The routine may be called by the names e01sbf or nagf_interp_dim2_scat_eval.
e01sbf takes as input the arguments defining the interpolant of a set of scattered data points , for ,
as computed by
and evaluates the interpolant at the point .
If is equal to for some value of , the returned value will be equal to .
If is not equal to
for any , the derivatives in grads will be used to compute the interpolant. A triangle is sought which contains the point , and the vertices of the triangle along with the partial derivatives and values at the vertices are used to compute the value
. If the point lies outside the triangulation defined by the input arguments, the returned value is obtained by extrapolation. In this case, the interpolating function is extended linearly beyond the triangulation boundary. The method is described in more detail in Renka and Cline (1984) and the code is derived from Renka (1984).
e01sbf must only be called after a call to
Renka R L (1984) Algorithm 624: triangulation and interpolation of arbitrarily distributed points in the plane ACM Trans. Math. Software10 440–442
Renka R L and Cline A K (1984) A triangle-based interpolation method Rocky Mountain J. Math.14 223–237
On entry: the point at which the interpolant is to be evaluated.
9: – Real (Kind=nag_wp)Output
On exit: the value of the interpolant evaluated at the point .
10: – IntegerInput/Output
On entry: ifail must be set to , or to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of means that an error message is printed while a value of means that it is not.
If halting is not appropriate, the value or is recommended. If message printing is undesirable, then the value is recommended. Otherwise, the value is recommended. When the value or is used it is essential to test the value of ifail on exit.
On exit: unless the routine detects an error or a warning has been flagged (see Section 6).
6Error Indicators and Warnings
If on entry or , explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, .
On entry, triang does not contain a valid data point triangulation; triang may have been corrupted since the call to
Warning – the evaluation point lies outside the triangulation boundary. The returned value was computed by extrapolation.
An unexpected error has been triggered by this routine. Please
See Section 7 in the Introduction to the NAG Library FL Interface for further information.
Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library FL Interface for further information.
Dynamic memory allocation failed.
See Section 9 in the Introduction to the NAG Library FL Interface for further information.
Computational errors should be negligible in most practical situations.
8Parallelism and Performance
e01sbf is not thread safe and should not be called from a multithreaded user program. Please see Section 1 in FL Interface Multithreading for more information on thread safety.
e01sbf is not threaded in any implementation.
The time taken for a call of e01sbf is approximately proportional to the number of data points, .
The results returned by this routine are particularly suitable for applications such as graph plotting, producing a smooth surface from a number of scattered points.