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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% GLE - Graphics Layout Engine <http://glx.sourceforge.io/> %
% %
% Modified BSD License %
% %
% Copyright (C) 2009 GLE. %
% %
% Redistribution and use in source and binary forms, with or without %
% modification, are permitted provided that the following conditions %
% are met: %
% %
% 1. Redistributions of source code must retain the above copyright %
% notice, this list of conditions and the following disclaimer. %
% %
% 2. Redistributions in binary form must reproduce the above %
% copyright notice, this list of conditions and the following %
% disclaimer in the documentation and/or other materials provided with %
% the distribution. %
% %
% 3. The name of the author may not be used to endorse or promote %
% products derived from this software without specific prior written %
% permission. %
% %
% THIS SOFTWARE IS PROVIDED BY THE AUTHOR "AS IS" AND ANY EXPRESS OR %
% IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED %
% WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE %
% ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY %
% DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL %
% DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE %
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% INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER %
% IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR %
% OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN %
% IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. %
% %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Contour}
\index{contour}
\index{.z file}
The contour block produces contour lines of a function $z = f(x,y)$.
The function $f(x,y)$ is given by a .z file. The .z file format is discussed on page~\pageref{zfile:pg}. Recall that a .z file can be created from sample data points, that is $(x,y,z)$ tuples, with the {\sf fitz} block (Section~\ref{fitz:sec}), or from an implicit definition of $f(x,y)$ with a {\sf letz} block (Section~\ref{letz:sec}).
\begin{minipage}[c]{8cm}
\begin{Verbatim}
include "contour.gle"
begin contour
data "saddle.z"
values 0.5 1 1.5 2 3
end contour
begin graph
title "Saddle Plot Contour Lines"
data "saddle-cdata.dat"
d1 line color blue
end graph
contour_labels "saddle-clabels.dat" "fix 1"
\end{Verbatim}
\end{minipage}
\hfill
\begin{minipage}[c]{7cm}
\ifdefined\APPLE
% surface countours cause seg fault on macOS
\else
\mbox{\input{utilities/fig/saddle-contour.inc}}
\fi
\end{minipage}
The contour block can contain the following commands:
\begin{commanddescription}
\item[{\sf data {\it file\$}}]\index{data} Specifies the name of the .z file.
\item[{\sf values $v_1,\ldots, v_n$}]\index{values} Specifies the z-values to contour at.
\item[{\sf values from $v_1$ to $v_n$ step $s$}] Specifies the z-values to contour at by means of from/to/step.
\item[{\sf smooth {\it integer}}]\index{smooth} Specifies the smoothing parameter.
\end{commanddescription}
The contour block creates the files ``data-clabels.dat'' and ``data-cdata.dat'' with the prefix ``data'' the name of the .z file. The file ``data-clabels.dat'' contains information for drawing labels on the contour plot. This is done by the subroutine {\sf contour\_labels} defined in the library ``contour.gle'' in the example above. The file ``data-cdata.dat'' contains the $(x,y)$ values of the contour lines. This file can be used as input to a graph block and plotted with the ``d1 line'' command as shown in the example above.
\section{Color Maps}
\label{colormap}
\index{colormap}
Color maps plot a function $z = f(x,y)$ by mapping $z$ to a color range. The following example combines a color map with a contour plot.
\begin{minipage}[c]{8cm}
\begin{Verbatim}
begin contour
data "volcano.z"
values from 130 to 190 step 10
end contour
begin graph
title "Auckland's Maunga Whau Volcano"
data "volcano-cdata.dat"
xaxis min 0 max 20
yaxis min 0 max 20
d1 line color black
colormap "volcano.z" 100 100
end graph
\end{Verbatim}
\end{minipage}
\hfill
\begin{minipage}[c]{7cm}
\ifdefined\APPLE
% surface countours cause seg fault on macOS
\else
\mbox{\input{utilities/fig/volcano.inc}}
\fi
\end{minipage}
The options to the colormap command are as follows:
\begin{commanddescription}
\item[{\sf colormap {\it fct} {\it pixels-x} {\it pixels-y} [color] [invert] [zmin $z_1$] [zmax $z_2$] [palette {\it pal}]}]
\mbox{}\\
\begin{itemize}
\item {\it fct} specifies the function to map. This can either be the name of a .z file, or it can be a function definition $f(x,y)$.
\item {\it pixels-x}, {\it pixels-x} specify the dimension of the color map. A color map is a stored as a bitmap image and ({\it pixels-x}, {\it pixels-x}) are the resolution of this bitmap. A larger resolution yields more detail, but at the cost of longer computation time and a larger file size.
\item {\it color} is an optional argument and indicates that the color map should be drawn in color (as opposed to grayscale).
\item {\it invert} is an optional argument that inverts the color map. That is, large function values will be drawn in black and small function values in white.
\item {\it zmin}, {\it zmax} are optional arguments that specify the range of the function.
\item {\it palette} is an optional argument that specifies the palette to use. A palette is a subroutine that maps $z$ values to colors. A number of example palette subroutines are included in the library ``color.gle''.
\end{itemize}
\end{commanddescription}
The following example is a color map of a two dimensional Gaussian.
\preglegraph{}
\begin{minipage}[c]{8cm}
\begin{Verbatim}
include "color.gle"
sub gauss x y
s = 0.75
return exp(-(x^2+y^2)/(2*s^2))
end sub
begin graph
title "2D Gaussian"
xaxis min -2 max 2
yaxis min -2 max 2
colormap gauss(x,y) 200 200 zmin 0 zmax 1 color
end graph
amove xg(xgmax)+0.3 yg(ygmin)
color_range_vertical zmin 0 zmax 1 zstep 0.1 format "fix 1"
\end{Verbatim}
\end{minipage}
\hfill
\begin{minipage}[c]{7cm}
\ifdefined\APPLE
% surface countours cause seg fault on macOS
\else
\mbox{\input{utilities/fig/gaussian.inc}}
\fi
\end{minipage}
\postglegraph{}
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