2.2.1.7 xyz_renka_nag
Brief Information
Convert XYZ data to matrix using NAG Renka-Cline gridding
Command Line Usage
1. xyz_renka_nag iz:=Col(3);
2. xyz_renka_nag iz:=Col(3) rows:=10 cols:=10;
3. xyz_renka_nag iz:=Col(3) om:=[MBook]MSheet!Mat(1);
X-Function Execution Options
Please refer to the page for additional option switches when accessing the x-function from script
Variables
Display
Name
|
Variable
Name
|
I/O
and
Type
|
Default
Value
|
Description
|
| Input
|
iz
|
Input
XYZRange
|
<active>
|
Specifies the input XYZ range.
|
| Rows
|
rows
|
Input
int
|
20
|
Rows in the output matrix.
|
| Columns
|
cols
|
Input
int
|
20
|
Columns in the output matrix.
|
| Output Matrix
|
om
|
Output
MatrixObject
|
<new>
|
The output matrix.
See the syntax here.
|
Description
This function calls NAG library to perform gridding by Renka-Cline method. The method is based on the algorithm that Renka and Cline developed in 1984. It includes three main steps:
1. Triangulation:
- Connect all the data points to do a Thiessen triangulation in the X-Y plane, which means that the triangles in the plane are as nearly equiangular as possible.
2. Gradient Estimation:
- Estimate a gradient in the x- and y-directions for each node as the partial derivatives of a quadratic function.
3. Interpolation:
- For an arbitrary point P, compute the interpolated value using the data values and gradient estimates at each of the three vertices of the triangle which contains P.
For the 200~1000 data points and uniformly distributed case, Renka-Cline method could be a best choice.
Examples
1. Import XYZ Random Gaussian.dat on the \Samples\Matrix Conversion and Gridding folder.
2. Type xyz_renka_nag 3 in the command window. Or type xyz_renka_nag -d to bring up the dialog.
Algorithm
Please refer to the NAG help document (e01sac, e01sbc, e01szc) for more information.
References
[1]. Robert J. Renka, Interpolation of Data on the Surface of a Sphere, 1984, ACM Transactions on Mathematical Software.
[2]. Robert J. Renka, A Triangle-based C1 Interpolation Method, Rocky Mountain J. Math. Vol. 14, 1984, pp. 223-237.
Related X-Functions
xyz_regular, xyz_renka, xyz_shep, xyz_shep_nag, xyz_sparse, xyz_tps
Keywords:worksheet
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