/**
* Robert Krzyzanowski
* Buffon's Needle
* MTH341 Enrichment
*/

#include <windows.h>
#include <fstream>
#include <GL/glut.h>
#include <iostream>
#include <conio.h>
#include <iomanip>
#include <stdio.h>
#include <math.h>
#include <vector>
#include <time.h>
#include <iomanip>
using namespace std;

typedef vector<float> needle;
vector<needle> needles;

void main(int, char**);
void display(void);
void drawField(void);
void dropNeedle(void);
void drawNeedles(void);
void displayInfo(void);
bool needleOnLine(needle n);

// Pre-defined colors
enum colorDefs {PBLACK, PWHITE, PRED, PBLUE, PGREEN, PCYAN, PMAGENTA, PYELLOW, PGRAY};
float colors[9][3] = {{0.0f,0.0f,0.0f}, {1.0f,1.0f,1.0f}, {1.0f,0.0f,0.0f},
{0.0f,0.0f,0.5f}, {0.0f,0.5f,0.0f}, {0.0f, 0.8f, 0.8f}, {0.4f, 0.0f, 0.4f},
{1.0f, 1.0f, 0.0f}, {0.5f, 0.5f, 0.5f}};

// Graphical variables.
int scrWidth = 800, scrHeight = 800;							// Screen width and height.
int scrX = 250, scrY = 100;										//Screen X and Y.
char*  winTitle = "Buffon's Needles by Robert Krzyzanowski";	// Window title.

float D = 100;
float L = 0;
int C = 5;

int lastClock = 0;

int needlesOnD = 0;

void main(int argc, char** argv)
{
	glutInit(&argc, argv);

	glutInitDisplayMode(GLUT_RGB | GLUT_DOUBLE);
	glutInitWindowSize(scrWidth, scrHeight);
	glutInitWindowPosition(scrX,scrY);
	glutCreateWindow(winTitle);
	glutDisplayFunc(display);
	glutIdleFunc(display);
	glClearColor(1.0, 1.0, 1.0, 1.0);
	glColor3f(0.0, 0.0, 0.0);

	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	gluOrtho2D(0.0, (float)scrWidth, 0.0, (float)scrHeight);
	glMatrixMode(GL_MODELVIEW);

	srand(time(NULL));	
	for(int i =0;i<100;i++)rand();

	if (argc >= 2) D = atof(argv[1]);
	if (argc >= 3) L = atof(argv[1]);
	if (argc >= 4) C = atoi(argv[1]); if (C <= 0) C = 5;
	if (D<=0)D=100;if(L<=0)L=((float)rand()/RAND_MAX)*D;

	glutMainLoop();
	cout << "\n\nPress enter to end.\n"; while (getch()!='\r');	
}

void display(void)
{
	glClear(GL_COLOR_BUFFER_BIT);

	glColor3fv(colors[PWHITE]);
	glBegin(GL_QUADS);
		glVertex2f(0.0f, 0.0f);
		glVertex2f(0.0f, scrHeight);
		glVertex2f(scrWidth, scrHeight);
		glVertex2f(scrWidth, 0.0f);
	glEnd();

	if (clock() - lastClock > C) {
		lastClock = clock();

		dropNeedle();
	}

	drawField();
	drawNeedles();
}

void drawField() {
	glColor3fv(colors[PBLACK]);
	glBegin(GL_LINES);
	for(int i = 1; i*D < scrHeight; i++) {
		glVertex2f(0.0f, i*D);
		glVertex2f(scrWidth, i*D);
	}
	glEnd();
}

void dropNeedle() {
	needle n;
	n.push_back(((float)rand()/RAND_MAX)*scrWidth);
	n.push_back(((float)rand()/RAND_MAX)*scrHeight);
	n.push_back(((float)rand()/RAND_MAX)*3.14159);
	needles.push_back(n);
	if (needleOnLine(n)) needlesOnD++;

	displayInfo();
}

void drawNeedles() {
	glBegin(GL_LINES);
	for(int i = 0; i < needles.size(); i++) {
		needle n = needles[i];

		if ( needleOnLine(n) ) {
			glColor3fv(colors[PRED]);
		}
		else {
			glColor3fv(colors[PBLACK]);
		}

		glVertex2f(n[0] + L/2 * sin(n[2]), n[1] - L/2 * cos(n[2]));
		glVertex2f(n[0] - L/2 * sin(n[2]), n[1] + L/2 * cos(n[2]));		
	}
	glEnd(); 
}

double absf(float f) {
	return (f>0?f:-f);
}

void displayInfo() {
	system("cls");
	float ratio = (float)needlesOnD / needles.size() ;
	float Tratio = 2*L/(3.14159*D);
	double pi_est = 1/((double)needlesOnD / needles.size())*2*L/D;
	cout << "Buffon's Needle by Robert Krzyzanowski\n";
	cout << "**************************************\n";
	cout << "D: " << setprecision(2) << fixed << D << "\tL: " << setprecision(2) << fixed << L << endl;
	cout << "Needles dropped: " << needles.size() << endl;
	cout << "Needles on a line: " << needlesOnD << endl;
	cout << "Needles not on a line: " << (needles.size() - needlesOnD) << endl;
	cout << "Ratio: " << setprecision(3) << ratio << endl;
	cout << "Theoretical estimate: 2L/pi*D = " << Tratio << endl;
	cout << "Error: " << setprecision(2) <<(ratio>0?((float)absf(ratio-Tratio)/ratio*100):999) << "%" << endl;
	cout << "Estimate of pi: " << pi_est << endl;
}

bool needleOnLine(needle n) {
	return (abs(floor((n[1] + L/2 * cos(n[2]))/D) - floor((n[1] - L/2 * cos(n[2]))/D)) > 0);
}