P A C K A G E      DTENSBS

 

(Version 1982 )

 

 

Subprograms for interpolation of two and three  dimensional  gridded

data using tensor products of B-spline basis functions.  This  is  a

double precision version of the package TENSBS.

 

By two dimensional gridded data we mean data of the form

 

         (x(i), y(j), f(x(i),y(j)))  i=1,..,nx, j=1,..,ny.

 

The subprograms in this package  determine  a  piecewise  polynomial

function S(x,y) such that

 

        S(x(i),y(j)) = f(x(i),y(j))  i=1,..,nx, j=1,..,ny.

 

The function S takes the form

 

                        nx   ny

            S(x,y)  =  SUM  SUM  a   U (x) V (y)

                       i=1  j=1   ij  i     j

 

where U(i) and V(j) are fixed one-dimensional  piecewise  polynomial

functions (the B-spline basis functions of the reference). The  user

specifies the order (degree+1) of the polynomial pieces that  define

the function S in each direction.  The  resulting  interpolant  will

have continuous derivatives of up to order-2 in each direction.  For

example, if the user specifies order 4 in x and order 3 in  y,  then

the functions U(i) will be piecewise  cubic  polynomials  while  the

functions  V(j)  will  be  piecewise   quadratics.   The   resulting

interpolating function will have continuous first and second partial

derivatives  with  respect  to  x  and  continuous   first   partial

derivative with respect to y. (Lower continuity can be  obtained  by

using the option for user-specified "knots" -- see the reference.)

 

The subroutines in this package are

 

 

 DB2INK........computes   parameters   that   define   a   piecewise

               polynomial function that interpolates a given set  of

               two-dimensional gridded data.

 

 DB2VAL........evaluates the interpolating  function  determined  by

               DB2INK or one of its derivatives.

 

 DB3INK........computes   parameters   that   define   a   piecewise

               polynomial function that interpolates a given set  of

               three-dimensional gridded data.

 

 DB3VAL........evaluates the interpolating  function  determined  by

               DB3INK or one of its derivatives.

 

 

Reference

Carl de Boor, A Practical Guide  to  Splines,  Springer-Verlag,  New

     York, 1978.