Z Values Task

Graph ► Tasks ► Z Values

The Z Values task interprets the columns of a table as x-contiguous z-values and the rows of a table as y-contiguous z-values. The z-values correspond to height of cells on a 3D perspective plot or as cell amplitude on point fill plots. Some things to note about this task follows:

This task makes surface graphs, but of course, not really. It actually interpolates z-values on a regular grid with a bi-linear function as a basis over that cell.
The z-values are not actually plotted, that is a misnomer. What is actually plotted is a color gradation related to the z-values. For the flat (2D) point fill representation that gradation corresponds with the color map defined in the template. For the 3D perspective plot, the color mapping is remapped using a normal-to-observer amplitude to give a sense of reflection and hence 3D quality. Skins can be used to change some of the properties of the color mapping that are not available from the Preference tool settings.
The grid dimensions are inferred from the table's column and row lengths. Notice that deleting columns in the table may give unexpected results as the grid cells are considered contiguous. Also, each column length should be the same.

While importing data using Tables or Fetch keep in mind that the format is scalars separated by blanks.

Grid Definition

The numbers (a string representation) in the table are mapped onto a regular grid in the normal way in an x-contiguous and column-contiguous fashion. That is, lets say there are "n" z-values:

z₁ z₂ z₃ ... z_n

On a grid with definitions and relationships:

n_x	The number of z-values in the x-direction (column length)
n_y	The number of z-values in the y-direction (row length)
n	Must equal n_x n_y
x_min	The value of x-minimum set in the preferences
x_max	The value of x-maximum set in the preferences
y_min	The value of y-minimum set in the preferences
y_max	The value of y-maximum set in the preferences
Δx	= (x_max - x_min)/(n_x - 1)
Δy	= (y_max - y_min)/(n_y - 1)
i	The index of the i-th element in the list of z-values (starting at 1)
j	The index of the j-th z-value in the x-direction (starting at 1)
k	The index of the k-th z-value in the y-direction (starting at 1)
i	= (k-1) n_y + j

then for the z-value z_j,k (which is z_i = z_{(k-1) n_y + j}) the x and y values are defined as:

x_j = x_min + Δx (j - 1)

y_k = y_min + Δy (k - 1)

to form the triplet (3D point): {x_j, y_k, z_j,k}

which is to say that "successive column-contiguous z-values are ordered in a x-contiguous way on a regular grid in the x and y direction" and the units in the x and y direction are specified by separate parameters (x_min, x_max, y_min, y_max).

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