e01thc evaluates the three-dimensional interpolating function generated by
e01tgc and its first partial derivatives.
e01thc takes as input the interpolant
of a set of scattered data points
, for
, as computed by
e01tgc,
and evaluates the interpolant and its first partial derivatives at the set of points
, for
.
e01thc must only be called after a call to
e01tgc.
This function is derived from the function QS3GRD described by
Renka (1988).
Renka R J (1988) Algorithm 661: QSHEP3D: Quadratic Shepard method for trivariate interpolation of scattered data ACM Trans. Math. Software 14 151–152
Computational errors should be negligible in most practical situations.
Please consult the
X06 Chapter Introduction for information on how to control and interrogate the OpenMP environment used within this function. Please also consult the
Users' Note for your implementation for any additional implementation-specific information.
The time taken for a call to
e01thc will depend in general on the distribution of the data points. If
x,
y and
z are approximately uniformly distributed, then the time taken should be only
. At worst
time will be required.