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SUBROUTINE FITPC4 (T, XINT, YINT, ZINT, N, X, Y, Z, XPP, YPP,
X ZPP, ARCLEN, NSIGMA, SIGMA)
C$ (Fit Tensioned P-Spline - 3-D Closed - Function Evaluation)
C$ Given parameters computed previously by routine FITPC3 for
C$ a set of points forming a closed space curve, interpolate a
C$ point along the curve. The curve is closed in the sense
C$ that (X(N),Y(N),Z(N)) is connected to (X(1),Y(1),Z(1)).
C$
C$ All of the input arguments, except T, must be unchanged
C$ since FITPC3 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 closed curve.
C$ If T 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$ (02-FEB-83)