NAG Library Function Document

nag_2d_triang_eval (e01skc)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

1 Purpose

nag_2d_triang_eval (e01skc) evaluates at a given point the two-dimensional interpolant function computed by nag_2d_triang_interp (e01sjc).

2 Specification

#include <nag.h>

#include <nage01.h>

void	nag_2d_triang_eval (Integer m, const double x[], const double y[], const double f[], const Integer triang[], const double grads[], double px, double py, double pf, NagError fail)

3 Description

nag_2d_triang_eval (e01skc) takes as input the arguments defining the interpolant

F (x, y)

of a set of scattered data points

(x_{r}, y_{r}, f_{r})

, for

r = 1, 2, \dots, m

, as computed by nag_2d_shep_interp (e01sgc), and evaluates the interpolant at the point

(p x, p y)

(p x, p y)

is equal to

(x_{r}, y_{r})

for some value of

r

, the returned value will be equal to

f_{r}

(p x, p y)

is not equal to

(x_{r}, y_{r})

for any

r

, the derivatives in grads will be used to compute the interpolant. A triangle is sought which contains the point

(p x, p y)

, and the vertices of the triangle along with the partial derivatives and

f_{r}

values at the vertices are used to compute the value

F (p x, p y)

. If the point

(p x, p y)

lies outside the triangulation defined by the input arguments, the returned value is obtained by extrapolation. In this case, the interpolating function

f

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).

nag_2d_triang_eval (e01skc) must only be called after a call to nag_2d_shep_interp (e01sgc).

4 References

Renka R L (1984) Algorithm 624: triangulation and interpolation of arbitrarily distributed points in the plane ACM Trans. Math. Software 10 440–442

Renka R L and Cline A K (1984) A triangle-based

C^{1}

interpolation method Rocky Mountain J. Math. 14 223–237

5 Arguments

1: $m$ – IntegerInput
2: $x [m]$ – const doubleInput
3: $y [m]$ – const doubleInput
4: $f [m]$ – const doubleInput
5: $triang [7 \times m]$ – const IntegerInput
6: $grads [2 \times m]$ – const doubleInput: On entry: m, x, y, f, triang and grads must be unchanged from the previous call of nag_2d_triang_interp (e01sjc).
7: $px$ – doubleInput
8: $py$ – doubleInput: On entry: the point $(p x, p y)$ at which the interpolant is to be evaluated.
9: $pf$ – double *Output: On exit: the value of the interpolant evaluated at the point $(p x, p y)$ .
10: $fail$ – NagError *Input/Output: The NAG error argument (see Section 3.6 in the Essential Introduction).

6 Error Indicators and Warnings

NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.2.1.2 in the Essential Introduction for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INT: On entry, $m = 〈value〉$ .
Constraint: $m \geq 3$ .
NE_INTERNAL_ERROR: 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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.
NE_TRIANG_INVALID: On entry, triang does not contain a valid data point triangulation; triang may have been corrupted since the call to nag_2d_triang_interp (e01sjc).
NW_VALUE_EXTRAPOLATED: Warning – the evaluation point $(〈value〉, 〈value〉)$ lies outside the triangulation boundary. The returned value was computed by extrapolation.

7 Accuracy

Computational errors should be negligible in most practical situations.

8 Parallelism and Performance

Not applicable.

9 Further Comments

The time taken for a call of nag_2d_triang_eval (e01skc) is approximately proportional to the number of data points,

m

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.