3dtikz-pgf
I would like to represent the densest sphere packing in dimension 3
as the following picture, for a beamer presentation.
Is Tikz the way to go for it? It is not a real 3D drawing since I only want a fixed representation of the picture, right?
Thank you for your help.
Here is a modification of the example in section 3.6.5 of the The tikz-3dplot Package manual.
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{enumerate}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{tikz-3dplot}
\usepackage{hyperref}
\usepackage{ifthen}
\usepackage{pgfplots}
\usetikzlibrary{calc,3d,intersections, positioning,intersections,shapes}
\pgfplotsset{compat=1.11}
\begin{document}
\tdplotsetmaincoords{60}{110}
\begin{tikzpicture}[scale=2,line join=bevel,tdplot_main_coords,%
fill opacity=.5]
\tdplotsetpolarplotrange{0}{90}{0}{360}
\tdplotsphericalsurfaceplot[parametricfill]{60}{32}%
{1}{black}{\tdplotphi + 3*\tdplottheta}%
{\draw[color=black,thick,->] (0,0,0)
-- (2,0,0) node[anchor=north east]{$x$};}%
{\draw[color=black,thick,->] (0,0,0)
-- (0,2,0) node[anchor=north west]{$y$};}%
{\draw[color=black,thick,->] (0,0,0)
-- (0,0,2) node[anchor=south]{$z$};}%
\end{tikzpicture}
\end{document}
In addition, here is the pgfplots version:
\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{enumerate}
\usepackage{tikz}
\usepackage{xcolor}
\usepackage{tikz-3dplot}
\usepackage{hyperref}
\usepackage{ifthen}
\usepackage{pgfplots}
\usetikzlibrary{calc,3d,shapes, pgfplots.external}
\pgfplotsset{compat=1.11}
\begin{document}
\begin{tikzpicture}
\begin{axis}[width=\textwidth,
samples=50,domain=0:360,y domain=0:90,
xmin=-1.2,xmax=1.2,ymin=-1.2,ymax=1.2,zmin=0,zmax=1.2,
xlabel={$x$},ylabel={$y$},zlabel={$z$},
axis lines=center]
\addplot3[surf,opacity=0.5]
({cos(x)*cos(y)}, {sin(x)*cos(y)}, {sin(y)});
\end{axis}
\end{tikzpicture}
\end{document}
and here the pic:
Better use pgfplots (adapted from this post). The parametric fill with \theta+\phi looks pretty weird in my opinion.
\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\begin{document}
\begin{tikzpicture}
\begin{axis}
[
width=6cm,height=6cm,
axis equal,enlargelimits=false,
axis lines=none,
domain=0:180,samples=21,
y domain=0:360,samples y=21,
colormap/blackwhite,
view={100}{10},
]
\addplot3
[
surf,
z buffer=sort,
shader=flat,
point meta={acos(z/sqrt(x*x+y*y+z*z)) + atan2(y,x)}
] (
{sin(x)*cos(y)},
{sin(x)*sin(y)},
{cos(x)}
);
\end{axis}
\end{tikzpicture}
\end{document}
Best Answer
By nesting 2 for-loops one could do something like this: