e01ebf performs barycentric interpolation, at a given set of points, using a set of function values on a scattered grid and a triangulation of that grid computed by e01eaf.

2 Specification

Fortran Interface

Subroutine e01ebf (

m, n, x, y, f, triang, px, py, pf, ifail)

Integer, Intent (In)	::	m, n, triang(7*n)
Integer, Intent (Inout)	::	ifail
Real (Kind=nag_wp), Intent (In)	::	x(n), y(n), f(n), px(m), py(m)
Real (Kind=nag_wp), Intent (Out)	::	pf(m)

C Header Interface

#include <nag.h>

void	e01ebf_ (const Integer m, const Integer n, const double x[], const double y[], const double f[], const Integer triang[], const double px[], const double py[], double pf[], Integer *ifail)

The routine may be called by the names e01ebf or nagf_interp_dim2_triang_bary_eval.

3 Description

e01ebf takes as input a set of scattered data points

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

, for

r = 1, 2, \dots, n

, and a Thiessen triangulation of the

(x_{r}, y_{r})

computed by e01eaf, and interpolates at a set of points

({px}_{i}, {py}_{i})

, for

i = 1, 2, \dots, m

If the

i

th interpolation point

({px}_{i}, {py}_{i})

is equal to

(x_{r}, y_{r})

for some value of

r

, the returned value will be equal to

f_{r}

; otherwise a barycentric transformation will be used to calculate the interpolant.

For each point

({px}_{i}, {py}_{i})

, a triangle is sought which contains the point; the vertices of the triangle and

f_{r}

values at the vertices are then used to compute the value

F ({px}_{i}, {py}_{i})

If any interpolation point lies outside the triangulation defined by the input arguments, the returned value is the value provided,

f_{s}

, at the closest node

(x_{s}, y_{s})

e01ebf must only be called after a call to e01eaf.

4 References

Cline A K and Renka R L (1984) A storage-efficient method for construction of a Thiessen triangulation Rocky Mountain J. Math. 14 119–139

Lawson C L (1977) Software for

C^{1}

surface interpolation Mathematical Software III (ed J R Rice) 161–194 Academic Press

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: $m$ – Integer Input: On entry: $m$ , the number of points to interpolate.

Constraint: $m \geq 1$ .
2: $n$ – Integer Input: On entry: $n$ , the number of data points. n must be unchanged from the previous call of e01eaf.

Constraint: $n \geq 3$ .
3: $x (n)$ – Real (Kind=nag_wp) array Input
4: $y (n)$ – Real (Kind=nag_wp) array Input: On entry: the coordinates of the $r$ th data point, $(x_{r}, y_{r})$ , for $r = 1, 2, \dots, n$ . x and y must be unchanged from the previous call of e01eaf.
5: $f (n)$ – Real (Kind=nag_wp) array Input: On entry: the function values $f_{r}$ at $(x_{r}, y_{r})$ , for $r = 1, 2, \dots, n$ .
6: $triang (7 \times n)$ – Integer array Input: On entry: the triangulation computed by the previous call of e01eaf. See Section 9 in e01eaf for details of how the triangulation used is encoded in triang.
7: $px (m)$ – Real (Kind=nag_wp) array Input
8: $py (m)$ – Real (Kind=nag_wp) array Input: On entry: the coordinates $({px}_{i}, {py}_{i})$ , for $i = 1, 2, \dots, m$ , at which interpolated function values are sought.
9: $pf (m)$ – Real (Kind=nag_wp) array Output: On exit: the interpolated values $F ({px}_{i}, {py}_{i})$ , for $i = 1, 2, \dots, m$ .
10: $ifail$ – Integer Input/Output: On entry: ifail must be set to $0$ , $- 1$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.
A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $- 1$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $- 1$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $0$ is recommended. When the value $- 1$ or $1$ is used it is essential to test the value of ifail on exit.

On exit: $ifail = 0$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

If on entry

ifail = 0

- 1

, explanatory error messages are output on the current error message unit (as defined by x04aaf).

Errors or warnings detected by the routine:

$ifail = 1$: On entry, $n = 〈value〉$ .
Constraint: $n \geq 3$ .

$ifail = 2$: On entry, $m = 〈value〉$ .
Constraint: $m \geq 1$ .

$ifail = 3$: On entry, the triangulation information held in the array triang does not specify a valid triangulation of the data points. triang has been corrupted since the call to e01eaf.

$ifail = 4$: At least one evaluation point lies outside the nodal triangulation. For each such point the value returned in pf is that corresponding to a node on the closest boundary line segment.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.
See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$ifail = - 399$: 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.