PDA_BISPEV - Evaluates the bivariate spline approximation found by PDA_SURFIT.

Origin

DIERCKX / NETLIB

Description:
   Subroutine pda_bispev evaluates on a grid (x(i),y(j)),i=1,...,mx; 
   j=1,...,my a bivariate spline s(x,y) of degrees kx and ky, given in 
   the b-spline representation.

Calling Sequence:
   call pda_bispev( tx, nx, ty, ny, c, kx, ky, x, mx, y, my, z, wrk, lwrk, 
                    iwrk, kwrk, ier ) 

Input Parameters:
   tx    : Real array, length nx, which contains the position of the
           knots in the x-direction.

   nx    : Integer, giving the total number of knots in the x-direction

   ty    : Real array, length ny, which contains the position of the
           knots in the y-direction.

   ny    : Integer, giving the total number of knots in the y-direction

   c     : Real array, length (nx-kx-1)*(ny-ky-1), which contains the
           b-spline coefficients.

   kx,ky : Integer values, giving the degrees of the spline.

   x     : Real array of dimension (mx). Before entry x(i) must be set to 
           the x co-ordinate of the i-th grid point along the x-axis. 
           tx(kx+1)<=x(i-1)<=x(i)<=tx(nx-kx), i=2,...,mx.

   mx    : Integer. On entry mx must specify the number of grid points along
           the x-axis. Mx >=1.

   y     : Real array of dimension (my). Before entry y(j) must be set to 
           the y co-ordinate of the j-th grid point along the y-axis.
           ty(ky+1)<=y(j-1)<=y(j)<=ty(ny-ky), j=2,...,my.

   my    : Integer. On entry my must specify the number of grid points along
           the y-axis. My >=1.

   wrk   : Real array of dimension lwrk. Used as workspace.

   lwrk  : Integer, specifying the dimension of wrk. 
           lwrk >= mx*(kx+1)+my*(ky+1)

   iwrk  : Integer array of dimension kwrk. Used as workspace.

   kwrk  : Integer, specifying the dimension of iwrk. Kwrk >= mx+my.

Output Parameters:
   z     : Real array of dimension (mx*my). On successful exit z(my*(i-1)+j) 
           contains the value of s(x,y) at the point 
           (x(i),y(j)),i=1,...,mx;j=1,...,my.

   ier   : Integer error flag:

           0 : Normal return.
          10 : Invalid input data (see restrictions).

Restrictions:
   mx >=1, my >=1, lwrk>=mx*(kx+1)+my*(ky+1), kwrk>=mx+my
   tx(kx+1) <= x(i-1) <= x(i) <= tx(nx-kx), i=2,...,mx
   ty(ky+1) <= y(j-1) <= y(j) <= ty(ny-ky), j=2,...,my

Other Subroutines Required:
   pda_fpbisp, pda_fpbspl

References :
   de Boor C : "On calculating with b-splines", j. Approximation theory
                6 (1972) 50-62.
   Cox M.G.  : "The numerical evaluation of b-splines", j. inst. maths
                applics 10 (1972) 134-149.
   Dierckx P.: "Curve and surface fitting with splines", monographs on
                 numerical analysis, Oxford University Press, 1993.

Author :
   P. Dierckx
   Dept. Computer Science, k.u.leuven
   celestijnenlaan 200a, b-3001 heverlee, Belgium.
   e-mail : Paul.Dierckx@cs.kuleuven.ac.be

Latest Update : march 1987