NAG CL Interface
e01ebc (dim2_triang_bary_eval)
1
Purpose
e01ebc 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
e01eac.
2
Specification
void |
e01ebc (Integer m,
Integer n,
const double x[],
const double y[],
const double f[],
const Integer triang[],
const double px[],
const double py[],
double pf[],
NagError *fail) |
|
The function may be called by the names: e01ebc, nag_interp_dim2_triang_bary_eval or nag_2d_triang_bary_eval.
3
Description
e01ebc takes as input a set of scattered data points
, for
, and a Thiessen triangulation of the
computed by
e01eac, and interpolates at a set of points
, for
.
If the th interpolation point is equal to for some value of , the returned value will be equal to ; otherwise a barycentric transformation will be used to calculate the interpolant.
For each point , a triangle is sought which contains the point; the vertices of the triangle and values at the vertices are then used to compute the value .
If any interpolation point lies outside the triangulation defined by the input arguments, the returned value is the value provided, , at the closest node .
e01ebc must only be called after a call to
e01eac.
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 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 interpolation method Rocky Mountain J. Math. 14 223–237
5
Arguments
-
1:
– Integer
Input
-
On entry: , the number of points to interpolate.
Constraint:
.
-
2:
– Integer
Input
-
On entry:
, the number of data points.
n must be unchanged from the previous call of
e01eac.
Constraint:
.
-
3:
– const double
Input
-
4:
– const double
Input
-
On entry: the coordinates of the
th data point,
, for
.
x and
y must be unchanged from the previous call of
e01eac.
-
5:
– const double
Input
-
On entry: the function values
at , for .
-
6:
– const Integer
Input
-
On entry: the triangulation computed by the previous call of
e01eac. See
Section 9 in
e01eac for details of how the triangulation used is encoded in
triang.
-
7:
– const double
Input
-
8:
– const double
Input
-
On entry: the coordinates , for , at which interpolated function values are sought.
-
9:
– double
Output
-
On exit: the interpolated values , for .
-
10:
– NagError *
Input/Output
-
The NAG error argument (see
Section 7 in the Introduction to the NAG Library CL Interface).
6
Error Indicators and Warnings
- NE_ALLOC_FAIL
-
Dynamic memory allocation failed.
See
Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
- NE_BAD_PARAM
-
On entry, argument had an illegal value.
- NE_INT
-
On entry, .
Constraint: .
On entry, .
Constraint: .
- 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.
See
Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
- NE_NO_LICENCE
-
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.
- NE_TRIANG_INVALID
-
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
e01eac.
-
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.
7
Accuracy
Not applicable.
8
Parallelism and Performance
e01ebc is not threaded in any implementation.
The time taken for a call of e01ebc is approximately proportional to the number of interpolation points, .
10
Example
See
Section 10 in
e01eac.