/* Auteur: Nicolas JANEY         */
/* nicolas.janey@univ-fcomte.fr  */
/* Avril 2001                    */
/* Programmation du calcul       */
/* d'une courbe de Bezier        */

#include <stdio.h>
#include <stdlib.h>
#include <math.h>

typedef struct coord_3D {
  float x ;
  float y ;
  float z ; } coord_3D ;

typedef struct polygone {
  int n ;
  coord_3D *c ; } polygone ;

void pixel(float x,float y,float z) {
    printf("%f %f %f\n",x,y,z) ; 
  }

double power(double v,int p) {
  return(( !v && !p ) ?
    1.:
    pow(v,(double) p)) ;
}

/* En entree le polygone p, le nombre
de points n */

void bezier(polygone *p,int n) {
  int i,j ;
  float t,mt ;
  float *cn,x,y,z,fac ;
  cn =(float *) calloc(p->n,sizeof(float));
  cn[0] = 1 ;
  cn[1] =(float) (p->n-1) ;
  for ( i = 2 ; i < p->n ; i++ )
    cn[i] = cn[i-1] * (p->n - i) / i ;
  for ( i = 0 ; i < n ; i++ ) {
    t =(float) i/(n-1) ;
    mt = 1-t ;
    x = y = z = 0.0F ;
    for ( j = 0 ; j < p->n ; j++ ) {
      fac = cn[j]*(float) power(t,j)*
            (float) power(mt,p->n-1-j);
      x += fac * p->c[j].x ;
      y += fac * p->c[j].y ;
      z += fac * p->c[j].z ; }
    pixel(x,y,z) ; }
  free(cn) ;
}

int main(int argc,char **argv) {
  coord_3D c[8] = { {-6.0F,-6.0F, 3.0F},
                    {-6.0F,-1.0F, 1.0F},
                    {-5.0F, 2.0F,-1.0F},
                    {-1.0F, 3.0F, 1.0F},
                    { 2.0F, 1.0F, 4.0F},
                    { 4.0F, 2.0F, 2.0F},
                    { 5.0F, 5.0F,-2.0F},
                    { 6.0F, 6.0F,-4.0F} } ;
  polygone p = { 8,c } ;
  bezier(&p,50) ;
  return(0);
}