naginterfaces.library.interp.dim2_​triang_​bary_​eval

naginterfaces.library.interp.dim2_triang_bary_eval(x, y, f, triang, px, py)

dim2_triang_bary_eval 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 dim2_triangulate().

For full information please refer to the NAG Library document for e01eb

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/e01/e01ebf.html

Parameters

xfloat, array-like, shape $\left(n\right)$

The coordinates of the $\text{r}$th data point, $(x_r,y_r)$, for $\text{r}=1,2,\dots ,n$. $x$ and $y$ must be unchanged from the previous call of dim2_triangulate().

yfloat, array-like, shape $\left(n\right)$

The coordinates of the $\text{r}$th data point, $(x_r,y_r)$, for $\text{r}=1,2,\dots ,n$. $y$ and $y$ must be unchanged from the previous call of dim2_triangulate().

ffloat, array-like, shape $\left(n\right)$

The function values $f_{\text{r}}$ at $(x_{\text{r}},y_{\text{r}})$, for $\text{r}=1,2,\dots ,n$.

triangint, array-like, shape $(7\times n)$

The triangulation computed by the previous call of dim2_triangulate(). See Further Comments for details of how the triangulation used is encoded in $triang$.

pxfloat, array-like, shape $\left(m\right)$

The coordinates $({\text{px}}_{\text{i}},{\text{py}}_{\text{i}})$, for $\text{i}=1,2,\dots ,m$, at which interpolated function values are sought.

pyfloat, array-like, shape $\left(m\right)$

The coordinates $({\text{px}}_{\text{i}},{\text{py}}_{\text{i}})$, for $\text{i}=1,2,\dots ,m$, at which interpolated function values are sought.

Returns

pffloat, ndarray, shape $\left(m\right)$

The interpolated values $F({\text{px}}_{\text{i}},{\text{py}}_{\text{i}})$, for $\text{i}=1,2,\dots ,m$.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 3$.

(errno $2$)

On entry, $m=⟨value⟩$.

Constraint: $m\ge 1$.

(errno $3$)

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 dim2_triangulate().

Warns

NagAlgorithmicWarning

(errno $4$)

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.

Notes

dim2_triang_bary_eval takes as input a set of scattered data points $(x_{\text{r}},y_{\text{r}},f_{\text{r}})$, for $\text{r}=1,2,\dots ,n$, and a Thiessen triangulation of the $(x_r,y_r)$ computed by dim2_triangulate(), and interpolates at a set of points $({\text{px}}_i,{\text{py}}_i)$, for $\text{i}=1,2,\dots ,m$.

If the $i$th interpolation point $({\text{px}}_i,{\text{py}}_i)$ 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 $({\text{px}}_i,{\text{py}}_i)$, 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 $F({\text{px}}_i,{\text{py}}_i)$.

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 $(x_s,y_s)$.

dim2_triang_bary_eval must only be called after a call to dim2_triangulate().

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