xyz_renka

1 Brief Information
2 Command Line Usage
3 Variables
4 Description
5 Examples
6 References
7 Related X-Functions

Brief Information

Renka-Cline Gridding Method

Command Line Usage

1. xyz_renka iz:=Col(3);

2. xyz_renka iz:=Col(3) rows:=10 cols:=10;

3. xyz_renka iz:=Col(3) om:=[MBook]MSheet!Mat(1);

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 performs gridding 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 3 in the command window. Or type xyz_renka -d to bring up the dialog.

For more examples, please refer to XF Script Dialog (press F11).

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