 
 
 
P A C K A G E      TENSBS
 
(Version 1982 )
 
 
Subprograms for interpolation of two and three  dimensional  gridded
data using tensor products of B-spline basis functions.
 
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
 
 
B2INK..........computes   parameters   that   define   a   piecewise
               polynomial function that interpolates a given set  of
               two-dimensional gridded data.
 
B2VAL..........evaluates the interpolating  function  determined  by
               B2INK or one of its derivatives.
 
B3INK..........computes   parameters   that   define   a   piecewise
               polynomial function that interpolates a given set  of
               three-dimensional gridded data.
 
B3VAL..........evaluates the interpolating  function  determined  by
               B3INK or one of its derivatives.
 
 
Reference
 
Carl de Boor, A Practical Guide  to  Splines,  Springer-Verlag,  New
     York, 1978.
 
 
 
