Special Effects, Rotation

%
%   These macros allow you to rotate or flip a \TeX\ box.  Very useful for
%   sideways tables or upsidedown answers.
%
%   To use, create a box containing the information you want to rotate.
%   (An hbox or vbox will do.)  Now call \@rotr\boxnum to rotate the
%   material and create a new box with the appropriate (flipped) dimensions.
%   \@rotr rotates right, \@rotl rotates left, \@rotu turns upside down, and
%   \@rotf flips.  These boxes may contain other rotated boxes.
%
\newdimen\@rotdimen
\newbox\@rotbox

\def\@vspec#1{\special{ps:#1}}%  passes #1 verbatim to the output
\def\@rotstart#1{\@vspec{gsave currentpoint currentpoint translate
   #1 neg exch neg exch translate}}% #1 can be any origin-fixing transformation
\def\@rotfinish{\@vspec{currentpoint grestore moveto}}% gets back in synch
%
%   First, the rotation right. The reference point of the rotated box
%   is the lower right corner of the original box.
%
\def\@rotr#1{\@rotdimen=\ht#1\advance\@rotdimen by\dp#1%
   \hbox to\@rotdimen{\hskip\ht#1\vbox to\wd#1{\@rotstart{90 rotate}%
   \box#1\vss}\hss}\@rotfinish}
%
%   Next, the rotation left. The reference point of the rotated box
%   is the upper left corner of the original box.
%
\def\@rotl#1{\@rotdimen=\ht#1\advance\@rotdimen by\dp#1%
   \hbox to\@rotdimen{\vbox to\wd#1{\vskip\wd#1\@rotstart{270 rotate}%
   \box#1\vss}\hss}\@rotfinish}%
%
%   Upside down is simple. The reference point of the rotated box
%   is the upper right corner of the original box. (The box's height
%   should be the current font's xheight, \fontdimen5\font,
%   if you want that xheight to be at the baseline after rotation.)
%
\def\@rotu#1{\@rotdimen=\ht#1\advance\@rotdimen by\dp#1%
   \hbox to\wd#1{\hskip\wd#1\vbox to\@rotdimen{\vskip\@rotdimen
   \@rotstart{-1 dup scale}\box#1\vss}\hss}\@rotfinish}%
%
%   And flipped end for end is pretty ysae too. We retain the baseline.
%
\def\@rotf#1{\hbox to\wd#1{\hskip\wd#1\@rotstart{-1 1 scale}%
   \box#1\hss}\@rotfinish}%
%
%   Now the user interface for LaTeX:  \rotate[type]{text} where
%   ``type'' is `l' for left, `r' for right, `u' for upside-down, or
%   `f' for flip.  `l' is the default.
%
\def\rotate{\@ifnextchar[{\@rotate}{\@rotate[l]}}
\def\@rotate[#1]#2{\setbox\@rotbox=\hbox{#2}\@nameuse{@rot#1}\@rotbox}

%% LaTeX Macros for PostScript rotation of text
%% Sebastian Rahtz, Dept. of Computer Science, Southampton University
%%

%% 13-Mar-89 pad -  added "global" keyword to \special to stop
%%   dvi2ps from wrapping the rotated text
%%   up in @begin-, @start- and @endspecials.

%% these use the PostScript function /newram, defined in the PS header
%% file.

% environments to print text sideways

[...]

%% LaTeX Macros for PostScript rotation of text
%% Sebastian Rahtz, Dept. of Computer Science, Southampton University
%% Paul Barton-Davis, Dept. of Computer Science, University of Washington

%% 10-sep-91 pad -      added code supplied by Peter Bloomfield from
%%                      Tom Rockiki's dvips to eliminate dependence
%%                      on the prologue.
%%
%% 13-Mar-89 pad -  added "global" keyword to \special to stop
%%   dvi2ps from wrapping the rotated text
%%   up in @begin-, @start- and @endspecials.

%% \@verbps{TEXT} outputs TEXT directly to the DVI file, with no
%% surrounding context. Following are 3 definitions for 3 different
%% DVI->PostScript drivers. The key part of these is that the
%% \special's argument must NOT be enclosed in any context saving
%% mechanism. Each driver has a different method for specifying this.
%%
%% For Rockiki's dvips
%%
%\def\@verbps#1{\special{ps:#1}}
%%
%% For a modified dvi2ps that has the "global" modifier for pstext
%%
%\def\@verbps#1{\special{global pstext="#1"}}
%%
%% For Bechtolstein's dvitps
%%
\def\@verbps#1{\special{dvitps: Literal "#1"}}
%%
%% The box we put rotated text into
%%
\newsavebox{\swbox}\newlength{\spht}\newlength{\spwd}
%%
%% \begin{rotate}{DEGREES}
%% TEXT
%% \end{rotate}
%%
%% rotates TEXT by DEGREES, but puts TEXT into a box with zero size.
%%      Use this for special effects. The "turn" environment, below,
%%      is probably closer to what you want for normal rotation,
%%      because it calculates the correct box size.

\newenvironment{rotate}[1]{\def\rotangle{#1}\savebox{\swbox}\bgroup}{%
 \egroup
 \global\spwd=\dp\swbox
 \global\advance\spwd by \ht\swbox
 \global\spht=\wd\swbox%
 %% do the PostScript magic
 \@verbps{gsave currentpoint currentpoint translate
\rotangle\space rotate neg exch neg exch translate}%
 \dp\swbox=0pt\wd\swbox=0pt\ht\swbox=0pt%
 \usebox{\swbox}
 %% End the PostScript magic
 \@verbps{grestore}
}
%
% macros to calculate sines from 90 to -90
% Jim Walker,  Dept Mathematics,  University of South Carolina
%
\newdimen\x
\newdimen\y
\newdimen\xsquare
\newdimen\xfourth
{%
\catcode`\p=12
\catcode`\t=12
\gdef\numonly#1pt{%
\def\xx{#1}%
}%
}%
\def\MULTyBYx{%
\expandafter\numonly\the\x
\edef\b{\y=\xx\y}%
\b
}%
\def\calcsin{% Find sin(\x) and put it in \y. Say \x is in degrees.
\x=0.0174533\x % Convert to radians.
\y=\x
\MULTyBYx
\xsquare=\y
\MULTyBYx
\MULTyBYx
\xfourth=\y
\y=1pt
\advance\y by -0.1666666\xsquare
\advance\y by 0.008333333\xfourth
\MULTyBYx
}%
%
% Example of use:
%\x=23pt \calcsin \expandafter\numonly\the\y
% Now \xx should contain the sine of 23 degrees.
%
% given a box with width W and height H,  then its height after rotation by R
% is W * sin(R) + H * cos(R),  and it extends W * cos(R) to the right
% and H * sin(R) to the left
% (arithmetic courtesy of Nico Poppelier)
%
\newdimen\xh\newdimen\xw\newdimen\xtemp\newdimen\xcos\newdimen\xsin
\newdimen\xleft\newdimen\xright
\def\MULTxtempBYxcos{\expandafter\numonly\the\xcos\edef\b{\xtemp=\xx\xtemp}\b}%
\def\MULTxtempBYxsin{\expandafter\numonly\the\xsin\edef\b{\xtemp=\xx\xtemp}\b}%
%%
%%
%% \begin{turn}{DEGREES}
%% TEXT
%% \end{turn}
%%
%%     rotates TEXT by DEGREES, and puts into a box corresponding to
%%     the size of the rotated material. Use this to rotate text when
%%     you want the surrounding material to take account of the rotation.

\newenvironment{turn}[1]{\def\rotangle{#1}\savebox{\swbox}\bgroup}{%
 \egroup
 \global\spht=\dp\swbox
 \global\advance\spht by \ht\swbox
 \global\spwd=\wd\swbox%
 \xtemp=\rotangle pt % convert rotation to dimension
 \multiply\xtemp by -1
 \x=\xtemp\calcsin\xsin=\y
 \multiply\xtemp by -1\advance\xtemp by 90pt\x=\xtemp\calcsin\xcos=\y
 % \xsin =sin (R) and \xcos = cos(R)
 \xtemp=\spwd\MULTxtempBYxsin\xh=\xtemp
 \xtemp=\spht\MULTxtempBYxcos\advance\xh by \xtemp %\xh contains the height
 \xtemp=\spht\MULTxtempBYxsin\xleft=\xtemp
 \xtemp\spwd\MULTxtempBYxcos\xright=\xtemp % \xleft and \right are offsets
 \rule{\xleft}{0pt}%
 %% do the PostScript magic
 \@verbps{gsave currentpoint currentpoint translate
\rotangle\space rotate neg exch neg exch translate}%
 \dp\swbox=0pt\wd\swbox=0pt\ht\swbox=0pt%
 \rlap{\usebox{\swbox}}%
 \@verbps{grestore}
 \rlap{\rule{0pt}{\xh}}\rule{\xright}{0pt}%
}
%%
%%  Print it sideways
%%
\newenvironment{sideways}{\begin{turn}{-90}}{\end{turn}}