#include <stdio.h>
#include <windows.h>
#include <gl/glut.h>
#include <cmath>
#include <iostream>

using namespace std;

GLUnurbsObj* nobj;
GLfloat ctlarray[][3] = {
	{ -0.8,  0.8 },
	{ -0.6, -0.7 },
	{ 0.0,  0.5 },
	{ 0.7,  0.2 }
};

GLfloat bp[][4][2] = {
	{ { 0.0,0.0 },{ -0.5,-0.95 },{ 0.0,-0.95 },{ 0.5,-0.95 } } ,
	{ { -0.95,-0.5 },{ -0.5,-0.5 },{ 0.0,-0.5 },{ 0.5,-0.5 } },
	{ { 0.95,0.0 },{ -0.5,0.0 },{ 0.0,0.0 },{ 0.5,0.0 } },
	{ { -0.95,0.5 },{ -0.5,0.5 },{ 0.0,0.5 },{ 0.0,0.0 } }
};

int fact(int n) {
	int val = 1;
	for (int i = 2; i < n + 1; i++) {
		val = val * i;
	}
	return val;
}

int C(int n, int k) {
	return fact(n) / (fact(k) * fact(n - k));
}

float BezePoly(int n, int i, float t) {
	int c = C(n, i);
	return c * pow(t, i) * pow(1 - t, n - i);
}

float BezePoly3d(int n, int m, int i, int j, float u, float w) {
	int c1 = C(n, i);
	int c2 = C(m, j);
	return c1 * pow(u, i) * pow(1 - u, n - i) * c2 * pow(w, j) * pow(1 - w, m - j);
}

void Display()
{
	glClear(GL_COLOR_BUFFER_BIT);
	glPointSize(3.0);
	glColor3f(0.0, 1.0, 0.0);
	//int n = 3;
	/*glBegin(GL_POINTS);
	for (float t = 0.0; t < 1.0; t = t + 0.01) {
	GLfloat x = 0.0;
	GLfloat y = 0.0;
	for (int i = 0; i <= n; i++) {
	x = x + BezePoly(n, i, t) * ctlarray[i][0];
	y = y + BezePoly(n, i, t) * ctlarray[i][1];
	}
	cout << x << y << endl;
	glVertex3f(x, y, 0.5);
	}
	glEnd();
	glFlush();*/

	int n = 3;
	int m = 3;
	glBegin(GL_POINTS);
	for (int i = 0; i <= n; i++) {
		for (int j = 0; j <= n; j++) {
			glVertex3f(bp[i][j][0], bp[i][j][1], 0);
		}
	}

	for (float u = 0; u <= 1; u += 0.01) {
		for (float w = 0; w <= 1; w += 0.01) {
			GLfloat x = 0.0;
			GLfloat y = 0.0;
			for (int i = 0; i <= n; i++) {
				for (int j = 0; j <= m; j++) {
					x += bp[i][j][0] * BezePoly3d(n, m, i, j, u, w);
					y += bp[i][j][1] * BezePoly3d(n, m, i, j, u, w);
				}
			}
			glVertex3f(x, y, 0);
		}
	}
	glEnd();
	glFlush();
}


void main()
{
	glutInitDisplayMode(GLUT_RGBA | GLUT_SINGLE);
	glutInitWindowSize(960, 960);
	glutInitWindowPosition(100, 100);
	glutCreateWindow("  ");
	glutDisplayFunc(Display);
	glutMainLoop();
}