### 13.2 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.