#include <GL/glut.h>
#include <iostream.h>
#include <math.h>
#include <stdlib.h>

// Initial size of graphics window.
const int WIDTH = 800;
const int HEIGHT = 400;

// Number of beads on string.
const int LENGTH = 200;

const double PI = 3.14159;
double DT = 0.01;
double K = 1000.0;

class Bead
{
public:
	Bead () { x = 0.0; y = 0.0; v = 0.0; a = 0.0; }
	void update () { v += a * DT; y += v * DT; }
	void set (double nx, double ny) { x = nx; y = ny; v = 0.0; }
	void setAcc (double na) { a = na; }
	double getX () { return x; }
	double getY () { return y; }
	friend ostream & operator<< (ostream & os, Bead b);
private:
	double x;
	double y;
	double v;
	double a;
};

ostream & operator<< (ostream & os, Bead b)
{
	os << "(" << b.x << "," << b.y << ") " << b.v;
	return os;
}

Bead string[LENGTH + 1];


// Set string to fundamental (n = 1) or harmonic (2 <= n <= 10)
void harmonic (int n)
{
	string[0].set(0.0, 0.0);
	for (int i = 1; i < LENGTH; i++)
	{
		double x = double(i) / double(LENGTH);
		string[i].set(x, sin(n * PI * x));
	}
	string[LENGTH].set(1.0, 0.0);
}


// Set string to a shape determined by f(x).
void shape (double f (double))
{
	string[0].set(0.0, 0.0);
	for (int i = 1; i < LENGTH; i++)
	{
		double x = double(i) / double(LENGTH);
		string[i].set(x, f(x));
	}
	string[LENGTH].set(1.0, 0.0);
}


// Functions for various shapes on (0,1).

double flat (double x)
{
	return 0.0;
}

double triangle (double x)
{
	return x <= 0.5 ? 2.0 * x : 2.0 - 2.0 * x;
}

double sawtooth (double x)
{
	return x;
}

double square (double x)
{
	return x <= 0.5 ? 1.0 : -1.0;
}

double impulse (double x)
{
	return 0.495 < x && x < 0.505 ? 2.0 : 0.0;
}

double hump (double x)
{
	double h = 20.0 * (x - 0.5);
	return 1.5 * exp(- (h*h));
}


// Display the beads.
void display ()
{
	glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();
	glClear(GL_COLOR_BUFFER_BIT);
	glBegin(GL_LINE_STRIP);
		for (int i = 0; i <= LENGTH; i++)
		{
			if (i % 20 == 0)
				glColor3f(1.0, 1.0, 0.5);
			else
				glColor3f(0.0, 0.8, 1.0);
			glVertex2f(string[i].getX(), string[i].getY());
		}
	glEnd();
	glutSwapBuffers();
}


// Update velocity and position of each bead.
void idle ()
{
	for (int i = 1; i < LENGTH; i++)
		string[i].setAcc(K * (string[i-1].getY() + string[i+1].getY() - 2 * string[i].getY()));
	for (i = 1; i < LENGTH; i++)
		string[i].update();
	glutPostRedisplay();
}


// Kepp string visible in window.
void reshape (int w, int h)
{
	glViewport(0, 0, w, h);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	glOrtho(-0.1, 1.1, -1.5, 1.5, -1.0, 1.0);
}


// Set initial bead positions.
void keyboard (unsigned char key, int x, int y)
{
	switch (key)
	{
	case '0':
	case '1':
	case '2':
	case '3':
	case '4':
	case '5':
	case '6':
	case '7':
	case '8':
	case '9':
		harmonic(key + 1 - '0');
		break;
	case 'h':
	case 'H':
		shape(hump);
		break;
	case 'i':
	case 'I':
		shape(impulse);
		break;
	case 'q':
	case 'Q':
		shape(square);
		break;
	case 's':
	case 'S':
		shape(sawtooth);
		break;
	case 't':
	case 'T':
		shape(triangle);
		break;
    case '<':
        DT *= 0.8;
        break;
    case '>':
        DT /= 0.8;
        break;
	case 27:
		exit(0);
	}
}


// Explain key effects.
void help ()
{
	cout << "Vibrating String Simulation" << endl << endl;
	cout << "Press one of the following keys to set the initial shape of the string:" << endl << endl;
	cout << "0   Fundamental" << endl;
	cout << "1   First harmonic" << endl;
	cout << "2   Second harmonic " << endl;
	cout << "3   Third harmonic " << endl;
	cout << "4   Fourth harmonic " << endl;
	cout << "h   Hump (travelling wave)" << endl;
	cout << "i   Impulse" << endl;
	cout << "q   Square" << endl;
	cout << "s   Sawtooth" << endl;
	cout << "t   Triangle" << endl;
    cout << "<   Slow down" << endl;
    cout << ">   Speed up" << endl;
}


// OpenGL initialization.
void main (int argc, char **argv)
{
	glutInit(&argc, argv);
	glutInitDisplayMode(GLUT_DOUBLE | GLUT_RGB);
	glutInitWindowSize(int(WIDTH), int(HEIGHT));
	glutCreateWindow("Vibrating String");
	glutDisplayFunc(display);
	glutReshapeFunc(reshape);
	glutKeyboardFunc(keyboard);
	glutIdleFunc(idle);
	glPointSize(10.0);
	shape(flat);
	help();
	glutMainLoop();
}