include iostream include cmath include GL glut include GL GL using nam

#include <iostream>
#include <cmath>
#include <GL\glut.h>
#include <GL\GL.h>

using namespace std;

double f(double x, double y)
{
	double f;
	f = y*y - 2 * x*y - 3 * x*x;
	return f;
}

double g(double x, double y)
{
	double g;
	g = y*y - x*y - 2 * x*x - 4;
	return g;
}

double f_diff_x(double x, double y)
{
	double f_diff_x;
	f_diff_x = -2 * y - 6 * x;
	return f_diff_x;
}

double f_diff_y(double x, double y)
{
	double f_diff_y;
	f_diff_y = 2 * y - 2 * x;
	return f_diff_y;
}

double g_diff_x(double x, double y)
{
	double g_diff_x;
	g_diff_x = -y - 4 * x;
	return g_diff_x;
}

double g_diff_y(double x, double y)
{
	double g_diff_y;
	g_diff_y = 2 * y - x;
	return g_diff_y;
}

void display()
{
	//координатная плоскость
	glColor3f(0.0, 1.0, 0.0);
	glBegin(GL_LINES);
	glVertex2f(-550, 0);
	glVertex2f(550, 0);
	glEnd();

	glBegin(GL_LINES);
	glVertex2f(0, 150);
	glVertex2f(0, -150);
	glEnd();
	glPointSize(2.0);
	for (int i = -550; i < 550; i = i + 10)
	{
		if (i == 0)
		{
			glPointSize(4.0);
			glBegin(GL_POINTS);
			glColor3f(1.0, 1.0, 1.0);
			glVertex2d(i, 0);
			glEnd();
		}
		else
		{
			glPointSize(2.0);
			glBegin(GL_POINTS);
			glColor3f(1.0, 1.0, 1.0);
			glVertex2d(i, 0);
			glEnd();
		}
	}
	for (int i = -150; i < 150; i = i + 10)
	{
		if (i == 0)
		{
			glPointSize(4.0);
			glBegin(GL_POINTS);
			glColor3f(1.0, 1.0, 1.0);
			glVertex2d(0, i);
			glEnd();
		}
		else
		{
			glPointSize(2.0);
			glBegin(GL_POINTS);
			glColor3f(1.0, 1.0, 1.0);
			glVertex2d(0, i);
			glEnd();
		}
	}
	
	double x0[2] = { 15, 10 }; //начальное приближение
	double xk = x0[0];
	double yk = x0[1];
	double _xk; //промежуточное приближение
	double qk, pk, x_next, y_next, max;
	double eps = 0.0001;
	int t = 10;
	do 
	{
		_xk = xk - f(xk, yk) / f_diff_x(xk, yk);
		qk = (g(_xk, yk)*f_diff_x(xk, yk)) / (f_diff_x(xk, yk)*g_diff_y(_xk, yk) - f_diff_y(xk, yk)*g_diff_x(_xk, yk));
		pk = (f(xk, yk) - qk*f_diff_y(xk, yk)) / f_diff_x(xk, yk);
		x_next = xk - pk;
		y_next = yk - qk;

		glPointSize(3.0);

		glBegin(GL_POINTS);
			glColor3f(0.0, 0.0, 1.0);
			glVertex2d(xk * t, yk * t);
			glVertex2d(x_next * t, y_next * t);
		glEnd();

		glBegin(GL_LINE_STRIP);
			glColor3f(1.0, 0.0, 0.0);
			glVertex2d(xk * t, yk * t);
			glVertex2d(x_next * t, y_next * t);
		glEnd();

		glBegin(GL_LINE_STRIP);
			glColor3f(1.0, 0.0, 1.0);
			glVertex2d(xk * t, yk * t);
			glVertex2d(xk * t, 0);
		glEnd();

		glBegin(GL_LINE_STRIP);
		glColor3f(1.0, 0.0, 1.0);
		glVertex2d(xk * t, yk * t);
		glVertex2d(0, yk * t);
		glEnd();

		printf("curr: (%.5f ; %.5f)\n", xk, yk);
		printf("next: (%.5f ; %.5f)\n", x_next, y_next);

		xk = x_next;
		yk = y_next;
		max = (abs(pk) > abs(qk)) ? abs(pk) : abs(qk);
		cout << endl;
		
	} while (max > eps);
	glFlush();
}

int main(int argc, char **argv) {
	glutInit(&argc, argv); 
	glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB); 
	glutInitWindowSize(600*2, 165*2);
	glutInitWindowPosition(0, 0);
	glutCreateWindow("Sin");
	glClearColor(1.0, 1.0, 1.0, 1.0);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	glOrtho(-600.0, 600.0, -200.0, 200.0, -1.0, 1.0);
	glutDisplayFunc(display);
	glutMainLoop();
	return 0;
}