I've been where you are chasing down formulas for my Polygon/Prism c++ 
program. I don't know where I got my first parametric equations from 
(they where not perfect) I had to play with them until I got something 
close to what POV prisms does. Of course prisms uses 4 types of splines 
linear, quadratic, cubic and bezier. I have the formulas for the last 3.

void PCanvasPane :: ConDraw(point P,point P1, point P2, point P3)
     { double a_x,b_x,c_x,d_x,a_y,b_y,c_y,d_y,t;
       int Xp,Yp,Ox,Oy;
      if (Spl == 3)
         { a_x = P.x-3*P1.x+3*P2.x  -P3.x; a_y = P.y-3*P1.y+3*P2.y 
-P3.y;
           b_x =     3*P1.x-6*P2.x+3*P3.x; b_y =     3*P1.y-6*P2.y+3*P3.y;
           c_x =            3*P2.x-3*P3.x; c_y = 
3*P2.y-3*P3.y;
           d_x =                     P3.x; d_y =                     P3.y;
         }

      if (Spl == 2)
         {a_x=-.5*P.x+1.5*P1.x-1.5*P2.x+.5*P3.x; 
a_y=-.5*P.y+1.5*P1.y-1.5*P2.y+.5*P3.y;
          b_x=    P.x-2.5*P1.x+2.0*P2.x-.5*P3.x;  b_y= 
P.y-2.5*P1.y+2.0*P2.y-.5*P3.y;
          c_x=-.5*P.x         +.5 *P2.x;          c_y=-.5*P.y 
+.5 *P2.y;
          d_x=            P1.x;                   d_y=            P1.y; 


         }

      if (Spl == 1)
         {a_x=0;                    a_y=0;
          b_x= .5*P.x-P1.x+.5*P2.x; b_y= .5*P.y-P1.y+.5*P2.y;
          c_x=-.5*P.x     +.5*P2.x; c_y=-.5*P.y     +.5*P2.y;
          d_x=        P1.x;         d_y=        P1.y;
          }

     t = 0;
    do{
       /*if(Spl == 3 || Spl==2){
                 Xp = ax*pow(t,3) + bx*pow(t,2) + dx * t + P.x;// X function
                 Yp = ay*pow(t,3) + by*pow(t,2) + dy * t + P.y;// Y function
                   }
        Xp = a_x*pow(t,3) + b_x*pow(t,2) + c_x * t + d_x;// X funtion
        Yp = a_y*pow(t,3) + b_y*pow(t,2) + c_y * t + d_y;// Y funtion
       if (t>0) DrawLine (Xp*Dx+cx,Yp*Dy+cy,Ox,Oy);
       Ox=Xp*Dx+cx;
       Oy=Yp*Dy+cy;
       t+=.005;}
      while (t <= 1);

}

Here is what used. Hope it helps.
Spl means spline; 3 is bezier 2 is cubic 1 is cubic

You'll need to play with until you get what you want!
Have Fun!

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