pill.body.position = Vector2 { context.width / 2.f, context.height / 2.f }; pill.load(&renderer, 64, 100.f, 50.f); pill.body.rotationalVelocity = 0.3f; segmentList[0].load(&renderer, Vector4().fromColor(191, 251, 146, 255.f), Vector2 { 50.f, 0.f }, Vector2 { 50.f, static_cast(context.height) }); segmentList[1].load(&renderer, Vector4().fromColor(159, 224, 210, 255.f), Vector2 { context.width - 50.f, 0.f }, Vector2 { context.width - 50.f, static_cast(context.height) }); segmentList[2].load(&renderer, Vector4().fromColor(248, 255, 156, 255.f), Vector2 { 50.f, 50.f }, Vector2 { context.width - 50.f, 150.f }); segmentList[3].load(&renderer, Vector4().fromColor(205, 178, 214, 255.f), Vector2 { 50.f, 150.f }, Vector2 { context.width - 50.f, 50.f }); mainLoop.run(update); } float32 areaOfTriangle(Vector2 a, Vector2 b, Vector2 c) { // Refernce for this for the formula: https://www.onlinemath4all.com/area-of-triangle-using-determinant-formula.html return ABS(0.5 * (a.x * b.y - b.x * a.y + b.x * c.y - c.x * b.y + c.x * a.y - a.x * c.y)); } IntersectionResult getIntersection(Pill* pill, LineSegment* segment) { IntersectionResult result; Mat4x4 inverseModel = pill->shape.model.inverse(); Vector2 start = inverseModel * segment->start; Vector2 end = inverseModel * segment->end; Vector2 diff = end - start; float32 A = (diff.x * diff.x) / (pill->a * pill->a) + (diff.y * diff.y) / (pill->b * pill->b); float32 B = ((2 * start.x) * (end.x - start.x)) / (pill->a * pill->a) + ((2 * start.y) * (end.y - start.y)) / (pill->b * pill->b); float32 C = (start.x * start.x) / (pill->a * pill->a) + (start.y * start.y) / (pill->b * pill->b) - 1.f; float32 determinant = B * B - 4 * A * C; if (determinant < 0.f) { result.intersect = false; return result; } float32 t1 = (-B + sqrtf(determinant)) / (2 * A); float32 t2 = (-B - sqrtf(determinant)) / (2 * A); Vector2 pointOnLine = segment->getPointOnLine(t1); // This point is in world space and line space, since the line is in world space Vector2 pointOnEllipse = pointOnLine - pill->body.position; // This point is in ellipse space //float32 parametricTEllipse = atan2f( pointOnEllipse.y / pill->b , pointOnEllipse.x / pill->a ); //Vector2 tangent = { -pill->a * sinf(parametricTEllipse), pill->b * cosf(parametricTEllipse) }; //Vector2 normal = tangent.getPerp(); // Or, simply: Vector2 normal = { pointOnEllipse.x * (pill->b / pill->a), pointOnEllipse.y * (pill->a / pill->b) }; Vector2 normal = segment->getNormal(); result.intersect = true; result.relativeVelocity = pill->body.velocity - segment->body.velocity;; result.collisionNormal = normal; result.firstPointOfApplication = pointOnEllipse; result.secondPointOfApplication = pointOnLine; return result; } 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 cofOfRestition = (first->cofOfRestition + second->cofOfRestition) / 2.f; float32 lNumerator = (relativeVelocity * -(1.f + cofOfRestition)).dot(collisionNormal); float32 lLinearDenomPart = collisionNormal.dot(collisionNormal * (1.f / first->mass + 1.f / second->mass)); float32 lRotationalDenomPart = powf(firstPerp.dot(collisionNormal), 2.f) / first->momentOfInertia + powf(secondPerp.dot(collisionNormal), 2) / second->momentOfInertia; float32 lImpulseMagnitude = lNumerator / (lLinearDenomPart + lRotationalDenomPart); first->velocity = first->velocity + (collisionNormal * (lImpulseMagnitude / first->mass)); second->velocity = second->velocity - (collisionNormal * (lImpulseMagnitude / second->mass)); printf("%f\n", firstPerp.dot(collisionNormal * lImpulseMagnitude) / first->momentOfInertia); first->rotationalVelocity = first->rotationalVelocity + firstPerp.dot(collisionNormal * lImpulseMagnitude) / first->momentOfInertia; second->rotationalVelocity = second->rotationalVelocity - secondPerp.dot(collisionNormal * lImpulseMagnitude) / second->momentOfInertia; } void update(float32 deltaTimeSeconds, void* userData) { // Input pill.body.applyGravity(); // Update Pill copyPill = pill.copy(); pill.update(deltaTimeSeconds); // Intersections for (int32 lineIdx = 0; lineIdx < 4; lineIdx++) { IntersectionResult ir = getIntersection(&pill, &segmentList[lineIdx]); if (ir.intersect) { // Find the exact moment that the intersection happens by rewinding the simulation until we're not intersecting IntersectionResult subIr = ir; float32 subdividedTimeSeconds = deltaTimeSeconds; do { ir = subIr; pill = copyPill.copy(); subdividedTimeSeconds /= 2.f; pill.update(subdividedTimeSeconds); subIr = getIntersection(&pill, &segmentList[lineIdx]); if (subdividedTimeSeconds == 0.f) { printf("Error: Should not be happening.\n"); break; } } while (subIr.intersect); printf("Found intersection at timestamp: %f\n", subdividedTimeSeconds); resolveCollision(&pill.body, &segmentList[lineIdx].body, &ir); pill.update(deltaTimeSeconds - subdividedTimeSeconds); } } // Render renderer.render(); pill.shape.render(&renderer); for (int32 segmentIndex = 0; segmentIndex < 4; segmentIndex++) { segmentList[segmentIndex].render(&renderer); } } void unload() { mainLoop.stop(); pill.unload(); renderer.unload(); for (int32 segmentIndex = 0; segmentIndex < 4; segmentIndex++) { segmentList[segmentIndex].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; }