Accession Number : AD0762419

Title :   FORTRAN Subroutines for Bicubic Spline Interpolation

Descriptive Note : Final memorandum rept.

Corporate Author : NAVAL RESEARCH LAB WASHINGTON DC

Personal Author(s) : Cornyn, John J

PDF Url : AD0762419

Report Date : Jun 1973

Pagination or Media Count : 48

Abstract : Two CDC 3800 FORTRAN subroutines (BICUB1 and BICUB2) which perform bicubic spline interpolation of a tabulated function of two variables are described. Given the values X(1),...,X(N) and Y(1),...,Y(M) of two independent variables and the corresponding function values U(I,J)=f(X(I), Y(J)), I=1,...,N and J=1,...,M and certain normal derivatives (optional) along the boundaries of the x-y mesh, BICUB1 estimates the derivatives f(x), f(y), and f(xy) at each (I, J) mesh point. If the normal derivatives along the mesh boundaries are unknown, BICUB1 estimates them using a moving third order two dimensional Lagrange interpolating polynomial. Given the coordinates (XPT, YPT) and the derivatives calculated by BICUB1, BICUB2 obtains the coefficients of the bicubic polynomial for the rectangular region of the mesh containing (XPT, YPT) and estimates the functional value UPT=f(XPT,YPT). In effect, the routines pass a twice continuously differentiable piecewise bicubic polynomial, u(x,y) belongs to (C sup 2), through the given functional values.

Descriptors :   *COMPUTER PROGRAMS, *INTERPOLATION, APPROXIMATION(MATHEMATICS), SUBROUTINES

Subject Categories : Numerical Mathematics
      Computer Programming and Software

Distribution Statement : APPROVED FOR PUBLIC RELEASE