Ytukyg

I need help with drawing a 2D square lattice made of springs and balls (see the picture) on a convex surface, such as spherical one. Could you please let me know is there a possibility of making this in PSTricks or TikZ? Thanks a lot.

I have linked [1] a related example in PDF with a grid on a spherical surface.

[1] http://www.texample.net/media/tikz/examples/PDF/spherical-and-cartesian-grids.pdf

Welcome to TeX.SE! Here is a proposal.

documentclass[tikz,border=3.14mm]{standalone}

usetikzlibrary{decorations.pathmorphing}

begin{document}

begin{tikzpicture}

clip (-1,-1) rectangle (11,11);

foreach X in {-2,0,...,10}

{foreach Y in {-2,0,...,10}

 {draw[decorate,decoration={coil,aspect=0.5,amplitude=1.5mm, segment

length=1.5mm}] (X,Y) -- ++(0,2) -- ++(2,0);

node[circle,text=white,font=sffamilybfserieslarge,inner

color=blue,outer color=black] at (X,Y) {+};}}

end{tikzpicture}

end{document}

It is straightforward to embed this into a spherical coordinate system. (Big thanks to @caverac for pointing out what the question really is.)

documentclass[tikz,border=3.14mm]{standalone}

usepackage{tikz-3dplot}

usetikzlibrary{decorations.pathmorphing,calc}

makeatletter

%from https://tex.stackexchange.com/a/375604/121799

%along x axis

define@key{x sphericalkeys}{radius}{defmyradius{#1}}

define@key{x sphericalkeys}{theta}{defmytheta{#1}}

define@key{x sphericalkeys}{phi}{defmyphi{#1}}

tikzdeclarecoordinatesystem{x spherical}{% %%%rotation around x

    setkeys{x sphericalkeys}{#1}%

    pgfpointxyz{myradius*cos(mytheta)}{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}}



%along y axis

define@key{y sphericalkeys}{radius}{defmyradius{#1}}

define@key{y sphericalkeys}{theta}{defmytheta{#1}}

define@key{y sphericalkeys}{phi}{defmyphi{#1}}

tikzdeclarecoordinatesystem{y spherical}{% %%%rotation around x

    setkeys{y sphericalkeys}{#1}%

    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*cos(mytheta)}{myradius*sin(mytheta)*sin(myphi)}}



%along z axis

define@key{z sphericalkeys}{radius}{defmyradius{#1}}

define@key{z sphericalkeys}{theta}{defmytheta{#1}}

define@key{z sphericalkeys}{phi}{defmyphi{#1}}

tikzdeclarecoordinatesystem{z spherical}{% %%%rotation around x

    setkeys{z sphericalkeys}{#1}%

    pgfpointxyz{myradius*sin(mytheta)*cos(myphi)}{myradius*sin(mytheta)*sin(myphi)}{myradius*cos(mytheta)}}





makeatother % https://tex.stackexchange.com/a/438695/121799



begin{document}

tdplotsetmaincoords{70}{130}

begin{tikzpicture}[tdplot_main_coords]

pgfmathsetmacro{R}{16}

    path[clip]

    plot[variable=x,domain=2.5:52.5]

     (z spherical cs:radius=R,theta=80-2.5,phi=x)

     -- plot[variable=x,domain=2.5:52.5]

     (z spherical cs:radius=R,theta=80-x,phi=52.5)

     -- plot[variable=x,domain=52.5:2.5]

     (z spherical cs:radius=R,theta=80-52.5,phi=x)

     -- plot[variable=x,domain=52.5:2.5]

     (z spherical cs:radius=R,theta=80-x,phi=2.5);

    foreach X in {0,5,...,55}

     {draw[decorate,decoration={coil,aspect=0.5,amplitude=1.5mm, segment

length=1.5mm}] plot[variable=x,domain=0:55]

     (z spherical cs:radius=R,theta=80-X,phi=x);

     draw[decorate,decoration={coil,aspect=0.5,amplitude=1.5mm, segment

length=1.5mm}] plot[variable=x,domain=0:55]

     (z spherical cs:radius=R,theta=80-x,phi=X);

     }

    foreach X in {5,10,...,50}

    {foreach Y in {5,10,...,50}

     {path let p1=($(z spherical cs:radius=R,theta=80-X+1,phi=Y)-(z

     spherical cs:radius=R,theta=80-X,phi=Y)$),

     p2=($(z spherical cs:radius=R,theta=80-X,phi=Y+1)-(z

     spherical cs:radius=R,theta=80-X,phi=Y)$),

     n1={veclen(x1,y1)/12},n2={veclen(x2,y2)/12},n3={sqrt(n1*n2)}

     in %pgfextra{typeout{X,Y:n1,n2}}

     node[scale=n3,transform shape,circle,text=white,font=sffamilybfserieslarge,inner

color=blue,outer color=black] at (z spherical cs:radius=R,theta=80-X,phi=Y) {+};}}

end{tikzpicture}

end{document}

As for your additional request: yes, it is possible. However, things depend on what you really want to achieve in the end. Here I present some example that heavily relies on Fritz's stellar answer. However, when trying to polish it by drawing things on different layers, I encountered unexpected problems. In any case, I have no idea what your real aim is. (See e.g. this great post for additional possibilities.) I would kindly like to ask you to make additional requests in form of a new question, which list all the requirements. Asking questions is free, after all. I leave you with

documentclass[border=3.14mm,tikz]{standalone}

usepackage{pgfplots}

usepackage{xxcolor}

pgfplotsset{compat=1.16}

usetikzlibrary{decorations.pathmorphing,decorations.markings}

% Declare nice sphere shading: http://tex.stackexchange.com/a/54239/12440

pgfdeclareradialshading[tikz@ball]{ball}{pgfqpoint{0bp}{0bp}}{%

 color(0bp)=(tikz@ball!0!white);

 color(7bp)=(tikz@ball!0!white);

 color(15bp)=(tikz@ball!70!black);

 color(20bp)=(black!70);

 color(30bp)=(black!70)}

makeatother



% Style to set TikZ camera angle, like PGFPlots `view`

tikzset{viewport/.style 2 args={

    x={({cos(-#1)*1cm},{sin(-#1)*sin(#2)*1cm})},

    y={({-sin(-#1)*1cm},{cos(-#1)*sin(#2)*1cm})},

    z={(0,{cos(#2)*1cm})}

}}



% Styles to plot only points that are before or behind the sphere.

pgfplotsset{only foreground/.style={

    restrict expr to domain={rawx*CameraX + rawy*CameraY + rawz*CameraZ}{-0.05:100},

}}

pgfplotsset{only background/.style={

    restrict expr to domain={rawx*CameraX + rawy*CameraY + rawz*CameraZ}{-100:0.05}

}}



% Automatically plot transparent lines in background and solid lines in foreground

defaddFGBGplot[#1]#2;{

    addplot3[#1,only background, opacity=0.25] #2;

    addplot3[#1,only foreground] #2;

}



% attempt to do similar things for discrete plots

defaddFGBGSampleplot[#1]#2;{

    %addplot3[#1,only background,gray!50] #2;

    addplot3[#1,only foreground] #2;

}





newcommand{ViewAzimuth}{-30}

newcommand{ViewElevation}{30}



tikzset{spring/.style={decorate,decoration={coil,aspect=0.5,amplitude=1.5mm, segment

length=1.5mm}}}

% pgfmanual p. 1087

pgfdeclareradialshading{ballshading}{pgfpoint{-10bp}{10bp}}

 {color(0bp)=(cyan!15!white); color(9bp)=(cyan!75!white);

 color(18bp)=(cyan!70!black); color(25bp)=(cyan!50!black); color(50bp)=(black)}



pgfdeclareplotmark{crystal ball}{pgfpathcircle{pgfpoint{0ex}{0ex}}{2ex}

  pgfshadepath{ballshading}{0}

  pgfusepath{}}

begin{document}

begin{tikzpicture}

    % Compute camera unit vector for calculating depth

    pgfmathsetmacro{CameraX}{sin(ViewAzimuth)*cos(ViewElevation)}

    pgfmathsetmacro{CameraY}{-cos(ViewAzimuth)*cos(ViewElevation)}

    pgfmathsetmacro{CameraZ}{sin(ViewElevation)}

    pgfmathsetmacro{R}{12}

    path[use as bounding box] (-R,-R) rectangle (R,R); % Avoid jittering animation

    % Draw a nice looking sphere

    begin{scope}

        clip (0,0) circle (R);

        begin{scope}[transform canvas={rotate=-20}]

            shade [ball color=white] (0,0.5) ellipse (R*1.8 and R*1.5);

        end{scope}

    end{scope}

    begin{axis}[

        hide axis,

        view={ViewAzimuth}{ViewElevation},     % Set view angle

        every axis plot/.style={very thin},

        disabledatascaling,                      % Align PGFPlots coordinates with TikZ

        anchor=origin,                           % Align PGFPlots coordinates with TikZ

        viewport={ViewAzimuth}{ViewElevation}, % Align PGFPlots coordinates with TikZ

    ]

        % plot latitude circles

        pgfplotsinvokeforeach{-75,-45,...,75}

        {addFGBGplot[spring,domain=0:2*pi, samples=51, samples y=1]

        ({R*cos(#1)*cos(deg(x))}, {R*cos(#1)*sin(deg(x))}, {R*sin(#1)});}

        % plot longitude circles

        pgfplotsinvokeforeach{0,30,...,150}

        {addFGBGplot[spring,domain=0:2*pi, samples=51, samples y=1]

        ({R*cos(#1)*cos(deg(x))}, {R*sin(#1)*cos(deg(x))}, {R*sin(deg(x))});     

        }

        % plot longitude circles

        pgfplotsinvokeforeach{0,30,...,330}

        {addFGBGSampleplot[only marks,mark=crystal ball,samples at={-75,-45,...,75}]

        ({R*cos(#1)*cos(x)}, {R*sin(#1)*cos(x)}, {R*sin(x)});        

        }

    end{axis}

end{tikzpicture}

end{document}