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SUBROUTINE FITK2 (T, XS, YS, N, X, Y, XP, YP, S, SIGMA)
C$ (Planar Tensioned Spline Interpolation)
C$ This subroutine performs the mapping of points in the
C$ interval (0.0..1.0) onto a curve in the plane. The
C$ subroutine FITK1 should be called earlier to determine
C$ certain necessary parameters. The resulting curve has a
C$ parametric representation both of whose components are
C$ splines under tension and functions of the polygonal
C$ arclength parameter.
C$
C$ On input--
C$
C$ T........contains a REAL value of absolute value less than
C$ or equal to 1.0 to be mapped to a point on the
C$ curve. The sign of T is ignored and the interval
C$ (0.0..1.0) is mapped onto the entire curve. If T
C$ is negative, this indicates that this subroutine
C$ has been called previously (with all other input
C$ variables unaltered) and that this value of T
C$ exceeds the previous value in absolute value.
C$ With such information the subroutine is able to
C$ map the point much more rapidly. Thus if the user
C$ seeks to map a sequence of points onto the same
C$ curve, efficiency is gained by ordering the values
C$ increasing in magnitude and setting the signs of
C$ all but the first, negative.
C$ N........contains the number of points which were
C$ interpolated to determine the curve.
C$ X and Y......are arrays containing the X- and Y-coordinates
C$ of the interpolated points.
C$ XP and YP....are the arrays output from FITK1 containing
C$ curvature information,
C$ S........contains the polygonal arclength of the curve.
C$ SIGMA....contains the tension factor (its sign is ignored).
C$
C$ The parameters N, X, Y, XP, YP, S, and SIGMA should be
C$ input unaltered from the output of FITK1.
C$
C$ On output--
C$
C$ XS and YS.....contain the X- and Y-coordinates of the image
C$ point on the curve.
C$ T,N,X,Y,XP,YP,S and SIGMA....are unaltered.
C$
C$ Author: A.K. Cline, "Scalar and Planar Valued Curve
C$ Fitting Using Splines Under Tension", Comm. A.C.M.
C$ 17, 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$ (09-FEB-82)