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FITPO4

       SUBROUTINE  FITPO4 (T, XINT, YINT, ZINT, N, X, Y, Z, XPP, YPP,
      X     ZPP, ARCLEN, NSIGMA, SIGMA)
 C$    (Fit Tensioned P-Spline - 3-D Open - Function Evaluation)
 C$    Given parameters computed previously by routine FITPO3  for
 C$    a set of points forming an open space curve, interpolate  a
 C$    point along the curve.
 C$
 C$    All of the  input arguments,  except T,  must be  unchanged
 C$    since FITPO3  was  called, and  none  are changed  in  this
 C$    routine.  They are:
 C$
 C$    T..............A value of absolute value less than or equal
 C$                   to 1.0 to be mapped to a point on the curve.
 C$                   The sign of  T is ignored  and the  interval
 C$                   0..1 is mapped onto the entire curve.  If  T
 C$                   is  negative,   this  indicates   that   the
 C$                   subroutine has been called previously  (with
 C$                   all other  input  variables  unaltered)  and
 C$                   that this value  of T  exceeds the  previous
 C$                   value  in   absolute   value.    With   such
 C$                   information the  subroutine is  able to  map
 C$                   the point much  more rapidly.   Thus if  the
 C$                   user seeks to map a sequence of points  onto
 C$                   the same  curve,  efficiency  is  gained  by
 C$                   ordering  the  values  of  T  increasing  in
 C$                   magnitude and setting the  signs of all  but
 C$                   the first, negative.
 C$
 C$    N..............Number of  original  data  points.  N .LE. 1
 C$                   will always return the  first data point  as
 C$                   the interpolated value.
 C$
 C$    X(*),
 C$    Y(*),
 C$    Z(*)...........Original data points.
 C$
 C$    NSIGMA.........Number of tension parameters supplied in the
 C$                   array SIGMA(*).   NSIGMA  should be  in  the
 C$                   range 1..N.
 C$
 C$    SIGMA(*).......Tension parameters in  range  0.0..infinity.
 C$                   The sign of each parameter is ignored.
 C$
 C$    ARCLEN.........Arc length of the  curve.
 C$
 C$    XPP(*),
 C$    YPP(*),
 C$    ZPP(*).........Arrays  of  length  N  containing  parameter
 C$                   values required  for  the  interpolation.
 C$
 C$    The output arguments are:
 C$
 C$    XINT,
 C$    YINT,
 C$    ZINT......The interpolated point on the curve.
 C$
 C$    (20-JUL-89)