The function may be called by the names: e01skc, nag_interp_dim2_triang_eval or nag_2d_triang_eval.
e01skc 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).
e01skc 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: – double *Output
On exit: the value of the interpolant evaluated at the point .
10: – NagError *Input/Output
The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).
6Error Indicators and Warnings
Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
On entry, argument had an illegal value.
On entry, .
An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL 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 CL Interface for further information.
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.
Computational errors should be negligible in most practical situations.
8Parallelism and Performance
e01skc is not threaded in any implementation.
The time taken for a call of e01skc is approximately proportional to the number of data points, .
The results returned by this function are particularly suitable for applications such as graph plotting, producing a smooth surface from a number of scattered points.