Programmation C/Courbe de Bézier

Ce code permet de tracer une courbe de Bézier définie par 4 points de contrôle. C'est donc une courbe cubique. Cet algorithme est une implémentation de l'algorithme de de Casteljau.

Pour adapter ce code C à votre système, il vous suffit de remplacer la procédure de tracé de segment (ici en OpenGL).

La structure Global_Bezier contient les 4 points de contrôle de la courbe de Bézier à tracer. level contient le nombre d'appel récursif.

typedef struct {
        float x, y;
 } point;

 typedef struct {
       point P[4];
 } Bezier;

 /* Variables globales */
 Bezier Global_Bezier;
 int level=1;

 // Draw a line with color (r,v,b)
 void DrawLine(int x1, int y1, int x2, int y2,float r, float v, float b)
 {
   glColor3f(r,v,b);
   glBegin(GL_LINES);
   glVertex2i(x1,y1);
   glVertex2i(x2,y2);
   glEnd();
   glFlush();
 }

 void DrawBezierBase(Bezier p,float r,float v,float b)
 {
   DrawLine(p.P[0].x,p.P[0].y,p.P[1].x,p.P[1].y,r,v,b);
   DrawLine(p.P[1].x,p.P[1].y,p.P[2].x,p.P[2].y,r,v,b);
   DrawLine(p.P[2].x,p.P[2].y,p.P[3].x,p.P[3].y,r,v,b);
 }

 void DrawBezierRecursive (Bezier b, int level) 
 {
         if (level <= 0) {
 	  /* draw a line segment */
               DrawLine((int) (b.P[0].x + 0.5), (int) (b.P[0].y + 0.5),
                               (int) (b.P[3].x + 0.5), (int) (b.P[3].y + 0.5),1,1,1);
         } else {
                 Bezier left, right;                 
                 /* subdivide into 2 Bezier segments */
                 left.P[0].x = b.P[0].x;
                 left.P[0].y = b.P[0].y;
                 left.P[1].x = (b.P[0].x + b.P[1].x) / 2;
                 left.P[1].y = (b.P[0].y + b.P[1].y) / 2;
                 left.P[2].x = (b.P[0].x + 2*b.P[1].x + b.P[2].x) / 4;
                 left.P[2].y = (b.P[0].y + 2*b.P[1].y + b.P[2].y) / 4;
                 left.P[3].x = (b.P[0].x + 3*b.P[1].x + 3*b.P[2].x + b.P[3].x) / 8;
                 left.P[3].y = (b.P[0].y + 3*b.P[1].y + 3*b.P[2].y + b.P[3].y) / 8;
                 DrawBezierBase(left,0,1,0);
                 right.P[0].x = left.P[3].x;
                 right.P[0].y = left.P[3].y;
                 right.P[1].x = (b.P[1].x + 2*b.P[2].x + b.P[3].x) / 4;
                 right.P[1].y = (b.P[1].y + 2*b.P[2].y + b.P[3].y) / 4;
                 right.P[2].x = (b.P[2].x + b.P[3].x) / 2;
                 right.P[2].y = (b.P[2].y + b.P[3].y) / 2;
                 right.P[3].x = b.P[3].x;
                 right.P[3].y = b.P[3].y;
                 DrawBezierBase(right,0,0,1);
                 /* draw the 2 segments recursively */
                 DrawBezierRecursive (left, level -1);
                 DrawBezierRecursive (right, level -1);
         }
 }

 void DrawBezier()
 {
       DrawBezierBase(Global_Bezier,1,0,0);
       DrawBezierRecursive(Global_Bezier,level);
 }