Evaluate partial derivatives of NURBS surface

openNURBS
1

Hello,

Given my NURBS surface and a 2D parameter (s,t), I want to evaluate its surface coordinate P and its derivatives Ds, Dt, Dss, Dst, Dtt at (s,t).

From the SDK I guess I’d need to use this method

ON_BOOL32
ON_NurbsSurface::Evaluate( // returns false if unable to evaluate
   double s, double t,       // evaluation parameter
   int der_count,  // number of derivatives (>=0)
   int v_stride,   // v[] array stride (>=Dimension())
   double* v,      // v[] array of length stride*(ndir+1)
   int side,       // optional - determines which side to evaluate from
                   //         0 = default
                   //         1 = from NE quadrant
                   //         2 = from NW quadrant
                   //         3 = from SW quadrant
                   //         4 = from SE quadrant
   int hint[2]       // optional - evaluation hint (int) used to speed
                   //            repeated evaluations
   ) const

I assume I should set der_count as 2 and the output will be v.
However, I don’t understand what v_stride is, and how the data is stored inside v. Is there any example showing this?

Many thanks,
Pablo

2

You’re probably better off using the ON_Surface::Ev1Der or ON_Surface::Ev2Der.
Their function signatures are easier to understand.

  ON_BOOL32 Ev1Der( // returns false if unable to evaluate
         double u, double v,   // evaluation parameters (s,t)
         ON_3dPoint& point,    // returns value of surface
         ON_3dVector& du,      // first partial derivatives (Ds)
         ON_3dVector& dv,      // (Dt)
         int quadrant = 0,     // optional - determines which side to evaluate from
                               //         0 = default
                               //         1 from NE quadrant
                               //         2 from NW quadrant
                               //         3 from SW quadrant
                               //         4 from SE quadrant
         int* hint = 0         // optional - evaluation hint (int[2]) used to speed
                               //            repeated evaluations
         ) const;

  ON_BOOL32 Ev2Der( // returns false if unable to evaluate
         double u, double v,   // evaluation parameters (s,t)
         ON_3dPoint& point,    // returns value of surface
         ON_3dVector& du,      // first partial derivatives (Ds)
         ON_3dVector& dv,      // (Dt)
         ON_3dVector& duu,     // second partial derivatives (Dss)
         ON_3dVector& duv,     // (Dst)
         ON_3dVector& dvv,     // (Dtt)
         int quadrant= 0,      // optional - determines which side to evaluate from
                               //         0 = default
                               //         1 from NE quadrant
                               //         2 from NW quadrant
                               //         3 from SW quadrant
                               //         4 from SE quadrant
         int* hint = 0         // optional - evaluation hint (int[2]) used to speed
                               //            repeated evaluations
         ) const;
3

Thanks for the info! I wonder if there’s also an EvDer for third order? For derivatives Ds^2t and Dst^2.

Pablo

4

In that case you’ll probably need to figure out the Evaluate function. I’m sure it can do higher order derivatives (but keep in mind your curves, surfaces must be of higher degree as well).