circlesplottikz-pgf
I have not idea how to call these things, but I just saw a paper with the following figure
and I was wondering how one would go about doing it in LaTeX. The closest thing I saw on TeXample.net was the Ford Circles example, but that's for a very specific case. I would like to see a way use this as a plotting device. At this point, I am not even sure how to do it in "normal" programming language, so perhaps the question is ill-placed.
At any rate, I'd love to hear what people think!
In the pgf manual page 130 (ver. 3.10), you have the exact example. I just copy it from there for convenience in case anybody needs. It requires \usetikzlibrary{calc}
\begin{tikzpicture}
\draw[help lines] (0,0) grid (3,2);
\coordinate (a) at (3,2);
\node [circle,draw] (c) at (1,1) [minimum size=40pt] {$c$};
\draw[red] (a) -- (tangent cs:node=c,point={(a)},solution=1) --
(c.center) -- (tangent cs:node=c,point={(a)},solution=2) -- cycle;
\end{tikzpicture}
Here's a way of doing this with PGFPlots: The first plot is simply a ycomb plot, and the second I would draw using separate plots for the areas (with a trailing \closedcycle to get the filling right) and the lines.
\documentclass{article}
\usepackage{pgfplots}
\usepackage{filecontents}
\begin{filecontents}{data.dat}
3.045784 3.415896
3.405784 4.025693
3.785784 4.522530
4.125784 5.538449
4.485784 6.704992
4.805784 6.978939
5.145784 7.113496
5.425784 8.916397
6.065784 9.487712
6.365784 10.876397
6.685784 10.693497
7.025784 11.364131
7.345784 11.442530
7.665784 12.582530
8.005784 13.125693
8.225784 13.738450
8.585784 14.247891
8.865784 14.982530
\end{filecontents}
\begin{document}
\pgfplotsset{
compat=1.5,
width=10cm,
height=5cm
}
\begin{tikzpicture}
\begin{axis}[
ymin=0,
xtick=\empty,
ytick=\empty,
axis background/.style={fill=gray!10},
]
\addplot [ycomb, red, very thick, mark=*, mark options={red!60!black}] table {data.dat};
\end{axis}
\end{tikzpicture}
\begin{tikzpicture}
\begin{axis}[
ymin=0,
xtick=\empty,
ytick=\empty,
axis background/.style={fill=gray!10},
enlarge x limits=false
]
\addplot [draw=none, fill=orange!40!yellow] table {data.dat} \closedcycle;
\addplot [draw=gray, very thick] table {data.dat};
\addplot [draw=none, fill=red!60] table [
x expr=\thisrowno{0}+8.865784-3.045784,
y expr=\thisrowno{1}+14.982530-3.415896
] {data.dat} \closedcycle;
\addplot [draw=red!70!black, very thick] table [
x expr=\thisrowno{0}+8.865784-3.045784,
y expr=\thisrowno{1}+14.982530-3.415896
] {data.dat};
\end{axis}
\end{tikzpicture}
\end{document}
Best Answer
As already observed by Michael Palmer your question boils down to a circle packing problem. I am not an expert in the subject but I know at least one person who is. His name is Ken Stephenson from University of Tennessee. Please check out his gallery! He is also providing algorithms and Java based software which can be used to create those magnificent pictures on his webpage.
On the another hand, I am very interested in an alternative solution in the classical sense of Mittag Leffler (power series) of N-body problem which is solved for 3 bodies by Karl Sundman and N>3 by my Ph.D. advisor Qiudong Wang. The solution boils down to a construction of the explicit Riemann mapping which can be done algorithmically via discrete version of Riemann mapping (circle packing). If you would like to look into that problem please contact me via private e-mail and we can try to write a paper together.
Sorry, no TeX answer here and probably even if we attack problem we will not use TeX as a programming language but very interesting problem never the less.