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14.2 Three-Dimensional Graphics

The g F (calc-graph-fast-3d) command makes a three-dimensional graph. It works only if you have GNUPLOT 3.0 or later; with GNUPLOT 2.0, you will see a GNUPLOT error message if you try this command.

The g F command takes three values from the stack, called “x”, “y”, and “z”, respectively. As was the case for 2D graphs, there are several options for these values.

In the first case, “x” and “y” are each vectors (not necessarily of the same length); either or both may instead be interval forms. The “z” value must be a matrix with the same number of rows as elements in “x”, and the same number of columns as elements in “y”. The result is a surface plot where z_ij’ is the height of the point at coordinate ‘(x_i, y_j)’ on the surface. The 3D graph will be displayed from a certain default viewpoint; you can change this viewpoint by adding a ‘set view’ to the ‘*Gnuplot Commands*’ buffer as described later. See the GNUPLOT documentation for a description of the ‘set view’ command.

Each point in the matrix will be displayed as a dot in the graph, and these points will be connected by a grid of lines (isolines).

In the second case, “x”, “y”, and “z” are all vectors of equal length. The resulting graph displays a 3D line instead of a surface, where the coordinates of points along the line are successive triplets of values from the input vectors.

In the third case, “x” and “y” are vectors or interval forms, and “z” is any formula involving two variables (not counting variables with assigned values). These variables are sorted into alphabetical order; the first takes on values from “x” and the second takes on values from “y” to form a matrix of results that are graphed as a 3D surface.

If the “z” formula evaluates to a call to the fictitious function ‘xyz(x, y, z)’, then the result is a “parametric surface.” In this case, the axes of the graph are taken from the x and y values in these calls, and the “x” and “y” values from the input vectors or intervals are used only to specify the range of inputs to the formula. For example, plotting ‘[0..360], [0..180], xyz(sin(x)*sin(y), cos(x)*sin(y), cos(y))’ will draw a sphere. (Since the default resolution for 3D plots is 5 steps in each of “x” and “y”, this will draw a very crude sphere. You could use the g N command, described below, to increase this resolution, or specify the “x” and “y” values as vectors with more than 5 elements.

It is also possible to have a function in a regular g f plot evaluate to an xyz call. Since g f plots a line, not a surface, the result will be a 3D parametric line. For example, ‘[[0..720], xyz(sin(x), cos(x), x)]’ will plot two turns of a helix (a three-dimensional spiral).

As for g f, each of “x”, “y”, and “z” may instead be variables containing the relevant data.