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SUBROUTINE FITP1 (N, X, Y, XP, YP, TEMP, S, SIGMA)
C$ (Closed Curve Tensioned Spline Fit)
C$ This subroutine determines the parameters necessary to
C$ compute a spline under tension forming a closed curve in
C$ the plane and passing through a sequence of pairs
C$ (X(1),Y(1)),...,(X(N),Y(N)). For actual computation of
C$ points on the curve it is necessary to call SUBROUTINE
C$ FITP2.
C$
C$ On input--
C$
C$ N........is the number of points to be interpolated
C$ (N.GE.2),
C$ X(*).....is an array containing the N X-coordinates of the
C$ points,
C$ Y(*).....is an array containing the N Y-coordinates of the
C$ points,
C$ XP(*)....is an array of length at least N,
C$ YP(*)....is an array of length at least N,
C$ TEMP(*)..is an array of length at least 2*N, which is used
C$ for scratch storage,
C$ SIGMA....contains the tension factor. This is a non-zero
C$ quantity (whose sign is ignored) which indicates
C$ the curviness desired. If ABS(SIGMA) is very
C$ large (e.g. 50.0) the resulting curve is very much
C$ like a polygon. A standard value for SIGMA is
C$ approximately 1.0 in absolute value.
C$
C$ On output--
C$
C$ N,X,Y, and SIGMA.....are unaltered,
C$ XP and YP.....contain information about the curvature of
C$ the curve at the given nodes,
C$ S........contains the polygonal arclength of the curve.
C$
C$ Author: A.K. Cline, "Scalar and Planar Valued Curve Fitting
C$ Using Splines Under Tension", Comm. A.C.M. 17,
C$ 218-225 (1974). (Algorithm 476).
C$
C$ Modifications by Nelson H.F. Beebe, Department of Chemistry
C$ Aarhus University, Aarhus, Denmark, to provide a more
C$ transportable program, and to compute SINH(X) more
C$ accurately than 0.5*(EXP(X)-EXP(-X)) for small arguments.
C$ (03-APR-82)