#include<GL/glut.h>
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include <iostream>
#include <vector>
#include <algorithm>
#include <numeric>

using std::cout;

typedef struct points {
 float x;
 float y;
}XY;

std::vector<XY> liste_pts;

/*typedef struct ctrl {
        XY *list;
        int nbCtrlPoints;
        void ajouter(XY p){
                      this->list[this->nbCtrlPoints] = p;
                      this->nbCtrlPoints+=1;
                      }
        }CtrlPoints;
*/
int factoriel(int x) // no comment
{
  int r = 1;
  for (int i=2 ; i<=x ; i++) r*=i;
  return r;
}

float Berstein(int i, int n, double t)
{
  float t1 = 1.0f-t;
  return factoriel(n)/(factoriel(i)*factoriel(n-i))*pow(t,i)*pow(t1,n-i);
}


XY CalcBezier(std::vector<XY> liste_pts, double t, int n)
{
	int i;
	XY p;
	p.x=0;
	p.y=0;
	for(i=0;i<n;i++)
	{
       	p.x+=Berstein(i, n-1, t)*liste_pts[i].x;
       	p.y+=Berstein(i, n-1, t)*liste_pts[i].y;
    	}
	return p;
}



void drawBezier(XY p1, std::vector<XY> liste_pts, int n){
	double t;
	int i;
	XY p, p_prec;
	p_prec = p1;
	for(i=0;i<n;i++){
		printf("\nx= %f y= %f", liste_pts[i].x, liste_pts[i].y);
	}
	for(i = 0; i <= 100 ; i++){
  		t = i / 100.0;
  		p = CalcBezier(liste_pts,t,n);
		//printf("\nx:%f y:%f", p.x, p.y);
		glBegin(GL_LINE_STRIP);
			glVertex2f(p_prec.x,p_prec.y);
			glVertex2f(p.x,p.y);
		glEnd();
		p_prec = p;
	}
}

void init(void)
{
	glClearColor(1.0, 1.0, 1.0, 1.0);
}

void display(void)
{
	XY p1;
    int i,j,n;
    	FILE* fp;
	fp=fopen("ptsctrl2.txt","r");
	if (fp==NULL){
		printf("\nErreur d'ouverture du fichier");
		exit(1);
		}
	else{
		fscanf(fp,"\nnombre : %d", &n);
		liste_pts.reserve( n );
		for(i=0;i<n;i++){
			fscanf(fp,"\nx= %f y= %f", &liste_pts[i].x, &liste_pts[i].y);
		}
	}
	fclose(fp);
	for(i=0;i<n;i++){
		printf("\nx= %f y= %f", liste_pts[i].x, liste_pts[i].y);
	}
	glClear(GL_COLOR_BUFFER_BIT);
	glColor3f(0.0, 0.0, 0.0);
	glPointSize(5.0);
	glColor3f(1.0, 1.0, 0.0);
	glPointSize(5.0);
	glColor3f(1.0,1.0,0.0);
	for(i=0;i<4;i++){
		glBegin(GL_POINTS);
			glVertex2f(liste_pts[i].x, liste_pts[i].y);
		glEnd();
	}
	p1.x=liste_pts[0].x;
	p1.y=liste_pts[0].y;
	drawBezier(p1,liste_pts,n);
	glFlush();
}

void reshape(int w, int h)
{
	glViewport(0, 0, (GLsizei) w, (GLsizei) h);
	glMatrixMode(GL_PROJECTION);
	glLoadIdentity();
	if (w<=h)
		glOrtho(-5.0, 5.0, -5.0*(GLfloat)h/(GLfloat)w, 5.0*(GLfloat)h/(GLfloat)w, -5.0, 5.0);
	else
		glOrtho(-5.0*(GLfloat)w/(GLfloat)h, 5.0*(GLfloat)w/(GLfloat)h, -5.0, 5.0, -5.0, 5.0);
	glMatrixMode(GL_MODELVIEW);
	glLoadIdentity();
}

int main(int argc, char** argv)
{
    glutInit(&argc, argv);
	glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
	glutInitWindowSize(500, 500);
	glutInitWindowPosition(100, 100);
	glutCreateWindow(argv[0]);
	init();
	glutDisplayFunc(display);
	glutReshapeFunc(reshape);
	glutMainLoop();
	return 0;
}