naginterfaces.library.interp.dim2_​triangulate

naginterfaces.library.interp.dim2_triangulate(x, y)

dim2_triangulate generates a triangulation for a given set of two-dimensional points using the method of Renka and Cline.

For full information please refer to the NAG Library document for e01ea

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/e01/e01eaf.html

Parameters

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

The $x$ coordinates of the $n$ data points.

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

The $y$ coordinates of the $n$ data points.

Returns

triangint, ndarray, shape $(7\times n)$

A data structure defining the computed triangulation, in a form suitable for passing to dim2_triang_bary_eval(). Details of how the triangulation is encoded in $triang$ are given in Further Comments. These details are most likely to be of use when plotting the computed triangulation.

Raises

NagValueError

(errno $1$)

On entry, $n=⟨value⟩$.

Constraint: $n\ge 3$.

(errno $2$)

On entry, all the $(x,y)$ pairs are collinear.

Notes

dim2_triangulate creates a Thiessen triangulation with a given set of two-dimensional data points as nodes. This triangulation will be as equiangular as possible (Cline and Renka (1984)). See Renka and Cline (1984) for more detailed information on the algorithm, a development of that by Lawson (1977). The code is derived from Renka (1984).

The computed triangulation is returned in a form suitable for passing to dim2_triang_bary_eval() which, for a set of nodal function values, computes interpolated values at a set of points.

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