\documentclass{article} \usepackage{graphicx} \title{The \texttt{threeddice} package} \author{Dan Luecking} \date{2010/11/30} \begin{document} \catcode`_=12 {\catcode`\_=\active \global\let_\sb} \maketitle \section{Introduction} Running \texttt{mpost} on \texttt{threeddice.mp} produces 26 figure files. Six of them are are \texttt{die3d-1.mps}% \footnote{If your \texttt{mpost} version is less that 0.9, you will get figure files with names like \texttt{threeddice.1}. You should update your \TeX{} system.} through \texttt{die3d-6.mps}. These are pictures of a single die face with the number of dots indicated by the numerical part. Three of these would look the same if rotated by multiples of $90$ degrees. The other three could look different. It is up to the users to perform this rotation if they want a different view. The twelve files with 2-digit numerical part are 3D pictures of dice with two faces showing, as if your were looking directly at a horizontal edge. You will have to rotate it $\pm90$ degrees if you want the edge to be vertical, or $180$ degrees if you prefer the positions of the top and front face to be exchanged. The eight files with 3-digit numerical suffix are 3D pictures of dice with three faces showing, as if your were looking directly at one of the corners. They show a top face and a left and right face flanking a vertical edge. You can get 16 other views by rotating them $\pm120$ degrees. These rotations put one of the side faces on top. \section{Modifications} These figures were taken from an actual right handed die, and are all the permissable views of such a die, apart from size of dots and the actual orientation of the patterns of dots. As near as I could determine from internet searches, there are no official standards for the following. \begin{itemize} \item The 2-spot face has dots in opposite corners, but which two corners? On my die, if the 1-spot is on top, the 2-spot to the left and the 3-spot to the right (figure \texttt{die3d-123.mps}), the dots on the 2-spot face are in upper left and lower right. It seems it could just as well have been the other two corners. \item Similar question for the 3-spot face: three dots in a diagonal between opposite corners, but which two corners? In the previous example (figure \texttt{die3d-123.mps}), the diagonal is from lower left to upper right. \item The 6-spot face has two lines of three, parallel to two edges, but which two edges? In \texttt{die3d-246.mps} the lines of dots are horizontal, but it seems they could just as well have been vertical. \end{itemize} If you want some other orientation of these faces you will need to edit \texttt{threeddice.mp}: for the 2-spot face exchange the definitions of \texttt{pips2} and \texttt{pips7}; for the 3-spot face exchange \texttt{pips3} and \texttt{pips8}; for the 6-spot face exchange \texttt{pips6} and \texttt{pips11}. You can also change the size of the dots by giving a different value to \texttt{dot_diam}. The dice have rounded corners, you can change their radius by changing \texttt{corner_rad}. The dots are placed so there is at least \texttt{face_margin} of space between the dots and the straight edge of the face. You can change this variable as well. For other effects, you are on your own. A common requirement is that faces with fewer dots have larger dots. This is relatively easy to do, but requires changing the definitions of the 9 picture variables \texttt{pips1} through \texttt{pips11}. Naturally, the \texttt{graphics} and \texttt{graphicx} packages let you scale these as you want. If you would prefer to change the unscaled sizes, edit \texttt{threeddice.mp} to change \texttt{die_size} from 1cm to the desired size. Finally, to get views of a left-handed die, simply reflect the views of the right-handed die. \section{Appendix} \parindent 0pt These are the six single faces: \bigskip \includegraphics{die3d-1.mps}\quad \includegraphics{die3d-2.mps}\quad \includegraphics{die3d-3.mps}\quad \includegraphics{die3d-4.mps}\quad \includegraphics{die3d-5.mps}\quad \includegraphics{die3d-6.mps} \bigskip \filbreak The two-faced dice are ugly, so let me first show you the eight three-faced dice: \bigskip \includegraphics{die3d-123.mps}\quad \includegraphics{die3d-135.mps}\quad \includegraphics{die3d-142.mps}\quad \includegraphics{die3d-154.mps} \bigskip \includegraphics{die3d-246.mps}\quad \includegraphics{die3d-263.mps}\quad \includegraphics{die3d-365.mps}\quad \includegraphics{die3d-456.mps} \bigskip \filbreak Finally, the twelve two-faced dice: \bigskip \includegraphics{die3d-12.mps}\quad \includegraphics{die3d-13.mps}\quad \includegraphics{die3d-14.mps}\quad \includegraphics{die3d-15.mps}\quad \includegraphics{die3d-23.mps}\quad \includegraphics{die3d-24.mps} \bigskip \includegraphics{die3d-26.mps}\quad \includegraphics{die3d-35.mps}\quad \includegraphics{die3d-36.mps}\quad \includegraphics{die3d-45.mps}\quad \includegraphics{die3d-46.mps}\quad \includegraphics{die3d-56.mps} \filbreak \end{document}