point evaluation of NURBS curve given an axial coordinate -

my question how second coordinate (in 2d) of point lies on curve defined nurbs curve given axial coordinate. have knot vector, control points, weights , basis functions.

i looked through similar questions (how find out y coordinate of specific point in bezier curve in canvas?) did not find answer far. thanks, m

this not easy task if need implement scratch. nevertheless, codes this:

 each non-null knot interval in knot vector of nurbs {     extract bezier curve b(t) nurbs knot interval [a, b];     compute minimum , maximum x values of bezier curve's control points.      if ( x0 within [xmin, xmax] )     {         t0 = a;         t1 = b;         epsilon = 1.0e-06; // small value;
  
       while ( (t1-t0) > epsilon )        {           subdivide b(t) @ t=0.5 generate 2 bezier curves: b1(t) , b2(t);           compute [xmin1, xmax1] b1(t) , [xmin2, xmax2] b2(t);           if ( x0 within [xmin1, xmax1] )           {               b(t) = b1(t);               t0 = a;               t1 = (a+b)/2;           }             else           {               b(t) = b2(t);               t0 = (a+b)/2;               t1 = b;           }         } // end while loop         return ((t0+t1)/2);  // parameter value looking    } // end if() 
  
} // end loop
  

the (t0+t1)/2 parameter value looking for. please note might find multiple solutions given same x0 value.