Gridding refers to methods that interpolate a set of scattered points onto a grid mesh. This grid mesh can then be used to represent a surface that establishes the spatial relationships between the scattered points.

The GTGRID function provides you with several unique gridding methods, each designed to treat a certain class of data in an optimum manner. The choice of gridding method is made primarily based on the distribution of the input points.

The representation of gridded data within PV‑WAVE GTGRID is actually a matrix of z values, where each pair of indices corresponds to a pair of x-y coordinates. Given a set of observations, in x-y space, the GTGRID function generates estimates of the z values at points, called nodes, on a grid.

Node coordinates are defined by specifying the ranges of x and y and the number of grid nodes along each axis. Once a grid definition is specified, generating the z values at each node can involve up to three stages, depending on the gridding method you choose. These stages include:

These stages are discussed in the following sections.

The first stage employed by the GTGRID function in producing a gridded dataset is to calculate primary estimates of the z values. The primary estimates attempt to determine z values and map the data points onto specified grid nodes. GTGRID calculates primary gridding estimates in the immediate vicinity of the input points, using the input points as control. The search radius determines which neighboring points are used in each calculation and the METHOD controls how far from each point a grid node is computed.

Because all the GTGRID methods are designed to create a single-valued function of two variables, some averaging of the input points will occur whenever the independent variables are very close to each other. Using the Method keyword you can specify how the primary estimates are calculated—by the Direct, Scatter, Cluster, or Weighted method.

Generally, you select a method that is based on the distribution of the input data.

The second stage employed by the GTGRID function in producing a gridded dataset is to calculate secondary estimates of z values. Secondary estimates are not calculated when the Direct method is used (that is, when the keyword Method = 'Direct').

Secondary estimates are calculated at grid nodes that were too remote to be considered in the primary estimates. The secondary estimates use the previously defined grid nodes as control. This secondary gridding process may be performed several times, each time using the previously computed values as additional input.

GTGRID improves the secondary estimates by effectively doubling the grid interval when computing grid nodes that are not near to input points. As the distance increases from the input points, doubling occurs again. This reduces the computations by a factor of sixteen to one. In other words, you can use four times as many grid nodes as you would on another system for about the same amount of computer time. Nodes that were skipped are then quickly filled using a bi-cubic interpolation scheme.

To compute secondary estimates, a procedure very similar to the Scatter method is used. The main differences between secondary estimates and the Scatter method are:

As a simple definition, a fault can be considered a gross discontinuity of data. A simple example might be the break in continuity in the slope of a roof where it joins a wall.

GTGRID accepts fault values in the form of x-fault and y-fault vectors, which are specified as arguments to the Xfault and Yfault keywords.

To define faults to be used by GTGRID, each fault point is assumed to be connected to its predecessor unless it is a terminator. A terminator is defined as an x-y pair of 0.0, 0.0. The next point following a terminator is a starting point for a new sequence of fault points.

Connected fault points define the location of lines where discontinuities are desired in the interpolation. If a sequence of points is closed, the interior of the polygon described is considered 'null' or undefined. The total number of fault segments cannot exceed 15,000. Faults must always be expressed in the same coordinate system as the input data.

Creases are not supported in PV‑WAVE GTGRID version 3.0.

Smoothing seeks to minimize curvature of the surface by adjusting the secondary estimates. You control the amount of smoothing (number of smoothing passes) with the Nsmooth keyword. The greater the number of smoothing passes, the closer the resulting surface is to the solution of the biharmonic equation, which approximates a thin metal plate deformed into the desired shape.

Each smoothing pass modifies those secondary grid estimates that do not conform to the minimum curvature model based on its adjacent grid node neighbors. (The minimum curvature model refers the deformation of a “thin metal plate” so that it passes through data points. The deformation produced is defined by how much force is required to “push” the plate to an elevation of z at a particular point.) These updated values are then used as input values to the next pass. This recursive, numerical solution to the biharmonic equation converges slowly, but usually will give acceptable results with as few as 10 passes.