BSPPP(3)

SYNOPSIS
SUBROUTINE BSPPP (T, A, N, K, LDC, C, XI, LXI, WORK)

NAME
bsppp - Convert the B-representation of a B-spline to the piecewise polynomial (PP) form.

LIBRARY
SLATEC

CATEGORY
E3, K6

TYPE
SINGLE PRECISION (BSPPP-S, DBSPPP-D)

KEYWORDS
B-SPLINE, PIECEWISE POLYNOMIAL

AUTHOR
Amos, D. E., (SNLA)

DESCRIPTION
Written by Carl de Boor and modified by D. E. Amos Abstract BSPPP is the BSPLPP routine of the reference. BSPPP converts the B-representation (T,A,N,K) to the piecewise polynomial (PP) form (C,XI,LXI,K) for use with PPVAL. Here XI(*), the break point array of length LXI, is the knot array T(*) with multiplicities removed. The columns of the matrix C(I,J) contain the right Taylor derivatives for the polynomial expansion about XI(J) for the intervals XI(J) .LE. X .LE. XI(J+1), I=1,K, J=1,LXI. Function PPVAL makes this evaluation at a specified point X in XI(1) .LE. X .LE. XI(LXI(1) .LE. X .LE. XI+1) Description of Arguments Input T - knot vector of length N+K A - B-spline coefficient vector of length N N - number of B-spline coefficients N = sum of knot multiplicities-K K - order of the B-spline, K .GE. 1 LDC - leading dimension of C, LDC .GE. K Output C - matrix of dimension at least (K,LXI) containing right derivatives at break points XI - XI break point vector of length LXI+1 LXI - number of break points, LXI .LE. N-K+1 WORK - work vector of length K*(N+3) Error Conditions Improper input is a fatal error

REFERENCES
Carl de Boor, Package for calculating with B-splines, SIAM Journal on Numerical Analysis 14, 3 (June 1977), pp. 441-472.

ROUTINES CALLED
BSPDR, BSPEV, XERMSG

REVISION HISTORY (YYMMDD)
800901 DATE WRITTEN
890831 Modified array declarations. (WRB)
890831 REVISION DATE from Version 3.2
891214 Prologue converted to Version 4.0 format. (BAB)
900315 CALLs to XERROR changed to CALLs to XERMSG. (THJ)
900326 Removed duplicate information from DESCRIPTION section. (WRB)
920501 Reformatted the REFERENCES section. (WRB)