# 14.2 XYZ Gridding Methods

Worksheet data can be converted into a matrix. There are two main kinds of worksheet to matrix conversion methods in Origin: Direct Conversion and XYZ Gridding. Direct conversion copies the worksheet into a matrix (data arranged in the matrix looks just like the original worksheet). Gridding methods convert XYZ data into a matrix using a selected algorithm.

An Origin matrix is a rectangular array of Z values whose columns are linearly mapped to X values and whose rows are linearly mapped to Y values. If the original worksheet XYZ data is regular, we can convert the data into a matrix directly since every XY location has a representative Z value. If the data is randomly distributed, 2D gridding methods should be used to take a series of random (x, y, z) points to estimate the values of z on a rectangular grid for each (x, y) pair.

For Direct conversion, X and Y mapping values can be included in the conversion, but must be linear within an adjustable tolerance.

For random data gridding methods, we can describe the problem mathematically that, given a set of irregular distributed points (xi,yi,zi), construct a function F(x,y) which interpolates the data by F(xi,yi) = zi. In the X-Y plane, the data points must be distinct. The constructed surface is continuous and has continuous first derivatives.

When interpolating, the data points near the grid point to be estimated will contribute more (with higher weight). Regarding the range to cover in estimation, there are global and local strategies, in which global algorithms will calculate all the data points to estimate each grid while local strategies only use the information within a certain range. There may be some difference in the gridding results of each, and the global algorithm is more computationally intense.

Note: Collinear data in a set is not allowed because it does not define a surface, so collinear points need to be removed. Also, multiple z values at a specific (x, y) point may have multiple options for determining a composite z value.

Origin provides the XYZ2Mat X-Function for XYZ Gridding. Origin also provides the XYZ2MatLog X-Function, which calculates logarithmic values for X and Y before performing XYZ Gridding on the data (Log(X), Log(Y), Z).

The XYZ Gridding methods are available for both XYZ2Mat and XYZ2MatLog X-Functions, please see table below:

Method XY Spacing of Data Relative Speed Key User-Specified Parameters Supports Extrapolation?
Regular Regular Fast None

No

Sparse Sparse Fast General settings

No

Renka- Cline Random Fast General settings

Yes

Shepard Random Intermediate General settings +
• Weight Function Locality Factor

No

TPS Random Intermediate General settings +
• Smoothing Factor
• Extrapolation Method

Yes

Kriging Random Slow General settings +