Drawing balls in a rectangle

Question

I am trying to replicate the following figure here

and this is what I have so far

\documentclass[12pt,a4paper]{standalone}

\usepackage{tikz,tkz-euclide,pgfplots}
\usetkzobj{all}
\newcommand{\ball}[2]{%
        \begin{scope}[shift = {(#1,#2)}
            \fill[red] (0,0) circle (0.5);
            \clip (0,0) circle (0.5);
            \shade[shading=ball,ball color=white,1] (0.15,0.25) circle (0.7);
        \end{scope}}

\begin{document}%

    \begin{tikzpicture}     
        \def\height{0.75}
        \def\length{3}

        \tkzDefPoint(0,0){A}         \tkzDefPoint(0.9*\length,-\height){B}
        \tkzDefPoint(2*\length,0){C} \tkzDefPoint(1.1*\length, \height){D}
        \tkzDrawPolygon(A,B,C,D)

        \begin{scope}[shift={(0,2)}]
                \tkzDefPoint(0,0){A1}         \tkzDefPoint(0.9*\length,-\height){B1}
                \tkzDefPoint(2*\length,0){C1} \tkzDefPoint(1.1*\length, \height){D1}
                \tkzDrawPolygon(A1,B1,C1,D1)
        \end{scope}

        \tkzDrawSegments(A,A1 B1,B C1,C D1,D);  
%               \ball{2}{2}
    \end{tikzpicture}
\end{document}

By using the tips I got from this question. I think I almost got it, but the code will not compile when uncommenting the last line. What is the reason for this?

Other means create this image would also appreciated, it is always refreshing to see different approaches to a problem.

Answer 1

A possible solution:

\documentclass[png,border=10pt,tikz]{standalone}

\usepackage{tikz,tkz-euclide,pdftexcmds}
\usetikzlibrary{backgrounds}
\pgfdeclarelayer{foreground}
\pgfsetlayers{background,main,foreground}
\usetkzobj{all}

\makeatletter

\pgfdeclareradialshading[tikz@ball]{my ball}{\pgfqpoint{5bp}{10bp}}{%
 color(0bp)=(tikz@ball!10!white);
 color(8bp)=(tikz@ball!65!white);
 color(12bp)=(tikz@ball);
 color(25bp)=(tikz@ball!70!black);
 color(50bp)=(black)}

\pgfdeclareradialshading[tikz@ball]{new ball}{\pgfqpoint{12bp}{12bp}}{%
 color(0cm)=(tikz@ball!10!white);
 color(0.5cm)=(tikz@ball!50!white);
 color(0.75cm)=(tikz@ball);
 color(0.9cm)=(tikz@ball!80!black);
 color(1cm)=(tikz@ball!60!black)} 

% code by percusse:
% https://tex.stackexchange.com/a/74237/13304
\pgfdeclareradialshading{ball shadow}{\pgfpointorigin}%
{color(0cm)=(black);
color(2mm)=(gray!70);
color(3mm)=(gray!30);
color(7mm)=(white)
} 

 % to make possible use "myball color=..." 
\tikzoption{my ball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{my ball}\tikz@addmode{\tikz@mode@shadetrue}}

\tikzoption{new ball color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{new ball}\tikz@addmode{\tikz@mode@shadetrue}}

\tikzoption{ball shadow color}{\pgfutil@colorlet{tikz@ball}{#1}\def\tikz@shading{ball shadow}\tikz@addmode{\tikz@mode@shadetrue}}


\newcommand{\ball}[3][white]{%
        \begin{scope}[shift = {(#2,#3)}]
          \node[shading=ball shadow,xscale=2,yscale=0.3,circle,minimum size=7mm] 
            at (0.15,-0.225){};
          % test to decide which shading use: special one for white balls
          % not 100% efficient: maybe it's better to use directly a custom
          % white ball shading, but this way one could always use 
          % "my ball color=green" say
          \ifnum\pdf@strcmp{#1}{white}=\z@%  
            \shade[my ball color=#1] (0.15,0.25) circle (0.5);
          \else
            \shade[new ball color=#1] (0.15,0.25) circle (0.5);
          \fi
        \end{scope}
}
\makeatother

\begin{document}%

\begin{tikzpicture}     
    \def\height{0.75}
    \def\length{3}

    \tkzDefPoint(0,0){A}         \tkzDefPoint(0.9*\length,-1.1\height){B}
    \tkzDefPoint(1.9*\length,0){C} \tkzDefPoint(1.1*\length, \height){D}
    %\tkzDrawPolygon(A,B,C,D) % Beware to put the right segments in foreground
    % now this can not be a polygon: need to be split
    % Same would apply to the shifted one if the balls touch the upper layer
    \tkzDrawSegments(C,D D,A);

    \begin{scope}[shift={(0,2)}]
            \tkzDefPoint(0,0){A1}\tkzDefPoint(0.9*\length,-\height){B1}
            \tkzDefPoint(1.9*\length,0){C1} \tkzDefPoint(1.1*\length, \height){D1}
            \tkzDrawPolygon(A1,B1,C1,D1)
    \end{scope}

    \tkzDrawSegments(A,A1 C1,C D1,D);
    \begin{pgfonlayer}{foreground}
      \tkzDrawSegments(B,B1);
      % other segments in foreground
      \tkzDrawSegments(A,B B,C);
    \end{pgfonlayer}

    % balls: beware the order matters
    \ball{1}{0.15}
    \ball[orange]{2.6}{0.35}
    \ball{1.85}{-0.2}
    \ball[orange]{4.3}{0.25}
    \ball[orange]{3.425}{-0.1}
\end{tikzpicture}
\end{document}

The result:

The tricks are:

• define the shading in a similar way as How to shade mindmap concepts? so that the \ball command, besides the usual capability of being shifted, can also set the color;
• draw specific segments, like the segment B,B1 in the foreground layer: in such a way balls seem to be in background;
• draw the balls with a precise order: to not use too much the pgfonlayer enviroment, the simplest thing to do is to first draw the balls behind, proceeding then with the other ones.