Who does not enjoy lego bricks, raise a hand! In this post, I am sharing an elegant and efficient way of plotting bricks under 3d view in TikZ. Briefly speaking, it utilizes canvas transforms to plot facets, and describes boundaries of studs in a simple way with cylindrical coordinates based on the azimuth angle (localizing extreme edges might be a challenge on its own).
While there are other packages, like TikZbricks, this method seems simpler in terms of complexity and brings some educational value in terms of cylinders geometry.
And here is the code (see also this online note)
\documentclass[12pt]{standalone}
\usepackage{pgfplots}
\usepackage{tikz-3dplot}
\begin{document}
\pgfmathsetmacro{\pinradius}{0.25}
% elevation and azimuth for 3D-view
\def\rotx{60}
\def\rotz{120}
\newcommand{\brick}[8]{
\pgfmathsetmacro{\posx}{#1}
\pgfmathsetmacro{\posy}{#2}
\pgfmathsetmacro{\posz}{#3}
\pgfmathsetmacro{\cubex}{#4}
\pgfmathsetmacro{\cubey}{#5}
\pgfmathsetmacro{\cubez}{#6}
% cube by rectangle facets
\begin{scope}
\begin{scope}[canvas is yx plane at z=\posz,transform shape]
\draw[fill=#8] (\posy,\posx) rectangle ++(\cubey,\cubex);
\end{scope}
\begin{scope}[canvas is yx plane at z=\posz+\cubez,transform shape]
\draw[fill=#8] (\posy,\posx) rectangle ++(\cubey,\cubex);
\end{scope}
\begin{scope}[canvas is yz plane at x=\posx+\cubex,transform shape]
\draw[fill=#8] (\posy,\posz) rectangle ++(\cubey,\cubez) node[pos=.5] {#7};
\end{scope}
\begin{scope}[canvas is xz plane at y=\posy+\cubey,transform shape]
\draw[fill=#8] (\posx,\posz) rectangle ++(\cubex,\cubez);
\end{scope}
\end{scope}
% studs by arcs and extreme edges
\foreach \i in {1,...,\cubey}{
\foreach \j in {1,...,\cubex}{
% upper part - full circle
\draw [thin] (\posx-0.5+\j,\posy-0.5+\i,\posz+\cubez+0.15) circle (\pinradius);
% lower part - arc
\begin{scope}[canvas is xy plane at z=\posz+\cubez]
\draw[thin] ([shift=(\rotz:\pinradius)] \posx-0.5+\j,\posy-0.5+\i) arc (\rotz:\rotz-180:\pinradius);
\end{scope}
\begin{scope}[shift={(\posx-0.5+\j,\posy-0.5+\i)}]
% edges easily identified in cylindrical coordinates!
\pgfcoordinate{edge1_top}{ \pgfpointcylindrical{\rotz}{\pinradius}{\posz+\cubez+0.15} };
\pgfcoordinate{edge1_bottom}{ \pgfpointcylindrical{\rotz}{\pinradius}{\posz+\cubez} };
\draw[] (edge1_top) -- (edge1_bottom);
\pgfcoordinate{edge1_top}{ \pgfpointcylindrical{\rotz+180}{\pinradius}{\posz+\cubez+0.15} };
\pgfcoordinate{edge1_bottom}{ \pgfpointcylindrical{\rotz+180}{\pinradius}{\posz+\cubez} };
\draw[] (edge1_top) -- (edge1_bottom);
\end{scope}
}
}
}
\tdplotsetmaincoords{\rotx}{\rotz}
\begin{tikzpicture}[tdplot_main_coords,]
% draw axes
\coordinate (O) at (0,0,0);
\coordinate (A) at (5,0,0);
\coordinate (B) at (0,5,0);
\coordinate (C) at (0,0,5);
\draw[-latex] (O) -- (A) node[below] {$x$};
\draw[-latex] (O) -- (B) node[above] {$y$};
\draw[-latex] (O) -- (C) node[left] {$z$};
% draw brick
\brick{0}{1}{0}{3}{3}{1}{Lego}{blue!50};
\brick{0}{1}{2}{2}{3}{1}{Enjoys}{green!50};
\brick{0}{1}{4}{1}{3}{1}{Everybody}{red!50};
\end{tikzpicture}
\end{document}
