Managing Curves
===============

The `g f' command is really shorthand for the following commands:
`C-u g d  g a  g p'.  Likewise, `g F' is shorthand for
`C-u g d  g A  g p'.  You can gain more control over your graph
by using these commands directly.

The `g a' (`calc-graph-add') command adds the "curve" represented by
the two values on the top of the stack to the current graph.  You can
have any number of curves in the same graph.  When you give the `g p'
command, all the curves will be drawn superimposed on the same axes.

The `g a' command (and many others that affect the current graph) will
cause a special buffer, `*Gnuplot Commands*', to be displayed in
another window.  This buffer is a template of the commands that will
be sent to GNUPLOT when it is time to draw the graph.  The first `g a'
command adds a `plot' command to this buffer.  Succeeding `g a'
commands add extra curves onto that `plot' command.  Other
graph-related commands put other GNUPLOT commands into this buffer.
In normal usage you never need to work with this buffer directly, but
you can if you wish.  The only constraint is that there must be only
one `plot' command, and it must be the last command in the buffer.  If
you want to save and later restore a complete graph configuration, you
can use regular Emacs commands to save and restore the contents of the
`*Gnuplot Commands*' buffer.

If the values on the stack are not variable names, `g a' will invent
variable names for them (of the form `PlotDataN') and store the values
in those variables.  The "x" and "y" variables are what go into the
`plot' command in the template.  If you add a curve that uses a
certain variable and then later change that variable, you can replot
the graph without having to delete and re-add the curve.  That's
because the variable name, not the vector, interval or formula itself,
is what was added by `g a'.

A numeric prefix argument on `g a' or `g f' changes the way stack
entries are interpreted as curves.  With a positive prefix argument
`n', the top `n' stack entries are "y" values for `n' different curves
which share a common "x" value in the `n+1'st stack entry.  (Thus `g
a' with no prefix argument is equivalent to `C-u 1 g a'.)

A prefix of zero or plain `C-u' means to take two stack entries, "x"
and "y" as usual, but to interpret "y" as a vector of "y" values for
several curves that share a common "x".

A negative prefix argument tells Calc to read `n' vectors from the
stack; each vector `[x, y]' describes an independent curve.  This is
the only form of `g a' that creates several curves at once that don't
have common "x" values.  (Of course, the range of "x" values covered
by all the curves ought to be roughly the same if they are to look
nice on the same graph.)

For example, to plot `sin(n x)' for integers `n' from 1 to 5, you
could use `v x' to create a vector of integers (`n'), then `V M '' or
`V M $' to map `sin(n x)' across this vector.  The resulting vector of
formulas is suitable for use as the "y" argument to a `C-u g a' or
`C-u g f' command.

The `g A' (`calc-graph-add-3d') command adds a 3D curve to the graph.
It is not legal to intermix 2D and 3D curves in a single graph.  This
command takes three arguments, "x", "y", and "z", from the stack.
With a positive prefix `n', it takes `n+2' arguments (common "x" and
"y", plus `n' separate "z"s).  With a zero prefix, it takes three
stack entries but the "z" entry is a vector of curve values.  With a
negative prefix `-n', it takes `n' vectors of the form `[x, y, z]'.
The `g A' command works by adding a `splot' (surface-plot) command to
the `*Gnuplot Commands*' buffer.

(Although `g a' adds a 2D `plot' command to the `*Gnuplot Commands*'
buffer, Calc changes this to `splot' before sending it to GNUPLOT if
it notices that the data points are evaluating to `xyz' calls.  It
will not work to mix 2D and 3D `g a' curves in a single graph,
although Calc does not currently check for this.)

The `g d' (`calc-graph-delete') command deletes the most recently
added curve from the graph.  It has no effect if there are no curves
in the graph.  With a numeric prefix argument of any kind, it deletes
all of the curves from the graph.

The `g H' (`calc-graph-hide') command "hides" or "unhides" the most
recently added curve.  A hidden curve will not appear in the actual
plot, but information about it such as its name and line and point
styles will be retained.

The `g j' (`calc-graph-juggle') command moves the curve
at the end of the list (the "most recently added curve") to the
front of the list.  The next-most-recent curve is thus exposed for
`g d' or similar commands to use.  With `g j' you can work
with any curve in the graph even though curve-related commands only
affect the last curve in the list.

The `g p' (`calc-graph-plot') command uses GNUPLOT to draw the graph
described in the `*Gnuplot Commands*' buffer.  Any GNUPLOT parameters
which are not defined by commands in this buffer are reset to their
default values.  The variables named in the `plot' command are written
to a temporary data file and the variable names are then replaced by
the file name in the template.  The resulting plotting commands are
fed to the GNUPLOT program.  See the documentation for the GNUPLOT
program for more specific information.  All temporary files are
removed when Emacs or GNUPLOT exits.

If you give a formula for "y", Calc will remember all the values that
it calculates for the formula so that later plots can reuse these
values.  Calc throws out these saved values when you change any
circumstances that may affect the data, such as switching from Degrees
to Radians mode, or changing the value of a parameter in the formula.
You can force Calc to recompute the data from scratch by giving a
negative numeric prefix argument to `g p'.

Calc uses a fairly rough step size when graphing formulas over
intervals.  This is to ensure quick response.  You can "refine" a plot
by giving a positive numeric prefix argument to `g p'.  Calc goes
through the data points it has computed and saved from previous plots
of the function, and computes and inserts a new data point midway
between each of the existing points.  You can refine a plot any number
of times, but beware that the amount of calculation involved doubles
each time.

Calc does not remember computed values for 3D graphs.  This means the
numerix prefix argument, if any, to `g p' is effectively ignored if
the current graph is three-dimensional.

The `g P' (`calc-graph-print') command is like `g p', except that it
sends the output to a printer instead of to the screen.  More
precisely, `g p' looks for `set terminal' or `set output' commands in
the `*Gnuplot Commands*' buffer; lacking these it uses the default
settings.  However, `g P' ignores `set terminal' and `set output'
commands and uses a different set of default values.  All of these
values are controlled by the `g D' and `g O' commands discussed below.
Provided everything is set up properly, `g p' will plot to the screen
unless you have specified otherwise and `g P' will always plot to the
printer.