path: root/2d/rigidbody/rigidbody_3/main.cpp

#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 <cstdio>
#include <cmath>
#include <emscripten/html5.h>
#include <unistd.h>
#include <pthread.h>
#include <cmath>
#include <cfloat>

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;
}