General ⇒ shear macros: rotatebox and scalebox are so primitive

[brac37]

rotatebox and scalebox are macros of the graphicx package. They are primitive in both senses, i.e. they are (1) limited and (2) generating.

Ok, that was the theoretical part. The practical part consists of two macros built on rotatebox and scalebox.

Code: Select all

\usepackage{graphicx}

%\hshearbox{vertical_prescale_times_shearfactor}{one_divide_by_shearfactor}{content}
% an initial vertical downscale is often necessary for a 3d projection
\newcommand{\hshearbox}[3]{\scalebox{0.866025}[#2]{\rotatebox{210}%
{\scalebox{1.73205}[-0.57735]{\rotatebox{60}{\scalebox{-1.1547}[#1]{#3}}}}}}

%\vshearbox{horizontal_prescale_times_shearfactor}{one_divide_by_shearfactor}{content}
% an initial horizontal downscale is often necessary for a 3d projection
\newcommand{\vshearbox}[3]{\scalebox{#2}[0.866025]{\rotatebox{210}%
{\scalebox{-0.57735}[1.73205]{\rotatebox{60}{\scalebox{#1}[-1.1547]{#3}}}}}}

One can use the fp package if one is to lazy for elementary computations.

But maybe, there is a more direct way to do shear transforms.

[brac37]

Here is an example.

Code: Select all

\documentclass{article}

\usepackage{graphicx,pstricks}

%\hshearbox{vertical_prescale_times_shearfactor}{one_divide_by_shearfactor}{content}
% an initial vertical downscale is often necessary for a 3d projection
\newcommand{\hshearbox}[3]{\scalebox{0.866025}[#2]{\rotatebox{210}%
{\scalebox{1.73205}[-0.57735]{\rotatebox{60}{\scalebox{-1.1547}[#1]{#3}}}}}}
%\vshearbox{horizontal_prescale_times_shearfactor}{one_divide_by_shearfactor}{content}
% an initial horizontal downscale is often necessary for a 3d projection
\newcommand{\vshearbox}[3]{\scalebox{#2}[0.866025]{\rotatebox{210}%
{\scalebox{-0.57735}[1.73205]{\rotatebox{60}{\scalebox{#1}[-1.1547]{#3}}}}}}

\newcommand{\tilenamebox}[1]{\rput[B]{0}(0,-2.5pt){$#1$}}
\newcommand{\tilestack}[3]{\begin{array}{@{}c@{}}\begin{picture}(42,55)(4,0)
\put(25,50){\hshearbox{0.333333}{1}{\tilenamebox{#1}}}
\put(20,37.5){\tilenamebox{#1}}
\put(40,42.5){\vshearbox{-0.333333}{-1}{\tilenamebox{#1}}}
\put(20,22.5){\tilenamebox{#2}}
\put(40,27.5){\vshearbox{-0.333333}{-1}{\tilenamebox{#2}}}
\put(20,07.5){\tilenamebox{#3}}
\put(40,12.5){\vshearbox{-0.333333}{-1}{\tilenamebox{#3}}}
\multiput(5,0)(0,15){4}{\line(1,0){30}\line(1,1){10}}
\put(05,45){\line(0,-3){45}\line(1,1){10}}
\put(35,45){\line(0,-3){45}}
\put(15,55){\line(1,0){30}\line(0,-1){45}}
\multiput(9,46)(2,0){13}{\hshearbox{1}{1}{\makebox(0,0)[lb]{\line(0,1){1.5}}}}
\multiput(17,54)(2,0){13}{\hshearbox{1}{1}{\makebox(0,0)[rt]{\line(0,-1){1.5}}}}
\end{picture}\end{array}}

\begin{document}
$$
\tilestack{y}{a}{b} \qquad \mbox{and} \qquad \tilestack{b}{a}{y}
$$
\end{document}