[Tex/LaTex] sphere and points in 3D – tikz or pstricks

3dpstrickstikz-pgf

I would like to generate a figure containing points within a cube of dimension 2x2x2. Inside this cube, is a sphere of diameter 2 (both centered on the origin). In this cube, I will draw several points: some of them inside the sphere (in a given color, say orange) and some outside the sphere (in white). I initially thought of using tikz, see the mwe:

\documentclass[]{standalone}
\usepackage{tikz}
\usepackage{ifthen}
\usepackage[nomessages]{fp}
\usepackage{xcolor}
\usetikzlibrary{3d,calc}

% ==========================
% parameters definition:
% ==========================

% colour of the cube
\colorlet{couleurcube}{black!25}
% colour of the sphere
\colorlet{couleursphere}{orange}
% colour of the points outside the sphere
\colorlet{couleurext}{white}
% colour of the points inside the sphere
\colorlet{couleurint}{orange}
% sphere radius
\def\rayonsphere{1}
% grid resolution
\def\resolution{6}
% grid colour
\colorlet{couleurgrille}{black!15}    

% automated adjustment of the point colour depending on its position with respect to the sphere
\newcommand{\tracepoint}[4]{
\FPeval{\somme}{clip(abs(#1)*abs(#1)+abs(#2)*abs(#2)+abs(#3)*abs(#3))}
\FPeval\rayon{clip(\somme^(0.5))}
\FPeval\difference{clip(\rayon-#4)}
\newdimen\ecart
\ecart = \difference pt
\ifthenelse{\ecart>0}{
\node[draw=black!75,shape=circle,fill=couleurext,minimum size=1.5mm,line width=0mm,inner sep=0] (x) at (#1,#2,#3) {};}{
\node[draw=black!75,shape=circle,fill=couleurint,minimum size=1.5mm,line width=0mm,inner sep=0] (x) at (#1,#2,#3) {};}}

\begin{document}
% graphique
\begin{tikzpicture}[background rectangle/.style={ultra thick,draw=none, top color=white, bottom color=white},scale=2]
    % tracé du cube en 3D
    \begin{scope}[x={(.7cm,.4cm)},z={(.9cm,-.4cm)}]    
        \begin{scope}[every path/.style={thick}]
            \node(C) at (0,0,0) {};
            % arêtes du cube derrière la sphère
            \draw[couleurcube,thick] (-1,-1,-1) -- (1,-1,-1);
            \draw[couleurcube,thick] (1,-1,-1) -- (1,1,-1);
            \draw[couleurcube,thick] (1,-1,-1) -- (1,-1,1);
            % 
            % background grid
            \foreach \x in {1,...,\resolution}
                {
                \draw[couleurgrille,thin] (-1+\x*2/\resolution,-1,-1) -- (-1+\x*2/\resolution,1,-1);
                \draw[couleurgrille,thin] (-1,-1+\x*2/\resolution,-1) -- (1,-1+\x*2/\resolution,-1);
                \draw[couleurgrille,thin] (-1+\x*2/\resolution,-1,-1) -- (-1+\x*2/\resolution,-1,1);
                \draw[couleurgrille,thin] (-1,-1,-1+\x*2/\resolution) -- (1,-1,-1+\x*2/\resolution);
                \draw[couleurgrille,thin] (1,-1,-1+\x*2/\resolution) -- (1,1,-1+\x*2/\resolution);
                \draw[couleurgrille,thin] (1,-1+\x*2/\resolution,-1) -- (1,-1+\x*2/\resolution,1);
                }
        \end{scope}
    \end{scope}

    % sphere        
    \filldraw[ball color=couleursphere,draw=none,opacity=0.55] (0,0) circle (\rayonsphere);
    \def\norme{\rayonsphere}

    % 3D cube
    \begin{scope}[x={(.7cm,.4cm)},z={(.9cm,-.4cm)}]    
        \begin{scope}[every path/.style={thick}]
            \node(C) at (0,0,0) {};
            \draw[couleurcube,thick] (1,1,-1) -- (-1,1,-1);
            \draw[couleurcube,thick] (-1,1,-1) -- (-1,-1,-1);
            \draw[couleurcube,thick] (-1,-1,-1) -- (-1,-1,1);
            \draw[couleurcube,thick] (1,1,-1) -- (1,1,1);
            \draw[couleurcube,thick] (-1,1,-1) -- (-1,1,1);
            \draw[couleurcube,thick] (-1,-1,1) -- (1,-1,1);
            \draw[couleurcube,thick] (1,-1,1) -- (1,1,1);
            \draw[couleurcube,thick] (1,1,1) -- (-1,1,1);
            \draw[couleurcube,thick] (-1,1,1) -- (-1,-1,1);
            % 
            % axes
            \draw[black,very thick] (-1,-1,-1) -- (-1,-1,1) node[midway,below=0.5cm] {$\xi_1$};
            \draw[black,very thick] (-1,-1,1) -- (1,-1,1) node[midway,below=0.5cm] {$\xi_2$};
            \draw[black,very thick] (1,-1,1) -- (1,1,1) node[midway,right=0.5cm] {$\xi_3$};
            \node[below=0.25cm,left] at (-1,-1,-1) {-1};
            \node[below=0.25cm,left] at (-1,-1,1) {1};
            \node[below=0.25cm,right] at (-1,-1,1) {-1};
            \node[below=0.25cm,right] at (1,-1,1) {1};
            \node[right=0.15cm] at (1,-1,1) {-1};
            \node[right=0.15cm] at (1,1,1) {1};
            %
            % points
            \tracepoint{0}{0}{0}{\norme};
            \tracepoint{-1}{0}{0}{\norme};
            \tracepoint{0}{-1}{0}{\norme};
            \tracepoint{0}{0}{-1}{\norme};
            \tracepoint{1}{0}{0}{\norme};
            \tracepoint{0}{1}{0}{\norme};
            \tracepoint{0}{0}{1}{\norme};
            \tracepoint{1}{1}{0}{\norme};
            \tracepoint{0}{1}{1}{\norme};
            \tracepoint{1}{0}{1}{\norme};
            \tracepoint{1}{-1}{0}{\norme};
            \tracepoint{0}{1}{-1}{\norme};
            \tracepoint{1}{0}{-1}{\norme};
            \tracepoint{-1}{1}{0}{\norme};
            \tracepoint{0}{-1}{1}{\norme};
            \tracepoint{-1}{0}{1}{\norme};
            \tracepoint{-1}{-1}{0}{\norme};
            \tracepoint{0}{-1}{-1}{\norme};
            \tracepoint{-1}{0}{-1}{\norme};
            %
        \end{scope}
    \end{scope}
\end{tikzpicture}                
\end{document}

This gives:

I am fairly unhappy with the result for two reasons: (1) tikz does not allow for a proper 3D view and, most importantly, I do not like the fact that all the data points seem to be "over" the sphere… So I tried to use pstricks with the following (partial since the automated function for points color is not yet implemented) mwe:

\documentclass[pstricks]{standalone}
\usepackage{pst-solides3d}

\newcommand{\tracepoint}[4]{
\FPeval{\somme}{clip(abs(#1)*abs(#1)+abs(#2)*abs(#2)+abs(#3)*abs(#3))}
\FPeval\rayon{clip(\somme^(0.5))}
\FPeval\difference{clip(\rayon-#4)}
\newdimen\ecart
\ecart = \difference pt
\ifthenelse{\ecart>0}{
\node[draw,shape=circle,fill=white,minimum size=1.5mm,line width=0mm,inner sep=0] (x) at (#1,#2,#3) {};% {\somme / \rayon / \difference};}{
\node[draw,shape=circle,fill=red,minimum size=1.5mm,line width=0mm,inner sep=0] (x) at (#1,#2,#3) {};% {\somme / \rayon / \difference};}}

\begin{document}

\psset{viewpoint=30 40 20 rtp2xyz,Decran=56}
  \begin{pspicture}(-3.5,-3.5)(3.5,3.5)
   \psSolid[object=cube,a=2,opacity=0.2,action=draw*]% ,fillcolor=blue
   \psSolid[object=sphere,r=1,linewidth=0.1pt,ngrid=50 50,fillcolor=red,opacity=0.1,action=draw*]%

   \psPoint(1.25,0,-1.25){x}\rput(x){$\xi_1$}
   \psPoint(0,1.25,-1.25){y}\rput(y){$\xi_2$}
   \psPoint(-1.25,1.25,0){z}\rput(z){$\xi_3$}
   
   \psdot[linecolor=black,fillcolor=orange,dotstyle=o,dotsize=2.5pt](0,0,0)
   %\tracepoint{0}{0}{1}{\norme};
   
  \end{pspicture}

\end{document}

which gives me:

I like the 3D view much better but, here again, I do not know how to draw points inside or outside the sphere…

Best Answer

This is too long for a comment but I'll be happy to remove it. You can draw the points twice, but really draw them if they are inside before you draw the sphere and after if they are outside. (I changed the radius because some points are right at surface of a sphere of radius 1.

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage{ifthen}
\usepackage[nomessages]{fp}
\usepackage{xcolor}
\usetikzlibrary{3d,calc}

% ==========================
% parameters definition:
% ==========================

% colour of the cube
\colorlet{couleurcube}{black!25}
% colour of the sphere
\colorlet{couleursphere}{orange}
% colour of the points outside the sphere
\colorlet{couleurext}{white}
% colour of the points inside the sphere
\colorlet{couleurint}{orange}
% sphere radius
\def\rayonsphere{1.2}
% grid resolution
\def\resolution{6}
% grid colour
\colorlet{couleurgrille}{black!15}  
\def\ImOut{-1}
% automated adjustment of the point colour depending on its position with respect to the sphere
\newcommand{\tracepoint}[4]{
\FPeval{\somme}{clip(abs(#1)*abs(#1)+abs(#2)*abs(#2)+abs(#3)*abs(#3))}
\FPeval\rayon{clip(\somme^(0.5))}
\FPeval\difference{clip(\ImOut*(\rayon-#4))}
\newdimen\ecart
\ecart = \difference pt
\ifthenelse{\ecart>0}{\typeout{#1,#2,#3,#4}
\node[draw=black!75,shape=circle,fill=couleurext,minimum size=1.5mm,line width=0mm,inner sep=0] (x) at (#1,#2,#3) {};}{
%\node[draw=black!75,shape=circle,fill=couleurint,minimum size=1.5mm,line width=0mm,inner sep=0] (x) at (#1,#2,#3) {};
}}

\begin{document}
% graphique
\begin{tikzpicture}[background rectangle/.style={ultra thick,draw=none, top
color=white, bottom color=white},scale=2]
    % tracé du cube en 3D
    \begin{scope}[x={(.7cm,.4cm)},z={(.9cm,-.4cm)}] 
        \begin{scope}[every path/.style={thick}]
            \node(C) at (0,0,0) {};
            % arêtes du cube derrière la sphère
            \draw[couleurcube,thick] (-1,-1,-1) -- (1,-1,-1);
            \draw[couleurcube,thick] (1,-1,-1) -- (1,1,-1);
            \draw[couleurcube,thick] (1,-1,-1) -- (1,-1,1);
            % 
            % background grid
            \foreach \x in {1,...,\resolution}
                {
                \draw[couleurgrille,thin] (-1+\x*2/\resolution,-1,-1) -- (-1+\x*2/\resolution,1,-1);
                \draw[couleurgrille,thin] (-1,-1+\x*2/\resolution,-1) -- (1,-1+\x*2/\resolution,-1);
                \draw[couleurgrille,thin] (-1+\x*2/\resolution,-1,-1) -- (-1+\x*2/\resolution,-1,1);
                \draw[couleurgrille,thin] (-1,-1,-1+\x*2/\resolution) -- (1,-1,-1+\x*2/\resolution);
                \draw[couleurgrille,thin] (1,-1,-1+\x*2/\resolution) -- (1,1,-1+\x*2/\resolution);
                \draw[couleurgrille,thin] (1,-1+\x*2/\resolution,-1) -- (1,-1+\x*2/\resolution,1);
                }
        \end{scope}
    \end{scope}
    \def\norme{\rayonsphere}
    \begin{scope}[x={(.7cm,.4cm)},z={(.9cm,-.4cm)}]
            \tracepoint{0}{0}{0}{\norme};
            \tracepoint{-1}{0}{0}{\norme};
            \tracepoint{0}{-1}{0}{\norme};
            \tracepoint{0}{0}{-1}{\norme};
            \tracepoint{1}{0}{0}{\norme};
            \tracepoint{0}{1}{0}{\norme};
            \tracepoint{0}{0}{1}{\norme};
            \tracepoint{1}{1}{0}{\norme};
            \tracepoint{0}{1}{1}{\norme};
            \tracepoint{1}{0}{1}{\norme};
            \tracepoint{1}{-1}{0}{\norme};
            \tracepoint{0}{1}{-1}{\norme};
            \tracepoint{1}{0}{-1}{\norme};
            \tracepoint{-1}{1}{0}{\norme};
            \tracepoint{0}{-1}{1}{\norme};
            \tracepoint{-1}{0}{1}{\norme};
            \tracepoint{-1}{-1}{0}{\norme};
            \tracepoint{0}{-1}{-1}{\norme};
            \tracepoint{-1}{0}{-1}{\norme};
    \end{scope}

    % sphere        
    \filldraw[ball color=couleursphere,draw=none,opacity=0.55] (0,0) circle (\rayonsphere);

    % 3D cube
    \begin{scope}[x={(.7cm,.4cm)},z={(.9cm,-.4cm)}] 
        \begin{scope}[every path/.style={thick}]
            \node(C) at (0,0,0) {};
            \draw[couleurcube,thick] (1,1,-1) -- (-1,1,-1);
            \draw[couleurcube,thick] (-1,1,-1) -- (-1,-1,-1);
            \draw[couleurcube,thick] (-1,-1,-1) -- (-1,-1,1);
            \draw[couleurcube,thick] (1,1,-1) -- (1,1,1);
            \draw[couleurcube,thick] (-1,1,-1) -- (-1,1,1);
            \draw[couleurcube,thick] (-1,-1,1) -- (1,-1,1);
            \draw[couleurcube,thick] (1,-1,1) -- (1,1,1);
            \draw[couleurcube,thick] (1,1,1) -- (-1,1,1);
            \draw[couleurcube,thick] (-1,1,1) -- (-1,-1,1);
            % 
            % axes
            \draw[black,very thick] (-1,-1,-1) -- (-1,-1,1) node[midway,below=0.5cm] {$\xi_1$};
            \draw[black,very thick] (-1,-1,1) -- (1,-1,1) node[midway,below=0.5cm] {$\xi_2$};
            \draw[black,very thick] (1,-1,1) -- (1,1,1) node[midway,right=0.5cm] {$\xi_3$};
            \node[below=0.25cm,left] at (-1,-1,-1) {-1};
            \node[below=0.25cm,left] at (-1,-1,1) {1};
            \node[below=0.25cm,right] at (-1,-1,1) {-1};
            \node[below=0.25cm,right] at (1,-1,1) {1};
            \node[right=0.15cm] at (1,-1,1) {-1};
            \node[right=0.15cm] at (1,1,1) {1};
            %
            % points
            \def\ImOut{1}
            \typeout{outside}
            \tracepoint{0}{0}{0}{\norme};
            \tracepoint{-1}{0}{0}{\norme};
            \tracepoint{0}{-1}{0}{\norme};
            \tracepoint{0}{0}{-1}{\norme};
            \tracepoint{1}{0}{0}{\norme};
            \tracepoint{0}{1}{0}{\norme};
            \tracepoint{0}{0}{1}{\norme};
            \tracepoint{1}{1}{0}{\norme};
            \tracepoint{0}{1}{1}{\norme};
            \tracepoint{1}{0}{1}{\norme};
            \tracepoint{1}{-1}{0}{\norme};
            \tracepoint{0}{1}{-1}{\norme};
            \tracepoint{1}{0}{-1}{\norme};
            \tracepoint{-1}{1}{0}{\norme};
            \tracepoint{0}{-1}{1}{\norme};
            \tracepoint{-1}{0}{1}{\norme};
            \tracepoint{-1}{-1}{0}{\norme};
            \tracepoint{0}{-1}{-1}{\norme};
            \tracepoint{-1}{0}{-1}{\norme};
            %
        \end{scope}
    \end{scope}
\end{tikzpicture}               
\end{document}

Personally I would use asymptote for this. (Compile with pdflatex -shell-escape .)

\documentclass{standalone}
\usepackage{asypictureB}
\begin{document}
\begin{asypicture}{name=AsySphere}
size(400); // sphere from https://tex.stackexchange.com/q/244771/121799
import three;
import solids;
//unitsize(4cm);
settings.render=8;
pen linestyle1 = rgb(1,1,1)+linewidth(1.5pt)+opacity(1);

//currentprojection=perspective( camera=(1,.4,.9), target = (0,0,0));
//currentlight=nolight;

revolution S=sphere(O,1);
draw(surface(S),surfacepen=brown+opacity(.3));

draw(shift(0,0,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(-1,0,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,-1,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,0,-1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(1,0,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,1,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,0,1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(1,1,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,1,1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(1,0,1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(1,-1,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,1,-1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(1,0,-1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(-1,1,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,-1,1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(-1,0,1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(-1,-1,0)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(0,-1,-1)*scale3(0.03)*unitsphere,linestyle1);
draw(shift(-1,0,-1)*scale3(0.03)*unitsphere,linestyle1);

\end{asypicture} 
\end{document}

Related Solutions

[Tex/LaTex] Elliptic Moebius map on sphere using Tikz

Changing the size of the arrows means changing the angular separation between the tip and tail of the arrow, since they appear in polar form. After reducing the angular separation, you also have to reduce the "bending" of the arrow for it to smear in the equator:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\usepackage{verbatim}

%% helper macros

\newcommand\pgfmathsinandcos[3]{%
  \pgfmathsetmacro#1{sin(#3)}%
  \pgfmathsetmacro#2{cos(#3)}%
}
\newcommand\LongitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % azimuth
  \tikzset{#1/.estyle={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % latitude
  \pgfmathsetmacro\yshift{\cosEl*\sint}
  \tikzset{#1/.estyle={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
}
\newcommand\DrawLongitudeCircle[2][1]{
  \LongitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1,dashed}}
   % angle of "visibility"
  \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
  \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
  %\draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}
\newcommand\DrawLatitudeCircle[2][2]{
  \LatitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1,line width=.7pt}}
  \pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
  % angle of "visibility"
  \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
  \draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
  %\draw[red,current plane,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}

%% document-wide tikz options and styles

\tikzset{%
  >=latex, % option for nice arrows
  inner sep=0pt,%
  outer sep=2pt,%
  mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,
    fill=black,circle}%
}

\begin{document}

\begin{tikzpicture}[scale=1.4] % "THE GLOBE" showcase

\def\R{2.5} % sphere radius
\def\angEl{35} % elevation angle
\def\angAz{-105} % azimuth angle
\def\angPhi{-40} % longitude of point P
\def\angBeta{0} % latitude of point P
%
\filldraw[ball color=white] (0,0) circle (\R);
\foreach \t in {-80,-60,...,80} { \DrawLatitudeCircle[\R]{\t} }
\foreach \t in {-5,-35,...,-175} { \DrawLongitudeCircle[\R]{\t} }
%
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\coordinate[mark coordinate] (N) at (0,\H);
\draw (N)  node[inner sep=1pt,below=0pt] {$\infty$}; %+(0.3ex,0.6ex)
%
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhi}
\LatitudePlane[equator]{\angEl}{0}
\draw[red,equator,->,thick] (\angAz:\R) to[bend right=11] (-80:\R);
\end{tikzpicture}

\end{document}

enter image description here

To draw the vector field over other latitudes one can define another planes at other latitudes, just as the original code defines "equator".

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc,fadings,decorations.pathreplacing}
\usepackage{verbatim}

%% helper macros

\newcommand\pgfmathsinandcos[3]{%
  \pgfmathsetmacro#1{sin(#3)}%
  \pgfmathsetmacro#2{cos(#3)}%
}
\newcommand\LongitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % azimuth
  \tikzset{#1/.estyle={cm={\cost,\sint*\sinEl,0,\cosEl,(0,0)}}}
}
\newcommand\LatitudePlane[3][current plane]{%
  \pgfmathsinandcos\sinEl\cosEl{#2} % elevation
  \pgfmathsinandcos\sint\cost{#3} % latitude
  \pgfmathsetmacro\yshift{\cosEl*\sint}
  \tikzset{#1/.estyle={cm={\cost,0,0,\cost*\sinEl,(0,\yshift)}}} %
}
\newcommand\DrawLongitudeCircle[2][4]{
  \LongitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1,dashed}}
   % angle of "visibility"
  \pgfmathsetmacro\angVis{atan(sin(#2)*cos(\angEl)/sin(\angEl))} %
  \draw[current plane] (\angVis:1) arc (\angVis:\angVis+180:1);
  %\draw[current plane,dashed] (\angVis-180:1) arc (\angVis-180:\angVis:1);
}
\newcommand\DrawLatitudeCircle[2][5]{
  \LatitudePlane{\angEl}{#2}
  \tikzset{current plane/.prefix style={scale=#1,line width=.7pt}}
  \pgfmathsetmacro\sinVis{sin(#2)/cos(#2)*sin(\angEl)/cos(\angEl)}
  % angle of "visibility"
  \pgfmathsetmacro\angVis{asin(min(1,max(\sinVis,-1)))}
  \draw[current plane] (\angVis:1) arc (\angVis:-\angVis-180:1);
  \draw[gray,current plane,dashed] (180-\angVis:1) arc (180-\angVis:\angVis:1);
}

%% document-wide tikz options and styles

\tikzset{%
  >=latex, % option for nice arrows
  inner sep=0pt,%
  outer sep=2pt,%
  mark coordinate/.style={inner sep=0pt,outer sep=0pt,minimum size=3pt,
    fill=black,circle}%
}

\begin{document}

\begin{tikzpicture}[scale=1.4] % "THE GLOBE" showcase

\def\R{2.5} % sphere radius
\def\angEl{35} % elevation angle
\def\angAz{-105} % azimuth angle
\def\angPhi{-40} % longitude of point P
\def\angBeta{0} % latitude of point P
%
\filldraw[ball color=white] (0,0) circle (\R);
\foreach \t in {-80,-60,...,80} { \DrawLatitudeCircle[\R]{\t} }
\foreach \t in {-5,-35,...,-175} { \DrawLongitudeCircle[\R]{\t} }
%
\pgfmathsetmacro\H{\R*cos(\angEl)} % distance to north pole
\coordinate[mark coordinate] (N) at (0,\H);
\draw (N)  node[inner sep=1pt,below=0pt] {$\infty$}; %+(0.3ex,0.6ex)
%
\LongitudePlane[xzplane]{\angEl}{\angAz}
\LongitudePlane[pzplane]{\angEl}{\angPhi}
\LatitudePlane[equator]{\angEl}{0}
\LatitudePlane[capr]{\angEl}{37}
\LatitudePlane[sag]{\angEl}{68}
\draw[red,equator,->,thick] (\angAz:\R) to[bend right=11] (-80:\R);
\draw[green,sag,->,thick] (\angAz:\R) to[bend right=11] (-80:\R);
\draw[blue,capr,->,thick] (\angAz:\R) to[bend right=11] (-80:\R);
\end{tikzpicture}

\end{document}

The result is the following (you can change the colors, I just display them in order for the arrows to be more trackable) : enter image description here

To add more arrows on the same circle you can use this code

\draw[red,equator,->,thick] (\angAz:\R) to[bend right=11] (-80:\R);
\draw[red,equator,->,thick] (-135:\R) to[bend right=11] (-110:\R);
\draw[red,equator,->,thick] (-75:\R) to[bend right=11] (-50:\R);
\draw[red,equator,->,thick] (-40:\R) to[bend right=8] (-25:\R);
\draw[blue,capr,->,thick] (\angAz:\R) to[bend right=11] (-80:\R);
\draw[blue,capr,->,thick] (-135:2.6) to[bend right=11] (-110:\R);
\draw[blue,capr,->,thick] (-75:\R) to[bend right=11] (-50:2.6);
\draw[blue,capr,->,thick] (-40:2.65) to[bend right=8] (-25:2.7);

enter image description here

[Tex/LaTex] Drawing 3D crystal lattice with tikz/pstricks

Here's an Asymptote solution:

\documentclass{standalone}
\usepackage{asymptote}

\begin{document}

\begin{asy}[width=10cm,height=10cm]
import three;

currentprojection=perspective(300,-650,500,center=true);


// define two types of ions
surface iona = scale3(20)*unitsphere;
surface ionb = scale3(25)*unitsphere;

// surface properties and color of the ions
material White = material(diffusepen=gray(0.4),emissivepen=gray(0.6));
material Red = material(diffusepen=red,emissivepen=lightred);

// style of lines connecting ions
pen thick=linewidth(2);

for(int x=-1; x<2; ++x) {
  for(int y=-1; y<2; ++y) {
    for(int z=-1; z<2; ++z) {
      draw(shift(100*(x,y,z))*iona,White);
    }
  }
}

for(int x=-1; x<2; ++x) {
  for(int y=-1; y<2; ++y) {
    for(int z=-1; z<2; ++z) {
      if(x<1) draw(100*(x,y,z)--100*(x+1,y,z),thick);
      if(y<1) draw(100*(x,y,z)--100*(x,y+1,z),thick);
      if(z<1) draw(100*(x,y,z)--100*(x,y,z+1),thick);
    }
  }
}

for(int x=-1; x<2; x+=2) {
  for(int y=-1; y<2; y+=2) {
    for(int z=-1; z<2; z+=2) {
      draw(shift(50*(x,y,z))*ionb,Red);
    }
  }
}
\end{asy}


\end{document}

To compile, first run pdflatex on the file, then asy on the generated .asy file, finally pdflatex once or twice again.

crystal lattice

Best Answer

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[Tex/LaTex] Elliptic Moebius map on sphere using Tikz

[Tex/LaTex] Drawing 3D crystal lattice with tikz/pstricks

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