e02dec calculates values of the bicubic spline
at prescribed points
, for
, from its augmented knot sets
and
and from the coefficients
, for
and
, in its B-spline representation
Here
and
denote normalized cubic B-splines, the former defined on the knots
to
and the latter on the knots
to
.
This function may be used to calculate values of a bicubic spline given in the form produced by
e01dac,
e02dcc and
e02ddc. It is derived from the routine B2VRE in
Anthony et al. (1982).
Cox M G (1978) The numerical evaluation of a spline from its B-spline representation J. Inst. Math. Appl. 21 135–143
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
- NE_END_KNOTS_CONS
-
On entry, the end knots must satisfy , , .
- NE_INT_ARG_LT
-
On entry, .
Constraint: .
On entry, must not be less than 8: .
On entry, must not be less than 8: .
- NE_NOT_INCREASING
-
The sequence is not increasing: , .
The sequence is not increasing: , .
- NE_POINT_OUTSIDE_RECT
-
On entry, point lies outside the rectangle bounded by , , , .
The method used to evaluate the B-splines is numerically stable, in the sense that each computed value of
can be regarded as the value that would have been obtained in exact arithmetic from slightly perturbed B-spline coefficients. See
Cox (1978) for details.
Background information to multithreading can be found in the
Multithreading documentation.