NAG FL Interface
e01ebf (dim2_​triang_​bary_​eval)

Settings help

FL Name Style:

FL Specification Language:

1 Purpose

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 (xr,yr,fr) , for r=1,2,,n, and a Thiessen triangulation of the (xr,yr) computed by e01eaf, and interpolates at a set of points (pxi,pyi) , for i=1,2,,m.
If the ith interpolation point (pxi,pyi) is equal to (xr,yr) for some value of r, the returned value will be equal to fr; otherwise a barycentric transformation will be used to calculate the interpolant.
For each point (pxi,pyi) , a triangle is sought which contains the point; the vertices of the triangle and fr values at the vertices are then used to compute the value F (pxi,pyi) .
If any interpolation point lies outside the triangulation defined by the input arguments, the returned value is the value provided, fs, at the closest node (xs,ys) .
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 C1 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 C1 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: m1.
2: n Integer Input
On entry: n, the number of data points. n must be unchanged from the previous call of e01eaf.
Constraint: n3.
3: x(n) Real (Kind=nag_wp) array Input
4: y(n) Real (Kind=nag_wp) array Input
On entry: the coordinates of the rth data point, (xr,yr), for r=1,2,,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 fr at (xr,yr), for r=1,2,,n.
6: triang(7×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 (pxi,pyi), for i=1,2,,m, at which interpolated function values are sought.
9: pf(m) Real (Kind=nag_wp) array Output
On exit: the interpolated values F(pxi,pyi), for i=1,2,,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 or −1, explanatory error messages are output on the current error message unit (as defined by x04aaf).
Errors or warnings detected by the routine:
On entry, n=value.
Constraint: n3.
On entry, m=value.
Constraint: m1.
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.
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.
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.
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.

7 Accuracy

Not applicable.

8 Parallelism and Performance

Background information to multithreading can be found in the Multithreading documentation.
e01ebf is not threaded in any implementation.

9 Further Comments

The time taken for a call of e01ebf is approximately proportional to the number of interpolation points, m.

10 Example

See e01eaf.