l3kernel 2678 (28aug11)

git-svn-id: svn://tug.org/texlive/trunk@23738 c570f23f-e606-0410-a88d-b1316a301751

1 files changed, 1983 insertions, 0 deletions

diff --git a/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
new file mode 100644
index 00000000000..87df9402d1d
--- /dev/null
+++ b/Master/texmf-dist/source/latex/l3kernel/l3coffins.dtx
@@ -0,0 +1,1983 @@
+% \iffalse meta-comment
+% 
+%% File: l3coffins.dtx Copyright(C) 2010,2011 The LaTeX3 Project
+%%
+%% It may be distributed and/or modified under the conditions of the
+%% LaTeX Project Public License (LPPL), either version 1.3c of this
+%% license or (at your option) any later version.  The latest version
+%% of this license is in the file
+%%
+%%    http://www.latex-project.org/lppl.txt
+%%
+%% This file is part of the "l3kernel bundle" (The Work in LPPL)
+%% and all files in that bundle must be distributed together.
+%%
+%% The released version of this bundle is available from CTAN.
+%%
+%% -----------------------------------------------------------------------
+%%
+%% The development version of the bundle can be found at
+%%
+%%    http://www.latex-project.org/svnroot/experimental/trunk/
+%%
+%% for those people who are interested.
+%%
+%%%%%%%%%%%
+%% NOTE: %%
+%%%%%%%%%%%
+%%
+%%   Snapshots taken from the repository represent work in progress and may
+%%   not work or may contain conflicting material!  We therefore ask
+%%   people _not_ to put them into distributions, archives, etc. without
+%%   prior consultation with the LaTeX Project Team.
+%%
+%% -----------------------------------------------------------------------
+%%
+%
+%<*driver|package>
+\RequirePackage{l3names,graphicx,color}
+\GetIdInfo$Id: l3coffins.dtx 2624 2011-08-18 19:02:45Z joseph $
+  {L3 Experimental coffin code layer}
+%</driver|package>
+%<*driver>
+\documentclass[full]{l3doc}
+\begin{document}
+  \DocInput{\jobname.dtx}
+\end{document}
+%</driver>
+% \fi
+% 
+% \title{^^A
+%   The \textsf{l3coffins} package\\ Coffin code layer^^A
+%   \thanks{This file describes v\ExplFileVersion,
+%     last revised \ExplFileDate.}^^A
+% }
+%         
+% \author{^^A
+%  The \LaTeX3 Project\thanks
+%    {^^A
+%      E-mail:
+%        \href{mailto:latex-team@latex-project.org}
+%          {latex-team@latex-project.org}^^A
+%    }^^A
+% }
+%
+% \date{Released \ExplFileDate}
+%
+% \maketitle
+%
+% \begin{documentation}
+%
+% The material in this module provides the low-level support system
+% for coffins. For details about the design concept of a coffin, see
+% the \pkg{xcoffins} module (in the \pkg{l3experimental} bundle).
+%
+% \section{Code-level coffin functions}
+% 
+% \begin{function}{\coffin_new:N, \coffin_new:c}
+%   \begin{syntax}
+%     \cs{coffin_new:N} \meta{coffin}
+%   \end{syntax}
+%   Creates a new \meta{coffin} or raises an error if the name is
+%   already taken. The declaration is global. The \meta{coffin} will 
+%   initially be empty.
+% \end{function}
+%
+% \begin{function}{\coffin_clear:N, \coffin_clear:c}
+%   \begin{syntax}
+%     \cs{coffin_clear:N} \meta{coffin}
+%   \end{syntax}
+%   Clears the content of the \meta{coffin} within the current \TeX{}
+%   group level.
+% \end{function}
+%
+%\begin{function}
+%  {\coffin_set_eq:NN, \coffin_set_eq:Nc, \coffin_set_eq:cN, \coffin_set_eq:cc}
+%   \begin{syntax}
+%    \cs{coffin_set_eq:NN} \meta{coffin1} \meta{coffin2}
+%   \end{syntax}
+%   Sets both the content and poles of \meta{coffin1} equal to those
+%   of \meta{coffin2} within the current \TeX\ group level.
+% \end{function}
+%
+% \begin{function}{\hcoffin_set:Nn, \hcoffin_set:cn}
+%   \begin{syntax}
+%     \cs{hcoffin_set:Nn} \meta{coffin} \Arg{material}
+%   \end{syntax}
+%   Typesets the \meta{material} in horizontal mode, storing the result
+%   in the \meta{coffin}. The standard poles for the \meta{coffin} are
+%   then set up based on the size of the typeset material.
+% \end{function}
+%
+% \begin{function}{\vcoffin_set:Nnn, \vcoffin_set:cnn}
+%   \begin{syntax}
+%     \cs{vcoffin_set:Nnn} \meta{coffin} \Arg{width} \Arg{material}
+%   \end{syntax}
+%   Typesets the \meta{material} in vertical mode constrained to the
+%   given \meta{width} and stores the result in the \meta{coffin}. The
+%   standard poles for the \meta{coffin} are then set up based on the 
+%   size of the typeset material.
+% \end{function}
+%
+% \begin{function}
+%   {\coffin_set_horizontal_pole:Nnn, \coffin_set_horizontal_pole:cnn}
+%   \begin{syntax}
+%     \cs{coffin_set_horizontal_pole:Nnn} \meta{coffin} 
+%     ~~\Arg{pole} \Arg{offset}
+%   \end{syntax}
+%   Sets the \meta{pole} to run horizontally through the \meta{coffin}.
+%   The \meta{pole} will be located at the \meta{offset} from the
+%   bottom edge of the bounding box of the \meta{coffin}. The
+%   \meta{offset} should be given as a dimension expression; this may
+%   include the terms \cs{TotalHeight}, \cs{Height}, \cs{Depth} and 
+%   \cs{Width}, which will evaluate to the appropriate dimensions of 
+%   the \meta{coffin}.
+% \end{function}
+%
+% \begin{function}
+%   {\coffin_set_vertical_pole:Nnn, \coffin_set_vertical_pole:cnn}
+%   \begin{syntax}
+%     \cs{coffin_set_vertical_pole:Nnn} \meta{coffin} 
+%     ~~\Arg{pole} \Arg{offset}
+%   \end{syntax}
+%   Sets the \meta{pole} to run vertically through the \meta{coffin}.
+%   The \meta{pole} will be located at the \meta{offset} from the
+%   left-hand edge of the bounding box of the \meta{coffin}. The
+%   \meta{offset} should be given as a dimension expression; this may
+%   include the terms \cs{TotalHeight}, \cs{Height}, \cs{Depth} and 
+%   \cs{Width}, which will evaluate to the appropriate dimensions of 
+%   the \meta{coffin}.
+% \end{function}
+%
+% \begin{function}{\coffin_rotate:Nn, \coffin_rotate:cn}
+%   \begin{syntax}
+%     \cs{coffin_rotate:Nn} \meta{coffin} \Arg{angle}
+%   \end{syntax}
+%   Rotates the \meta{coffin} by the given \meta{angle} (given in
+%   degrees counter-clockwise). This process will rotate both the
+%   coffin content and poles. Multiple rotations will not result in 
+%   the bounding box of the coffin growing unnecessarily.
+% \end{function}
+%
+% \begin{function}
+%   { 
+%     \coffin_attach:NnnNnnnn, \coffin_attach:cnnNnnnn,
+%     \coffin_attach:Nnncnnnn, \coffin_attach:cnncnnnn
+%   }
+%   \begin{syntax}
+%     \cs{coffin_attach:NnnNnnnn} 
+%     ~~\meta{coffin1} \Arg{coffin1-pole1} \Arg{coffin1-pole2}
+%     ~~\meta{coffin2} \Arg{coffin2-pole1} \Arg{coffin2-pole2}
+%     ~~\Arg{x-offset} \Arg{y-offset}
+%   \end{syntax}
+%   This function carries out alignment such that the bounding box
+%   of \meta{coffin1} is not altered, \emph{i.e.}~\meta{coffin2} can
+%   protrude outside of the bounding box of the coffin. The alignment 
+%   is carried out by first calculating \meta{handle1}, the
+%   point of intersection of \meta{coffin1-pole1} and 
+%   \meta{coffin1-pole2}, and \meta{handle2}, the point of intersection
+%   of \meta{coffin2-pole1} and \meta{coffin2-pole2}. \meta{coffin2} is
+%   then attached to \meta{coffin1} such that the relationship between
+%   \meta{handle1} and \meta{handle2} is described by the \meta{x-offset}
+%   and \meta{y-offset}. The two offsets should be given as dimension
+%   expressions.
+% \end{function}
+%
+% \begin{function}
+%   { 
+%     \coffin_join:NnnNnnnn, \coffin_join:cnnNnnnn,
+%     \coffin_join:Nnncnnnn, \coffin_join:cnncnnnn
+%   }
+%   \begin{syntax}
+%     \cs{coffin_join:NnnNnnnn} 
+%     ~~\meta{coffin1} \Arg{coffin1-pole1} \Arg{coffin1-pole2}
+%     ~~\meta{coffin2} \Arg{coffin2-pole1} \Arg{coffin2-pole2}
+%     ~~\Arg{x-offset} \Arg{y-offset}
+%   \end{syntax}
+%   This function carries out alignment such that the bounding box
+%   of \meta{coffin1} after the process will expand. The new bounding
+%   box will cover the area contain the bounding boxes of the two 
+%   original coffins. The alignment is carried out by first calculating
+%   \meta{handle1}, the point of intersection of \meta{coffin1-pole1} and
+%   \meta{coffin1-pole2}, and \meta{handle2}, the point of intersection
+%   of \meta{coffin2-pole1} and \meta{coffin2-pole2}. \meta{coffin2} is
+%   then attached to \meta{coffin1} such that the relationship between
+%   \meta{handle1} and \meta{handle2} is described by the \meta{x-offset}
+%   and \meta{y-offset}. The two offsets should be given as dimension
+%   expressions.
+% \end{function}
+%
+% \begin{function}{\coffin_typeset:Nnnnn, \coffin_typeset:cnnnn}
+%   \begin{syntax}
+%     \cs{coffin_typeset:Nnnnn} \meta{coffin} \Arg{pole1} \Arg{pole2}
+%     ~~\Arg{x-offset} \Arg{y-offset}
+%   \end{syntax}
+%   Typesetting is carried out by first calculating \meta{handle}, the
+%   point of intersection of \meta{pole1} and \meta{pole2}. The coffin
+%   is then typeset such that the relationship between the current 
+%   reference point in the document and the \meta{handle} is described
+%   by the \meta{x-offset} and \meta{y-offset}. The two offsets should 
+%   be given as dimension expressions. Typesetting a coffin is 
+%   therefore analogous to carrying out an alignment where the 
+%   \enquote{parent} coffin is the current insertion point.
+% \end{function}
+%
+% \begin{function}{\coffin_display_handles:cn, \coffin_display_handles:cn}
+%   \begin{syntax}
+%     \cs{coffin_display_handles:Nn} \meta{coffin} \Arg{colour}
+%   \end{syntax}
+%   This function first calculates the intersections between all of
+%   the \meta{poles} of the \meta{coffin} to give a set of 
+%   \meta{handles}. It then prints the  \meta{coffin} at the current 
+%   location in the source, with the  position of the \meta{handles} 
+%   marked on the coffin. The \meta{handles} will be labelled as part 
+%   of this process: the locations of the \meta{handles} and the labels 
+%   are both printed in the \meta{colour} specified.
+% \end{function}
+%
+% \begin{function}{\coffin_mark_handle:Nnnn, \coffin_mark_handle:cnnn}
+%   \begin{syntax}
+%     \cs{coffin_mark_handle:Nnnn} \meta{coffin} \Arg{pole1} \Arg{pole2}
+%     ~~\Arg{colour}
+%   \end{syntax}
+%   This function first calculates the \meta{handle} for the 
+%   \meta{coffin} as defined by the intersection of \meta{pole1} and
+%   \meta{pole2}. It then marks the position of the \meta{handle} 
+%   on the \meta{coffin}. The \meta{handle} will be labelled as part of
+%   this process: the location of the \meta{handle} and the label are
+%   both printed in the \meta{colour} specified.
+% \end{function}
+%
+% \begin{function}{\coffin_show_structure:N, \coffin_show_structure:c}
+%   \begin{syntax}
+%     \cs{coffin_show_structure:N} \meta{coffin}
+%   \end{syntax}
+%   This function shows the structural information about the
+%   \meta{coffin} in the terminal. The width, height and depth of the 
+%   typeset material are given, along with the location of all of the 
+%   poles of the coffin. 
+%  
+%   Notice that the poles of a coffin are defined by four values:
+%   the $x$ and $y$ co-ordinates of a point that the pole 
+%   passes through and the $x$- and $y$-components of a 
+%   vector denoting the direction of the pole. It is the ratio between
+%   the later, rather than the absolute values, which determines the
+%   direction of the pole.
+% \end{function}
+%
+% \end{documentation}
+%
+% \begin{implementation}
+%
+% \section{\pkg{l3coffins} Implementation}
+% 
+%    \begin{macrocode}
+%<*initex|package>
+%    \end{macrocode}
+%    
+%    \begin{macrocode}
+%<*package>
+\ProvidesExplPackage
+  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
+\package_check_loaded_expl:
+%</package>
+%    \end{macrocode}
+%
+% \subsection{Coffins: data structures and general variables}
+%
+% \begin{variable}{\l_coffin_tmp_box}
+% \begin{variable}{\l_coffin_tmp_dim}
+% \begin{variable}{\l_coffin_tmp_fp}
+% \begin{variable}{\l_coffin_tmp_tl}
+%   Scratch variables.
+%    \begin{macrocode}
+\box_new:N \l_coffin_tmp_box
+\dim_new:N \l_coffin_tmp_dim
+\fp_new:N  \l_coffin_tmp_fp
+\tl_new:N  \l_coffin_tmp_tl
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\c_coffin_corners_prop}
+%   The \enquote{corners}; of a coffin define the real content, as 
+%   opposed to the \TeX{} bounding box. They all start off in the same
+%   place, of course.
+%    \begin{macrocode}
+\prop_new:N \c_coffin_corners_prop
+\prop_put:Nnn \c_coffin_corners_prop { tl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_coffin_corners_prop { tr } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_coffin_corners_prop { bl } { { 0 pt } { 0 pt } }
+\prop_put:Nnn \c_coffin_corners_prop { br } { { 0 pt } { 0 pt } }
+%    \end{macrocode}
+% \end{variable}
+% 
+% \begin{variable}{\c_coffin_poles_prop}
+%   Pole positions are given for horizontal, vertical and reference-point
+%   based values.
+%    \begin{macrocode}
+\prop_new:N \c_coffin_poles_prop
+\tl_set:Nn \l_coffin_tmp_tl { { 0 pt } { 0 pt } { 0 pt } { 1000 pt } }
+\prop_put:Nno \c_coffin_poles_prop { l }  { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { hc } { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { r }  { \l_coffin_tmp_tl }
+\tl_set:Nn \l_coffin_tmp_tl { { 0 pt } { 0 pt } { 1000 pt } { 0 pt } }
+\prop_put:Nno \c_coffin_poles_prop { b }  { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { vc } { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { t }  { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { B }  { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { H }  { \l_coffin_tmp_tl }
+\prop_put:Nno \c_coffin_poles_prop { T }  { \l_coffin_tmp_tl }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_calc_a_fp}
+% \begin{variable}{\l_coffin_calc_b_fp}
+% \begin{variable}{\l_coffin_calc_c_fp}
+% \begin{variable}{\l_coffin_calc_d_fp}
+% \begin{variable}{\l_coffin_calc_result_fp}
+%   Used for calculations of intersections and in other internal places.
+%    \begin{macrocode}
+\fp_new:N \l_coffin_calc_a_fp
+\fp_new:N \l_coffin_calc_b_fp
+\fp_new:N \l_coffin_calc_c_fp
+\fp_new:N \l_coffin_calc_d_fp
+\fp_new:N \l_coffin_calc_result_fp
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_error_bool}
+%   For propagating errors so that parts of the code can work around them.
+%    \begin{macrocode}
+\bool_new:N \l_coffin_error_bool
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_offset_x_dim}
+% \begin{variable}{\l_coffin_offset_y_dim}
+%   The offset between two sets of coffin handles when typesetting. These
+%   values are corrected from those requested in an alignment for the
+%   positions of the handles.
+%    \begin{macrocode}
+\dim_new:N \l_coffin_offset_x_dim
+\dim_new:N \l_coffin_offset_y_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_pole_a_tl}
+% \begin{variable}{\l_coffin_pole_b_tl}
+%   Needed for finding the intersection of two poles.
+%    \begin{macrocode}
+\tl_new:N \l_coffin_pole_a_tl
+\tl_new:N \l_coffin_pole_b_tl
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_sin_fp}
+% \begin{variable}{\l_coffin_cos_fp}
+%   Used for rotations to get the sine and cosine values.
+%    \begin{macrocode}
+\fp_new:N \l_coffin_sin_fp
+\fp_new:N \l_coffin_cos_fp
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_x_dim}
+% \begin{variable}{\l_coffin_y_dim}
+% \begin{variable}{\l_coffin_x_prime_dim}
+% \begin{variable}{\l_coffin_y_prime_dim}
+%   For calculating intersections and so forth.
+%    \begin{macrocode}
+\dim_new:N \l_coffin_x_dim
+\dim_new:N \l_coffin_y_dim
+\dim_new:N \l_coffin_x_prime_dim
+\dim_new:N \l_coffin_y_prime_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_x_fp}
+% \begin{variable}{\l_coffin_y_fp}
+% \begin{variable}{\l_coffin_x_prime_fp}
+% \begin{variable}{\l_coffin_y_prime_fp}
+%   Used for calculations where there are clear $x$- and 
+%   $y$-components, for example during vector rotation.
+%    \begin{macrocode}
+\fp_new:N \l_coffin_x_fp
+\fp_new:N \l_coffin_y_fp
+\fp_new:N \l_coffin_x_prime_fp
+\fp_new:N \l_coffin_y_prime_fp
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_Depth_dim}
+% \begin{variable}{\l_coffin_Height_dim}
+% \begin{variable}{\l_coffin_TotalHeight_dim}
+% \begin{variable}{\l_coffin_Width_dim}
+%   Dimensions for the various parts of a coffin.
+%    \begin{macrocode}
+\dim_new:N \l_coffin_Depth_dim
+\dim_new:N \l_coffin_Height_dim
+\dim_new:N \l_coffin_TotalHeight_dim
+\dim_new:N \l_coffin_Width_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{macro}{\coffin_saved_Depth:}
+% \begin{macro}{\coffin_saved_Height:}
+% \begin{macro}{\coffin_saved_TotalHeight:}
+% \begin{macro}{\coffin_saved_Width:}
+%   Used to save the meaning of \cs{Depth}, \cs{Height}, \cs{TotalHeight}
+%   and \cs{Width}.
+%    \begin{macrocode}
+\cs_new_nopar:Npn \coffin_saved_Depth:       { }
+\cs_new_nopar:Npn \coffin_saved_Height:      { }
+\cs_new_nopar:Npn \coffin_saved_TotalHeight: { }
+\cs_new_nopar:Npn \coffin_saved_Width:       { }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Basic coffin functions}
+%
+% There are a number of basic functions needed for creating coffins and
+% placing material in them. This all relies on the following data
+% structures.
+%
+% \begin{macro}{\coffin_if_exist:NT}
+%   Several of the higher-level coffin functions will give multiple
+%   errors if the coffin does not exist. A cleaner way to handle this
+%   is provided here: both the box and the coffin structure are
+%   checked.
+%    \begin{macrocode}
+\cs_new_protected:Npn \coffin_if_exist:NT #1#2
+  {
+    \cs_if_exist:NTF #1
+      {
+        \cs_if_exist:cTF { l_coffin_poles_ \int_value:w #1 _prop }
+          { #2 }
+          { 
+            \msg_kernel_error:nnx { coffin } { unknown-coffin }
+              { \token_to_str:N #1 }
+          }
+      }
+      {
+        \msg_kernel_error:nnx { coffin } { unknown-coffin }
+          { \token_to_str:N #1 }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\coffin_clear:N, \coffin_clear:c}
+%   Clearing coffins means emptying the box and resetting all of the
+%   structures.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_clear:N #1
+  {
+    \coffin_if_exist:NT #1
+      {
+        \box_clear:N #1
+        \coffin_reset_structure:N #1
+      }
+  }
+\cs_generate_variant:Nn \coffin_clear:N { c }
+%    \end{macrocode}
+% \end{macro}
+% 
+% \begin{macro}{\coffin_new:N, \coffin_new:c}
+%   Creating a new coffin means making the underlying box and adding the
+%   data structures. These are created globally, as there is a need to
+%   avoid any strange effects if the coffin is created inside a group.
+%   This means that the usual rule about \cs{l_\ldots} variables has
+%   to be broken. 
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_new:N #1
+  {
+    \box_new:N #1
+    \prop_clear_new:c { l_coffin_corners_ \int_value:w #1 _prop }
+    \prop_clear_new:c { l_coffin_poles_   \int_value:w #1 _prop }
+    \prop_gset_eq:cN { l_coffin_corners_ \int_value:w #1 _prop } 
+      \c_coffin_corners_prop
+    \prop_gset_eq:cN { l_coffin_poles_ \int_value:w #1 _prop } 
+      \c_coffin_poles_prop
+  }
+\cs_generate_variant:Nn \coffin_new:N { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\hcoffin_set:Nn, \hcoffin_set:cn}
+%   Horizontal coffins are relatively easy: set the appropriate box,
+%   reset the structures then update the handle positions.
+%    \begin{macrocode}
+\cs_new_protected:Npn \hcoffin_set:Nn #1#2
+  {
+    \coffin_if_exist:NT #1
+      {
+        \hbox_set:Nn #1 
+          { 
+            \group_begin:
+%<*initex>
+              \color_set_current: % TODO
+%</initex>
+%<*package>
+              \set@color
+%</package>
+              #2 
+            \group_end: 
+          }
+        \coffin_reset_structure:N #1
+        \coffin_update_poles:N #1
+        \coffin_update_corners:N #1
+      }
+  }
+\cs_generate_variant:Nn \hcoffin_set:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\vcoffin_set:Nnn, \vcoffin_set:cnn}
+%   Setting vertical coffins is more complex. First, the material is 
+%   typeset with a given width. The default handles and poles are set as
+%   for a horizontal coffin, before finding the top baseline using a 
+%   temporary box.
+%    \begin{macrocode}
+\cs_new_protected:Npn \vcoffin_set:Nnn #1#2#3
+  {
+    \coffin_if_exist:NT #1
+      {
+        \vbox_set:Nn #1 
+          {
+            \dim_set:Nn \tex_hsize:D {#2}
+            \group_begin:
+%<*initex>
+              \color_set_current:
+%</initex>
+%<*package>
+              \set@color
+%</package>
+              #3 
+            \group_end: 
+          } 
+        \coffin_reset_structure:N #1
+        \coffin_update_poles:N #1
+        \coffin_update_corners:N #1
+        \vbox_set_top:Nn \l_coffin_tmp_box { \vbox_unpack:N #1 }
+        \coffin_set_pole:Nnx #1 { T }
+          {
+            { 0 pt }
+            { \dim_eval:n { \box_ht:N #1 - \box_ht:N \l_coffin_tmp_box } }
+            { 1000 pt }
+            { 0 pt }
+          }
+        \box_clear:N \l_coffin_tmp_box
+      }
+  }
+\cs_generate_variant:Nn \vcoffin_set:Nnn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \coffin_set_eq:NN, \coffin_set_eq:Nc,
+%     \coffin_set_eq:cN, \coffin_set_eq:cc
+%   }
+%   Setting two coffins equal is just a wrapper around other functions.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_set_eq:NN #1#2
+  {
+    \coffin_if_exist:NT #1
+      {
+        \box_set_eq:NN #1 #2
+        \coffin_set_eq_structure:NN #1 #2
+      }
+  }
+\cs_generate_variant:Nn \coffin_set_eq:NN { c , Nc , cc }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{variable}{\c_empty_coffin}
+% \begin{variable}{\l_coffin_aligned_coffin}
+% \begin{variable}{\l_coffin_aligned_internal_coffin}
+%   Special coffins: these cannot be set up earlier as they need
+%   \cs{coffin_new:N}. The empty coffin is set as a box as the full
+%   coffin-setting system needs some material which is not yet available.
+%    \begin{macrocode}
+\coffin_new:N \c_empty_coffin
+\hbox_set:Nn  \c_empty_coffin { }
+\coffin_new:N \l_coffin_aligned_coffin
+\coffin_new:N \l_coffin_aligned_internal_coffin
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \subsection{Coffins: handle and pole management}
+%
+% \begin{macro}{\coffin_get_pole:NnN}
+%   A simple wrapper around the recovery of a coffin pole, with some 
+%   error checking and recovery built-in.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_get_pole:NnN #1#2#3
+  {
+    \prop_get:cnNF
+      { l_coffin_poles_ \int_value:w #1 _prop } {#2} #3
+      { 
+        \msg_kernel_error:nnxx { coffin } { unknown-coffin-pole }
+          {#2} { \token_to_str:N #1 }
+        \tl_set:Nn #3 { { 0 pt } { 0 pt } { 0 pt } { 0 pt } }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_reset_structure:N}
+%   Resetting the structure is a simple copy job.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_reset_structure:N #1
+  {
+    \prop_set_eq:cN { l_coffin_corners_ \int_value:w #1 _prop } 
+      \c_coffin_corners_prop
+    \prop_set_eq:cN { l_coffin_poles_ \int_value:w #1 _prop } 
+      \c_coffin_poles_prop
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_set_eq_structure:NN}
+% Setting coffin structures equal simply means copying the property
+% list.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_set_eq_structure:NN #1#2
+  {
+    \prop_set_eq:cc { l_coffin_corners_ \int_value:w #1 _prop }
+      { l_coffin_corners_ \int_value:w #2 _prop }
+    \prop_set_eq:cc { l_coffin_poles_ \int_value:w #1 _prop }
+      { l_coffin_poles_ \int_value:w #2 _prop }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_set_user_dimensions:N}
+% \begin{macro}{\coffin_end_user_dimensions:}
+% \begin{macro}{\Depth}
+% \begin{macro}{\Height}
+% \begin{macro}{\TotalHeight}
+% \begin{macro}{\Width}
+%   These make design-level names for the dimensions of a coffin easy to
+%   get at.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_set_user_dimensions:N #1
+  {
+    \cs_set_eq:NN \coffin_saved_Height:      \Height
+    \cs_set_eq:NN \coffin_saved_Depth:       \Depth
+    \cs_set_eq:NN \coffin_saved_TotalHeight: \TotalHeight
+    \cs_set_eq:NN \coffin_saved_Width:       \Width
+    \cs_set_eq:NN \Height      \l_coffin_Height_dim
+    \cs_set_eq:NN \Depth       \l_coffin_Depth_dim
+    \cs_set_eq:NN \TotalHeight \l_coffin_TotalHeight_dim
+    \cs_set_eq:NN \Width       \l_coffin_Width_dim
+    \dim_set:Nn \Height      { \box_ht:N #1 }
+    \dim_set:Nn \Depth       { \box_dp:N #1 }
+    \dim_set:Nn \TotalHeight { \box_ht:N #1 - \box_dp:N #1 }
+    \dim_set:Nn \Width       { \box_wd:N #1 }
+  }
+\cs_new_protected_nopar:Npn \coffin_end_user_dimensions:
+  {
+    \cs_set_eq:NN \Height      \coffin_saved_Height:
+    \cs_set_eq:NN \Depth       \coffin_saved_Depth:
+    \cs_set_eq:NN \TotalHeight \coffin_saved_TotalHeight:
+    \cs_set_eq:NN \Width       \coffin_saved_Width:
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}
+%   {\coffin_set_horizontal_pole:Nnn, \coffin_set_horizontal_pole:cnn}
+% \begin{macro}{\coffin_set_vertical_pole:Nnn,\coffin_set_vertical_pole:cnn}
+% \begin{macro}{\coffin_set_pole:Nnn, \coffin_set_pole:Nnx}
+%   Setting the pole of a coffin at the user/designer level requires a 
+%   bit more care. The idea here is to provide a reasonable interface to
+%   the system, then to do the setting with full expansion. The
+%   three-argument version is used internally to do a direct setting.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_set_horizontal_pole:Nnn #1#2#3
+  {
+    \coffin_if_exist:NT #1
+      {
+        \coffin_set_user_dimensions:N #1
+        \coffin_set_pole:Nnx #1 {#2}
+          {
+            { 0 pt } { \dim_eval:n {#3} }
+            { 1000 pt } { 0 pt } 
+          }
+        \coffin_end_user_dimensions:
+      }
+  }
+\cs_new_protected_nopar:Npn \coffin_set_vertical_pole:Nnn #1#2#3
+  {
+    \coffin_if_exist:NT #1
+      {
+        \coffin_set_user_dimensions:N #1
+        \coffin_set_pole:Nnx #1 {#2}
+          {
+            { \dim_eval:n {#3} } { 0 pt } 
+            { 0 pt } { 1000 pt }
+          }
+        \coffin_end_user_dimensions:
+      }
+  }
+\cs_new_protected_nopar:Npn \coffin_set_pole:Nnn #1#2#3
+  { \prop_put:cnn { l_coffin_poles_ \int_value:w #1 _prop } {#2} {#3} }
+\cs_generate_variant:Nn \coffin_set_horizontal_pole:Nnn { c }
+\cs_generate_variant:Nn \coffin_set_vertical_pole:Nnn { c }
+\cs_generate_variant:Nn \coffin_set_pole:Nnn { Nnx }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_update_corners:N}
+%   Updating the corners of a coffin is straight-forward as at this stage
+%   there can be no rotation. So the corners of the content are just those
+%   of the underlying \TeX{} box.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_update_corners:N #1
+  {
+    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tl }
+      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
+    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { tr }
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
+    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { bl }
+      { { 0 pt } { \dim_eval:n { - \box_dp:N #1 } } }
+    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { br } 
+      { { \dim_use:N \box_wd:N #1 } { \dim_eval:n { - \box_dp:N #1 } } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_update_poles:N}
+%   This function is called when a coffin is set, and updates the poles to
+%   reflect the nature of size of the box. Thus this function only alters
+%   poles where the default position is dependent on the size of the box.
+%   It also does not set poles which are relevant only to vertical
+%   coffins.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_update_poles:N #1
+  {
+    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { hc } 
+      {
+        { \dim_eval:n { 0.5 \box_wd:N #1 } }
+        { 0 pt } { 0 pt } { 1000 pt }
+      }
+    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { r } 
+      {
+        { \dim_use:N \box_wd:N #1 }
+        { 0 pt } { 0 pt } { 1000 pt }
+      }
+    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { vc } 
+      {
+        { 0 pt }
+        { \dim_eval:n { ( \box_ht:N #1 - \box_dp:N #1 ) / 2 } }
+        { 1000 pt }
+        { 0 pt }
+      }
+    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { t }
+      {
+        { 0 pt }
+        { \dim_use:N \box_ht:N #1 }
+        { 1000 pt }
+        { 0 pt }
+      }
+    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { b } 
+      {
+        { 0 pt }
+        { \dim_eval:n { - \box_dp:N #1 } }
+        { 1000 pt }
+        { 0 pt }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Coffins: calculation of pole intersections}
+%
+% \begin{macro}{\coffin_calculate_intersection:Nnn}
+% \begin{macro}[aux]{\coffin_calculate_intersection:nnnnnnnn}
+% \begin{macro}[aux]{\coffin_calculate_intersection_aux:nnnnnN}
+%   The lead off in finding intersections is to recover the two poles
+%   and then hand off to the auxiliary for the actual calculation. There
+%   may of course not be an intersection, for which an error trap is 
+%   needed.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_calculate_intersection:Nnn #1#2#3
+  {
+    \coffin_get_pole:NnN #1 {#2} \l_coffin_pole_a_tl
+    \coffin_get_pole:NnN #1 {#3} \l_coffin_pole_b_tl
+    \bool_set_false:N \l_coffin_error_bool
+    \exp_last_two_unbraced:Noo
+      \coffin_calculate_intersection:nnnnnnnn
+        \l_coffin_pole_a_tl \l_coffin_pole_b_tl
+    \bool_if:NT \l_coffin_error_bool
+      {    
+        \msg_kernel_error:nn { coffin } { no-pole-intersection }
+        \dim_zero:N \l_coffin_x_dim
+        \dim_zero:N \l_coffin_y_dim
+      }
+  }
+%    \end{macrocode}
+%   The two poles passed here each have four values (as dimensions),
+%   ($a$, $b$, $c$, $d$) and 
+%   ($a'$, $b'$, $c'$, $d'$). These are arguments 
+%   $1$--$4$ and $5$--$8$, respectively. In both
+%   cases $a$ and  $b$ are the co-ordinates of a point on the 
+%   pole and $c$ and $d$ define the direction of the pole. Finding
+%   the intersection depends on the directions of the poles, which are 
+%   given by $d / c$ and $d' / c'$. However, if one of the poles
+%   is either horizontal or vertical then one or more of $c$, $d$,
+%   $c'$ and $d'$ will be zero and a special case is needed.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_calculate_intersection:nnnnnnnn
+  #1#2#3#4#5#6#7#8 
+  {
+    \dim_compare:nNnTF {#3} = { \c_zero_dim }
+%    \end{macrocode}
+%   The case where the first pole is vertical.  So the $x$-component
+%   of the interaction will be at $a$. There is then a test on the
+%   second pole: if it is also vertical then there is an error.
+%    \begin{macrocode}
+      {
+        \dim_set:Nn \l_coffin_x_dim {#1}
+        \dim_compare:nNnTF {#7} = \c_zero_dim
+          { \bool_set_true:N \l_coffin_error_bool }
+%    \end{macrocode}
+%   The second pole may still be horizontal, in which case the 
+%   $y$-component of the intersection will be $b'$. If not,
+%   \[
+%     y = \frac{d'}{c'} \left ( x - a' \right ) + b'
+%   \]
+%   with the $x$-component already known to be |#1|. This calculation
+%   is done as a generalised auxiliary.
+%    \begin{macrocode}
+          {
+            \dim_compare:nNnTF {#8} = \c_zero_dim
+              { \dim_set:Nn \l_coffin_y_dim {#6} }
+              { 
+                \coffin_calculate_intersection_aux:nnnnnN
+                  {#1} {#5} {#6} {#7} {#8} \l_coffin_y_dim
+              }
+          }
+      }
+%    \end{macrocode}
+%   If the first pole is not vertical then it may be horizontal. If so,
+%   then the procedure is essentially the same as that already done but
+%   with the $x$- and $y$-components interchanged.
+%    \begin{macrocode}
+      {
+        \dim_compare:nNnTF {#4} = \c_zero_dim
+          {
+            \dim_set:Nn \l_coffin_y_dim {#2}
+            \dim_compare:nNnTF {#8} = { \c_zero_dim }
+              { \bool_set_true:N \l_coffin_error_bool }
+              {
+                \dim_compare:nNnTF {#7} = \c_zero_dim
+                  { \dim_set:Nn \l_coffin_x_dim {#5} }
+%    \end{macrocode}
+%   The formula for the case where the second pole is neither horizontal
+%   nor vertical is
+%   \[
+%     x = \frac{c'}{d'} \left ( y - b' \right ) + a'
+%   \]
+%   which is again handled by the same auxiliary.
+%    \begin{macrocode}
+                  { 
+                    \coffin_calculate_intersection_aux:nnnnnN
+                      {#2} {#6} {#5} {#8} {#7} \l_coffin_x_dim
+                  } 
+              }
+          }
+%    \end{macrocode}
+%   The first pole is neither horizontal nor vertical. This still leaves
+%   the second pole, which may be a special case. For those possibilities,
+%   the calculations are the same as above with the first and second poles
+%   interchanged.
+%    \begin{macrocode}
+          {
+            \dim_compare:nNnTF {#7} = \c_zero_dim
+              {
+                \dim_set:Nn \l_coffin_x_dim {#5} 
+                \coffin_calculate_intersection_aux:nnnnnN
+                  {#5} {#1} {#2} {#3} {#4} \l_coffin_y_dim
+              }
+              {
+                \dim_compare:nNnTF {#8} = \c_zero_dim
+                  {
+                    \dim_set:Nn \l_coffin_x_dim {#6}  
+                    \coffin_calculate_intersection_aux:nnnnnN
+                      {#6} {#2} {#1} {#4} {#3} \l_coffin_x_dim
+                  }
+%    \end{macrocode}
+%   If none of the special cases apply then there is still a need to 
+%   check that there is a unique intersection between the two pole. This
+%   is the case if they have different slopes.
+%    \begin{macrocode}
+                { 
+                    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#3}
+                    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#4}
+                    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#7}
+                    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#8}
+                    \fp_div:Nn \l_coffin_calc_b_fp \l_coffin_calc_a_fp
+                    \fp_div:Nn \l_coffin_calc_d_fp \l_coffin_calc_c_fp
+                    \fp_compare:nNnTF
+                      \l_coffin_calc_b_fp = \l_coffin_calc_d_fp
+                      { \bool_set_true:N \l_coffin_error_bool }
+%    \end{macrocode}
+%   All of the tests pass, so there is the full complexity of the
+%   calculation:
+%   \[
+%     x = \frac { a ( d / c ) - a' ( d' / c' ) - b + b' }
+%              { ( d / c ) - ( d' / c' ) }
+%   \]
+%   and noting that the two ratios are already worked out from the test
+%   just performed. There is quite a bit of shuffling from dimensions to
+%   floating points in order to do the work. The $y$-values is then
+%   worked out using the standard auxiliary starting from the 
+%   $x$-position.
+%    \begin{macrocode}
+                      {
+                        \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#6}
+                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2} 
+                        \fp_sub:Nn \l_coffin_calc_result_fp
+                          { \l_coffin_calc_a_fp }
+                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#1}
+                        \fp_mul:Nn \l_coffin_calc_a_fp
+                          { \l_coffin_calc_b_fp }
+                        \fp_add:Nn \l_coffin_calc_result_fp
+                          { \l_coffin_calc_a_fp }
+                        \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#5}
+                        \fp_mul:Nn \l_coffin_calc_a_fp
+                          { \l_coffin_calc_d_fp }
+                        \fp_sub:Nn \l_coffin_calc_result_fp
+                          { \l_coffin_calc_a_fp }
+                        \fp_sub:Nn \l_coffin_calc_b_fp
+                          { \l_coffin_calc_d_fp }
+                        \fp_div:Nn \l_coffin_calc_result_fp
+                          { \l_coffin_calc_b_fp }
+                        \dim_set:Nn \l_coffin_x_dim
+                          { \fp_to_dim:N \l_coffin_calc_result_fp }
+                        \coffin_calculate_intersection_aux:nnnnnN
+                          { \l_coffin_x_dim }
+                          {#5} {#6} {#8} {#7} \l_coffin_y_dim
+                      }
+                  }
+              }
+          }
+      }
+  }
+%    \end{macrocode}
+%   The formula for finding the intersection point is in most cases the
+%   same. The formula here is
+%   \[
+%     \#6 = \frac{\#5}{\#4} \left ( \#1 - \#2 \right ) + \#3
+%   \]
+%   Thus |#4| and |#5| should be the directions of the pole while
+%   |#2| and |#3| are co-ordinates.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_calculate_intersection_aux:nnnnnN
+  #1#2#3#4#5#6 
+  {
+    \fp_set_from_dim:Nn \l_coffin_calc_result_fp {#1}
+    \fp_set_from_dim:Nn \l_coffin_calc_a_fp {#2}
+    \fp_set_from_dim:Nn \l_coffin_calc_b_fp {#3}
+    \fp_set_from_dim:Nn \l_coffin_calc_c_fp {#4}
+    \fp_set_from_dim:Nn \l_coffin_calc_d_fp {#5}
+    \fp_sub:Nn \l_coffin_calc_result_fp { \l_coffin_calc_a_fp }
+    \fp_div:Nn \l_coffin_calc_result_fp { \l_coffin_calc_d_fp }
+    \fp_mul:Nn \l_coffin_calc_result_fp { \l_coffin_calc_c_fp }
+    \fp_add:Nn \l_coffin_calc_result_fp { \l_coffin_calc_b_fp }
+    \dim_set:Nn #6 { \fp_to_dim:N \l_coffin_calc_result_fp }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Aligning and typesetting of coffins}
+%
+% \begin{macro}
+%   {
+%     \coffin_join:NnnNnnnn, \coffin_join:cnnNnnnn,
+%     \coffin_join:Nnncnnnn , \coffin_join:cnncnnnn
+%   }
+%   This command joins two coffins, using a horizontal and vertical pole
+%   from each coffin and making an offset between the two. The result
+%   is stored as the as a third coffin, which will have all of its handles
+%   reset to standard values. First, the more basic alignment function is
+%   used to get things started.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_join:NnnNnnnn #1#2#3#4#5#6#7#8
+  {
+    \coffin_align:NnnNnnnnN 
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
+%    \end{macrocode}
+%   Correct the placement of the reference point. If the $x$-offset 
+%   is negative then the reference point of the second box is to the left
+%   of that of the first, which is corrected using a kern. On the right
+%   side the first box might stick out, which will show up if it is wider
+%   than the sum of the $x$-offset and the width of the second box.
+%   So a second kern may be needed.
+%    \begin{macrocode}
+    \hbox_set:Nn \l_coffin_aligned_coffin
+      {
+        \dim_compare:nNnT { \l_coffin_offset_x_dim } < \c_zero_dim
+          { \tex_kern:D -\l_coffin_offset_x_dim }
+        \hbox_unpack:N \l_coffin_aligned_coffin 
+        \dim_set:Nn \l_coffin_tmp_dim
+          { \l_coffin_offset_x_dim - \box_wd:N #1 + \box_wd:N #4 }
+        \dim_compare:nNnT \l_coffin_tmp_dim < \c_zero_dim
+          { \tex_kern:D -\l_coffin_tmp_dim } 
+      }
+%    \end{macrocode}
+%   The coffin structure is reset, and the corners are cleared: only
+%   those from the two parent coffins are needed.
+%    \begin{macrocode}
+   \coffin_reset_structure:N \l_coffin_aligned_coffin
+    \prop_clear:c
+      {  l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _ prop }
+    \coffin_update_poles:N \l_coffin_aligned_coffin
+%    \end{macrocode}
+%   The structures of the parent coffins are now transferred to the new
+%   coffin, which requires that the appropriate offsets are applied. That
+%   will then depend on whether any shift was needed.
+%    \begin{macrocode}
+    \dim_compare:nNnTF \l_coffin_offset_x_dim < \c_zero_dim
+      {
+        \coffin_offset_poles:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
+        \coffin_offset_poles:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
+        \coffin_offset_corners:Nnn #1 { -\l_coffin_offset_x_dim } { 0 pt }
+        \coffin_offset_corners:Nnn #4 { 0 pt } { \l_coffin_offset_y_dim }
+      }
+      {
+        \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+        \coffin_offset_poles:Nnn #4
+          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim } 
+        \coffin_offset_corners:Nnn #1 { 0 pt } { 0 pt }
+        \coffin_offset_corners:Nnn #4
+          { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim } 
+      }
+    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin  
+    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+  }
+\cs_generate_variant:Nn \coffin_join:NnnNnnnn { c , Nnnc , cnnc }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}
+%   {
+%     \coffin_attach:NnnNnnnn, \coffin_attach:cnnNnnnn,
+%     \coffin_attach:Nnncnnnn, \coffin_attach:cnncnnnn
+%   }
+% \begin{macro}{\coffin_attach_mark:NnnNnnnn}
+%   A more simple version of the above, as it simply uses the size of the
+%   first coffin for the new one. This means that the work here is rather
+%   simplified compared to the above code. The function used when marking
+%   a position is hear also as it is similar but without the structure
+%   updates.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_attach:NnnNnnnn #1#2#3#4#5#6#7#8
+  {
+    \coffin_align:NnnNnnnnN 
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
+    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
+    \coffin_reset_structure:N \l_coffin_aligned_coffin
+    \prop_set_eq:cc
+      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
+      { l_coffin_corners_ \int_value:w #1 _prop }
+    \coffin_update_poles:N  \l_coffin_aligned_coffin
+    \coffin_offset_poles:Nnn #1 { 0 pt } { 0 pt }
+    \coffin_offset_poles:Nnn #4
+      { \l_coffin_offset_x_dim } { \l_coffin_offset_y_dim } 
+    \coffin_update_vertical_poles:NNN #1 #4 \l_coffin_aligned_coffin
+    \coffin_set_eq:NN #1 \l_coffin_aligned_coffin
+  }
+\cs_new_protected_nopar:Npn \coffin_attach_mark:NnnNnnnn #1#2#3#4#5#6#7#8
+  {
+    \coffin_align:NnnNnnnnN 
+      #1 {#2} {#3} #4 {#5} {#6} {#7} {#8} \l_coffin_aligned_coffin
+    \box_set_ht:Nn \l_coffin_aligned_coffin { \box_ht:N #1 }
+    \box_set_dp:Nn \l_coffin_aligned_coffin { \box_dp:N #1 }
+    \box_set_wd:Nn \l_coffin_aligned_coffin { \box_wd:N #1 }
+    \box_set_eq:NN #1 \l_coffin_aligned_coffin
+  }
+\cs_generate_variant:Nn \coffin_attach:NnnNnnnn { c , Nnnc , cnnc }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_align:NnnNnnnnN}
+%   The internal function aligns the two coffins into a third one, but
+%   performs no corrections on the resulting coffin poles. The process
+%   begins by finding the points of intersection for the poles for each
+%   of the input coffins. Those for the first coffin are worked out after
+%   those for the second coffin, as this allows the `primed'
+%   storage area to be used for the second coffin. The `real' box
+%   offsets are then calculated, before using these to re-box the 
+%   input coffins. The default poles are then set up, but the final result
+%   will depend on how the bounding box is being handled.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_align:NnnNnnnnN #1#2#3#4#5#6#7#8#9
+  {
+    \coffin_calculate_intersection:Nnn #4 {#5} {#6}
+    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
+    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
+    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l_coffin_offset_x_dim
+      { \l_coffin_x_dim - \l_coffin_x_prime_dim + #7 }
+    \dim_set:Nn \l_coffin_offset_y_dim
+      { \l_coffin_y_dim - \l_coffin_y_prime_dim + #8 }
+    \hbox_set:Nn \l_coffin_aligned_internal_coffin 
+      {
+        \box_use:N #1
+        \tex_kern:D -\box_wd:N #1
+        \tex_kern:D \l_coffin_offset_x_dim
+        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #4 }
+      }
+    \coffin_set_eq:NN #9 \l_coffin_aligned_internal_coffin
+  } 
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_offset_poles:Nnn}
+% \begin{macro}[aux]{\coffin_offset_pole:Nnnnnnn}
+%   Transferring structures from one coffin to another requires that the
+%   positions are updated by the offset between the two coffins. This is
+%   done by mapping to the property list of the source coffins, moving
+%   as appropriate and saving to the new coffin data structures. The
+%   test for a |-| means that the structures from the parent coffins
+%   are uniquely labelled and do not depend on the order of alignment.
+%   The pay off for this is that |-| should not be used in coffin pole
+%   or handle names, and that multiple alignments do not result in a
+%   whole set of values.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_offset_poles:Nnn #1#2#3
+  {
+    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
+      { \coffin_offset_pole:Nnnnnnn #1 {##1} ##2 {#2} {#3} }
+  }
+\cs_new_protected_nopar:Npn \coffin_offset_pole:Nnnnnnn #1#2#3#4#5#6#7#8
+  {
+    \dim_set:Nn \l_coffin_x_dim { #3 + #7 }
+    \dim_set:Nn \l_coffin_y_dim { #4 + #8 }
+    \tl_if_in:nnTF {#2} { - }
+      { \tl_set:Nn \l_coffin_tmp_tl { {#2} } }
+      { \tl_set:Nn \l_coffin_tmp_tl { { #1 - #2 } } }
+    \exp_last_unbraced:NNo \coffin_set_pole:Nnx \l_coffin_aligned_coffin
+      { \l_coffin_tmp_tl }
+      {
+        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
+        {#5} {#6}
+      }  
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_offset_corners:Nnn}
+% \begin{macro}[aux]{\coffin_offset_corners:Nnnnn}
+%   Saving the offset corners of a coffin is very similar, except that
+%   there is no need to worry about naming: every corner can be saved
+%   here as order is unimportant.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_offset_corners:Nnn #1#2#3
+  {
+    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
+      { \coffin_offset_corner:Nnnnn #1 {##1} ##2 {#2} {#3} }
+  }
+\cs_new_protected_nopar:Npn \coffin_offset_corner:Nnnnn #1#2#3#4#5#6
+  {
+    \prop_put:cnx 
+      { l_coffin_corners_ \int_value:w \l_coffin_aligned_coffin _prop }
+      { #1 - #2 }
+      {
+        { \dim_eval:n { #3 + #5 } }
+        { \dim_eval:n { #4 + #6 } }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_update_vertical_poles:NNN}
+% \begin{macro}[aux]{\coffin_update_T:nnnnnnnnN}
+% \begin{macro}[aux]{\coffin_update_B:nnnnnnnnN}
+%   The \texttt{T} and \texttt{B} poles will need to be recalculated
+%   after alignment. These functions find the larger absolute value for
+%   the poles, but this is of course only logical when the poles are
+%   horizontal.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_update_vertical_poles:NNN #1#2#3
+  {
+    \coffin_get_pole:NnN #3 { #1 -T } \l_coffin_pole_a_tl
+    \coffin_get_pole:NnN #3 { #2 -T } \l_coffin_pole_b_tl
+    \exp_last_two_unbraced:Noo \coffin_update_T:nnnnnnnnN
+      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
+    \coffin_get_pole:NnN #3 { #1 -B } \l_coffin_pole_a_tl
+    \coffin_get_pole:NnN #3 { #2 -B } \l_coffin_pole_b_tl
+    \exp_last_two_unbraced:Noo \coffin_update_B:nnnnnnnnN
+      \l_coffin_pole_a_tl \l_coffin_pole_b_tl #3
+  }
+\cs_new_protected_nopar:Npn \coffin_update_T:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+  {
+    \dim_compare:nNnTF {#2} < {#6}
+      {
+        \coffin_set_pole:Nnx #9 { T } 
+          { { 0 pt } {#6} { 1000 pt } { 0 pt } }
+      }
+      {
+        \coffin_set_pole:Nnx #9 { T } 
+          { { 0 pt } {#2} { 1000 pt } { 0 pt } }
+      }
+  }
+\cs_new_protected_nopar:Npn \coffin_update_B:nnnnnnnnN #1#2#3#4#5#6#7#8#9
+  {
+    \dim_compare:nNnTF {#2} < {#6}
+      {
+        \coffin_set_pole:Nnx #9 { B } 
+          { { 0 pt } {#2}  { 1000 pt } { 0 pt } }
+      }
+      {
+        \coffin_set_pole:Nnx #9 { B } 
+          { { 0 pt } {#6} { 1000 pt } { 0 pt } }
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_typeset:Nnnnn, \coffin_typeset:cnnnn}
+%   Typesetting a coffin means aligning it with the current position,
+%   which is done using a coffin with no content at all. This is done
+%   using the same approach as \cs{coffin_align:NnnNnnnnN} but without the
+%   offset corrections (which would be thrown away). The same is true
+%   for overlaying coffins, which uses the known size of an empty
+%   box!
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_typeset:Nnnnn #1#2#3#4#5
+  {
+    \coffin_align:NnnNnnnnN \c_empty_coffin { H } { l } 
+      #1 {#2} {#3} {#4} {#5} \l_coffin_aligned_coffin
+    \hbox_set:Nn \l_coffin_aligned_coffin
+      {
+        \dim_compare:nNnT { \l_coffin_offset_x_dim } < \c_zero_dim
+          { \tex_kern:D -\l_coffin_offset_x_dim }
+        \hbox_unpack:N \l_coffin_aligned_coffin 
+        \dim_set:Nn \l_coffin_tmp_dim
+          { \l_coffin_offset_x_dim + \box_wd:N #1 }
+        \dim_compare:nNnT { \l_coffin_tmp_dim } < \c_zero_dim
+          { \tex_kern:D -\l_coffin_tmp_dim } 
+      } 
+    \hbox_unpack:N \c_empty_box  
+    \box_use:N \l_coffin_aligned_coffin
+  }
+\cs_generate_variant:Nn \coffin_typeset:Nnnnn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \subsection{Rotating coffins}
+%
+% \begin{variable}{\l_coffin_bounding_prop}
+%   A property list for the bounding box of a coffin. This is only needed
+%   during the rotation, so there is just the one.
+%    \begin{macrocode}
+\prop_new:N \l_coffin_bounding_prop
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_bounding_shift_dim}
+%   The shift of the bounding box of a coffin from the real content.
+%    \begin{macrocode}
+\dim_new:N \l_coffin_bounding_shift_dim
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_left_corner_dim}
+% \begin{variable}{\l_coffin_right_corner_dim}
+% \begin{variable}{\l_coffin_bottom_corner_dim}
+% \begin{variable}{\l_coffin_top_corner_dim}
+%   These are used to hold maxima for the various corner values: these
+%   thus define the minimum size of the bounding box after rotation.
+%    \begin{macrocode}
+\dim_new:N \l_coffin_left_corner_dim
+\dim_new:N \l_coffin_right_corner_dim
+\dim_new:N \l_coffin_bottom_corner_dim
+\dim_new:N \l_coffin_top_corner_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{macro}{\coffin_rotate:Nn, \coffin_rotate:cn}
+%   Rotating a coffin requires several steps which can be conveniently 
+%   run together. The first step is to convert the angle given in degrees
+%   to one in radians. This is then used to set \cs{l_coffin_sin_fp} and
+%   \cs{l_coffin_cos_fp}, which are carried through unchanged for the rest
+%   of the procedure.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_rotate:Nn #1#2
+  {
+    \fp_set:Nn \l_coffin_tmp_fp {#2}
+    \fp_div:Nn \l_coffin_tmp_fp { 180 }
+    \fp_mul:Nn \l_coffin_tmp_fp { \c_pi_fp }
+    \fp_sin:Nn \l_coffin_sin_fp { \l_coffin_tmp_fp }
+    \fp_cos:Nn \l_coffin_cos_fp { \l_coffin_tmp_fp }
+%    \end{macrocode}
+%   The corners and poles of the coffin can now be rotated around the
+%    origin. This is best achieved using mapping functions.
+%    \begin{macrocode}
+    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
+      { \coffin_rotate_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
+      { \coffin_rotate_pole:Nnnnnn #1 {##1} ##2 }
+%    \end{macrocode}
+%   The bounding box of the coffin needs to be rotated, and to do this
+%   the corners have to be found first. They are then rotated in the same
+%   way as the corners of the coffin material itself.
+%    \begin{macrocode}
+    \coffin_set_bounding:N #1
+    \prop_map_inline:Nn \l_coffin_bounding_prop
+      { \coffin_rotate_bounding:nnn {##1} ##2 }
+%    \end{macrocode}
+%   At this stage, there needs to be a calculation to find where the
+%   corners of the content and the box itself will end up.
+%    \begin{macrocode}
+    \coffin_find_corner_maxima:N #1 
+    \coffin_find_bounding_shift:
+%<*initex>
+    \hbox_set:Nn #1 { \box_rotate:Nn #1 {#2} } % TODO
+%</initex>
+%<*package>
+    \hbox_set:Nn #1 { \rotatebox {#2} { \box_use:N #1 } }
+%</package>
+%    \end{macrocode}
+%   The correction of the box position itself takes place here. The idea
+%   is that the bounding box for a coffin is tight up to the content, and
+%   has the reference point at the bottom-left. The $x$-direction is
+%   handled by moving the content by the difference in the positions of
+%   the bounding box and the content left edge. The $y$-direction is
+%   dealt with by moving the box down by any depth it has acquired.
+%    \begin{macrocode}
+    \hbox_set:Nn #1 
+      {
+        \tex_kern:D \l_coffin_bounding_shift_dim
+        \tex_kern:D -\l_coffin_left_corner_dim
+        \box_move_down:nn { \l_coffin_bottom_corner_dim }
+          { \box_use:N #1 }
+      }
+%    \end{macrocode}
+%   If there have been any previous rotations then the size of the 
+%   bounding box will be bigger than the contents. This can be corrected
+%   easily by setting the size of the box to the height and width of the 
+%   content.
+%    \begin{macrocode}
+    \box_set_ht:Nn #1 
+      { \l_coffin_top_corner_dim - \l_coffin_bottom_corner_dim }
+    \box_set_dp:Nn #1 { 0 pt }  
+    \box_set_wd:Nn #1 
+      { \l_coffin_right_corner_dim - \l_coffin_left_corner_dim }
+%    \end{macrocode}
+%   The final task is to move the poles and corners such that they are 
+%   back in alignment with the box reference point.
+%    \begin{macrocode}
+    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
+      { \coffin_shift_corner:Nnnn #1 {##1} ##2 }
+    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
+      { \coffin_shift_pole:Nnnnnn #1 {##1} ##2 }
+  } 
+\cs_generate_variant:Nn \coffin_rotate:Nn { c }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_set_bounding:N}
+%   The bounding box corners for a coffin are easy enough to find: this
+%   is the same code as for the corners of the material itself, but
+%   using a dedicated property list.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_set_bounding:N #1
+  {
+   \prop_put:Nnx \l_coffin_bounding_prop { tl } 
+      { { 0 pt } { \dim_use:N \box_ht:N #1 } }
+    \prop_put:Nnx \l_coffin_bounding_prop { tr } 
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \box_ht:N #1 } }
+    \dim_set:Nn \l_coffin_tmp_dim { - \box_dp:N #1 }  
+    \prop_put:Nnx \l_coffin_bounding_prop { bl } 
+      { { 0 pt } { \dim_use:N \l_coffin_tmp_dim } }
+    \prop_put:Nnx \l_coffin_bounding_prop { br } 
+      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l_coffin_tmp_dim } }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_rotate_bounding:nnn}
+% \begin{macro}{\coffin_rotate_corner:Nnnn}
+%   Rotating the position of the corner of the coffin is just a case
+%   of treating this as a vector from the reference point. The same
+%   treatment is used for the corners of the material itself and the
+%   bounding box.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_rotate_bounding:nnn #1#2#3
+  {
+    \coffin_rotate_vector:nnNN {#2} {#3} \l_coffin_x_dim \l_coffin_y_dim
+    \prop_put:Nnx \l_coffin_bounding_prop {#1}
+      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }  
+  }
+\cs_new_protected_nopar:Npn \coffin_rotate_corner:Nnnn #1#2#3#4
+  {
+    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
+    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
+      { { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim } }  
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_rotate_pole:Nnnnnn}
+%   Rotating a single pole simply means shifting the co-ordinate of 
+%   the pole and its direction. The rotation here is about the bottom-left
+%   corner of the coffin.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_rotate_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \coffin_rotate_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
+    \coffin_rotate_vector:nnNN {#5} {#6} 
+      \l_coffin_x_prime_dim \l_coffin_y_prime_dim
+    \coffin_set_pole:Nnx #1 {#2}
+      {
+        { \dim_use:N \l_coffin_x_dim } { \dim_use:N \l_coffin_y_dim }
+        { \dim_use:N \l_coffin_x_prime_dim }
+        { \dim_use:N \l_coffin_y_prime_dim }
+      }  
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_rotate_vector:nnNN}
+%   A rotation function, which needs only an input vector (as dimensions)
+%   and an output space. The values \cs{l_coffin_cos_fp} and
+%   \cs{l_coffin_sin_fp} should previously have been set up correctly.
+%   Working this way means that the floating point work is kept to a 
+%   minimum: for any given rotation the sin and cosine values do no 
+%   change, after all.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_rotate_vector:nnNN #1#2#3#4
+  {
+    \fp_set_from_dim:Nn \l_coffin_x_fp {#1}
+    \fp_set_from_dim:Nn \l_coffin_y_fp {#2}
+    \fp_set_eq:NN \l_coffin_x_prime_fp \l_coffin_x_fp
+    \fp_set_eq:NN \l_coffin_tmp_fp     \l_coffin_y_fp
+    \fp_mul:Nn \l_coffin_x_prime_fp { \l_coffin_cos_fp }
+    \fp_mul:Nn \l_coffin_tmp_fp     { \l_coffin_sin_fp }
+    \fp_sub:Nn \l_coffin_x_prime_fp { \l_coffin_tmp_fp } 
+    \fp_set_eq:NN \l_coffin_y_prime_fp \l_coffin_y_fp
+    \fp_set_eq:NN \l_coffin_tmp_fp     \l_coffin_x_fp
+    \fp_mul:Nn \l_coffin_y_prime_fp { \l_coffin_cos_fp }
+    \fp_mul:Nn \l_coffin_tmp_fp     { \l_coffin_sin_fp }
+    \fp_add:Nn \l_coffin_y_prime_fp { \l_coffin_tmp_fp }
+    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_x_prime_fp }
+    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_y_prime_fp }
+  }
+%    \end{macrocode}
+% \end{macro}
+%
+% \begin{macro}{\coffin_find_corner_maxima:N}
+% \begin{macro}[aux]{\coffin_find_corner_maxima_aux:nn}
+%   The idea here is to find the extremities of the content of the 
+%   coffin. This is done by looking for the smallest values for the bottom
+%   and left corners, and the largest values for the top and right
+%   corners. The values start at the maximum dimensions so that the
+%   case where all are positive or all are negative works out correctly.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_find_corner_maxima:N #1
+  {
+    \dim_set:Nn \l_coffin_top_corner_dim   { -\c_max_dim }
+    \dim_set:Nn \l_coffin_right_corner_dim { -\c_max_dim }
+    \dim_set:Nn \l_coffin_bottom_corner_dim { \c_max_dim }
+    \dim_set:Nn \l_coffin_left_corner_dim   { \c_max_dim }
+    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop } 
+      { \coffin_find_corner_maxima_aux:nn ##2 }
+  }
+\cs_new_protected_nopar:Npn \coffin_find_corner_maxima_aux:nn #1#2
+  {
+    \dim_set_min:Nn \l_coffin_left_corner_dim   {#1}
+    \dim_set_max:Nn \l_coffin_right_corner_dim  {#1}
+    \dim_set_min:Nn \l_coffin_bottom_corner_dim {#2}
+    \dim_set_max:Nn \l_coffin_top_corner_dim    {#2} 
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_find_bounding_shift:}
+% \begin{macro}[aux]{\coffin_find_bounding_shift_aux:nn}
+%   The approach to finding the shift for the bounding box is similar to
+%   that for the corners. However, there is only one value needed here and
+%   a fixed input property list, so things are a bit clearer.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_find_bounding_shift:
+  {
+    \dim_set:Nn \l_coffin_bounding_shift_dim { \c_max_dim }
+    \prop_map_inline:Nn \l_coffin_bounding_prop
+      { \coffin_find_bounding_shift_aux:nn ##2 }
+  }
+\cs_new_protected_nopar:Npn \coffin_find_bounding_shift_aux:nn #1#2
+  { \dim_set_min:Nn \l_coffin_bounding_shift_dim {#1} }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_shift_corner:Nnnn}
+% \begin{macro}{\coffin_shift_pole:Nnnnnn}
+%   Shifting the corners and poles of a coffin means subtracting the
+%   appropriate values from the $x$- and $y$-components. For
+%   the poles, this means that the direction vector is unchanged.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_shift_corner:Nnnn #1#2#3#4
+  {
+    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _ prop } {#2}
+      {
+        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
+        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
+      }
+  }
+\cs_new_protected_nopar:Npn \coffin_shift_pole:Nnnnnn #1#2#3#4#5#6
+  {
+    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _ prop } {#2}
+      {
+        { \dim_eval:n { #3 - \l_coffin_left_corner_dim } }
+        { \dim_eval:n { #4 - \l_coffin_bottom_corner_dim } }
+        {#5} {#6}
+      }
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Coffin diagnostics}
+%
+% \begin{variable}{\l_coffin_display_coffin}
+% \begin{variable}{\l_coffin_display_coord_coffin}
+% \begin{variable}{\l_coffin_display_pole_coffin}
+%   Used for printing coffins with data structures attached.
+%    \begin{macrocode}
+\coffin_new:N \l_coffin_display_coffin
+\coffin_new:N \l_coffin_display_coord_coffin
+\coffin_new:N \l_coffin_display_pole_coffin
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_display_handles_prop}
+%   This property list is used to print coffin handles at suitable
+%   positions. The offsets are expressed as multiples of the basic offset
+%   value, which therefore acts as a scale-factor.
+%    \begin{macrocode}
+\prop_new:N \l_coffin_display_handles_prop
+\prop_put:Nnn \l_coffin_display_handles_prop { tl }
+  { { b } { r } { -1 } { 1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { thc }
+  { { b } { hc } { 0 } { 1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { tr }
+  { { b } { l } { 1 } { 1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { vcl }
+  { { vc } { r } { -1 } { 0 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { vchc }
+  { { vc } { hc } { 0 } { 0 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { vcr }
+  { { vc } { l } { 1 } { 0 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { bl }
+  { { t } { r } { -1 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { bhc }
+  { { t } { hc } { 0 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { br }
+  { { t } { l } { 1 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Tl }
+  { { t } { r } { -1 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Thc }
+  { { t } { hc } { 0 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Tr }
+  { { t } { l } { 1 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Hl }
+  { { vc } { r } { -1 } { 1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Hhc }
+  { { vc } { hc } { 0 } { 1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Hr }
+  { { vc } { l } { 1 } { 1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Bl }
+  { { b } { r } { -1 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Bhc }
+  { { b } { hc } { 0 } { -1 } }
+\prop_put:Nnn \l_coffin_display_handles_prop { Br }
+  { { b } { l } { 1 } { -1 } }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_display_offset_dim}
+%   The standard offset for the label from the handle position when
+%   displaying handles.
+%    \begin{macrocode}
+\dim_new:N  \l_coffin_display_offset_dim
+\dim_set:Nn \l_coffin_display_offset_dim { 2 pt }
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_display_x_dim}
+% \begin{variable}{\l_coffin_display_y_dim}
+%   As the intersections of poles have to be calculated to find which 
+%   ones to print, there is a need to avoid repetition. This is done
+%   by saving the intersection into two dedicated values.
+%    \begin{macrocode}
+\dim_new:N \l_coffin_display_x_dim
+\dim_new:N \l_coffin_display_y_dim
+%    \end{macrocode}
+% \end{variable}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_display_poles_prop}
+%   A property list for printing poles: various things need to be deleted
+%   from this to get a \enquote{nice} output.
+%    \begin{macrocode}
+\prop_new:N \l_coffin_display_poles_prop
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_display_font_tl}
+%   Stores the settings used to print coffin data: this keeps things 
+%   flexible.
+%    \begin{macrocode}
+\tl_new:N  \l_coffin_display_font_tl
+%<*initex>
+\tl_set:Nn \l_coffin_display_font_tl { } % TODO
+%</initex>
+%<*package>
+\tl_set:Nn \l_coffin_display_font_tl { \sffamily \tiny }
+%</package>
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{variable}{\l_coffin_handles_tmp_prop}
+%   Used for displaying coffins, as the handles need to be stored in this
+%   case, at least temporarily.
+%    \begin{macrocode}
+\prop_new:N \l_coffin_handles_tmp_prop
+%    \end{macrocode}
+% \end{variable}
+%
+% \begin{macro}{\coffin_mark_handle:Nnnn, \coffin_mark_handle:cnnn}
+% \begin{macro}[aux]{\coffin_mark_handle_aux:nnnnNnn}
+%   Marking a single handle is relatively easy. The standard attachment
+%   function is used, meaning that there are two calculations for the
+%   location. However, this is likely to be okay given the load expected.
+%   Contrast with the more optimised version for showing all handles which
+%   comes next.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_mark_handle:Nnnn #1#2#3#4
+  {
+    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+      {
+%<*initex>
+        \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: } % TODO
+%</initex>
+%<*package>
+        \color {#4} 
+        \rule { 1 pt } { 1 pt } 
+%</package>
+      }
+    \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
+      \l_coffin_display_pole_coffin { hc } { vc } { 0 pt } { 0 pt } 
+    \hcoffin_set:Nn \l_coffin_display_coord_coffin
+      {
+%<*initex>
+        % TODO
+%</initex>
+%<*package>
+        \color {#4} 
+%</package>
+        \l_coffin_display_font_tl
+        ( \tl_to_str:n { #2 , #3 } )
+      }
+    \prop_get:NnN \l_coffin_display_handles_prop
+      { #2 #3 } \l_coffin_tmp_tl
+    \quark_if_no_value:NTF \l_coffin_tmp_tl
+      {
+        \prop_get:NnN \l_coffin_display_handles_prop
+          { #3 #2 } \l_coffin_tmp_tl
+        \quark_if_no_value:NTF \l_coffin_tmp_tl
+          { 
+            \coffin_attach_mark:NnnNnnnn #1 {#2} {#3}
+              \l_coffin_display_coord_coffin { l } { vc }
+                { 1 pt } { 0 pt }
+          }
+          {
+            \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
+              \l_coffin_tmp_tl #1 {#2} {#3}
+          }  
+      }
+      {
+        \exp_last_unbraced:No \coffin_mark_handle_aux:nnnnNnn
+          \l_coffin_tmp_tl #1 {#2} {#3}
+      }
+  }
+\cs_new_protected_nopar:Npn \coffin_mark_handle_aux:nnnnNnn #1#2#3#4#5#6#7
+  {
+    \coffin_attach_mark:NnnNnnnn #5 {#6} {#7}
+      \l_coffin_display_coord_coffin {#1} {#2}
+      { #3 \l_coffin_display_offset_dim } 
+      { #4 \l_coffin_display_offset_dim }
+  }
+\cs_generate_variant:Nn \coffin_mark_handle:Nnnn { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_display_handles:Nn, \coffin_display_handles:cn}
+% \begin{macro}[aux]{\coffin_display_handles_aux:nnnnnn}
+% \begin{macro}[aux]{\coffin_display_handles_aux:nnnn}
+% \begin{macro}[aux]{\coffin_display_attach:Nnnnn}
+%   Printing the poles starts by removing any duplicates, for which the
+%   \texttt{H} poles is used as the definitive version for the baseline 
+%   and bottom. Two loops are then used to find the combinations of 
+%   handles for all of these poles. This is done such that poles are
+%   removed during the loops to avoid duplication.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_display_handles:Nn #1#2
+  {
+    \hcoffin_set:Nn \l_coffin_display_pole_coffin
+      {
+%<*initex>
+        \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: } % TODO
+%</initex>
+%<*package>
+        \color {#2} 
+        \rule { 1 pt } { 1 pt } 
+%</package>
+      }
+    \prop_set_eq:Nc \l_coffin_display_poles_prop
+      { l_coffin_poles_ \int_value:w #1 _prop }
+    \coffin_get_pole:NnN #1 { H } \l_coffin_pole_a_tl
+    \coffin_get_pole:NnN #1 { T } \l_coffin_pole_b_tl  
+    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
+      { \prop_del:Nn \l_coffin_display_poles_prop { T } }
+    \coffin_get_pole:NnN #1 { B } \l_coffin_pole_b_tl
+    \tl_if_eq:NNT \l_coffin_pole_a_tl \l_coffin_pole_b_tl
+      { \prop_del:Nn \l_coffin_display_poles_prop { B } }
+    \coffin_set_eq:NN \l_coffin_display_coffin #1  
+    \prop_clear:N \l_coffin_handles_tmp_prop
+    \prop_map_inline:Nn \l_coffin_display_poles_prop
+      {
+        \prop_del:Nn \l_coffin_display_poles_prop {##1}
+        \coffin_display_handles_aux:nnnnnn {##1} ##2 {#2}
+      }
+    \box_use:N \l_coffin_display_coffin  
+  }
+%    \end{macrocode}
+%   For each pole there is a check for an intersection, which here does
+%   not give an error if none is found. The successful values are stored
+%   and used to align the pole coffin with the main coffin for output.
+%   The positions are recovered from the preset list if available.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_display_handles_aux:nnnnnn #1#2#3#4#5#6
+  {
+    \prop_map_inline:Nn \l_coffin_display_poles_prop
+      { 
+        \bool_set_false:N \l_coffin_error_bool
+        \coffin_calculate_intersection:nnnnnnnn {#2} {#3} {#4} {#5} ##2
+        \bool_if:NF \l_coffin_error_bool
+          {
+            \dim_set:Nn \l_coffin_display_x_dim { \l_coffin_x_dim }
+            \dim_set:Nn \l_coffin_display_y_dim { \l_coffin_y_dim }
+            \coffin_display_attach:Nnnnn
+              \l_coffin_display_pole_coffin { hc } { vc }
+              { 0 pt } { 0 pt }
+            \hcoffin_set:Nn \l_coffin_display_coord_coffin
+              {
+%<*initex>
+                % TODO 
+%</initex>
+%<*package>
+                \color {#6} 
+%</package>
+                \l_coffin_display_font_tl
+                ( \tl_to_str:n { #1 , ##1 } )
+              }
+            \prop_get:NnN \l_coffin_display_handles_prop
+              { #1 ##1 } \l_coffin_tmp_tl
+            \quark_if_no_value:NTF \l_coffin_tmp_tl
+              {
+                \prop_get:NnN \l_coffin_display_handles_prop
+                  { ##1 #1 } \l_coffin_tmp_tl
+                \quark_if_no_value:NTF \l_coffin_tmp_tl
+                  {
+                    \coffin_display_attach:Nnnnn 
+                      \l_coffin_display_coord_coffin { l } { vc }
+                      { 1 pt } { 0 pt }
+                  }
+                  {  
+                    \exp_last_unbraced:No 
+                      \coffin_display_handles_aux:nnnn
+                      \l_coffin_tmp_tl
+                  }
+              }
+              {
+                \exp_last_unbraced:No \coffin_display_handles_aux:nnnn
+                  \l_coffin_tmp_tl
+              }
+          }
+      }
+  }
+\cs_new_protected_nopar:Npn \coffin_display_handles_aux:nnnn #1#2#3#4
+  {
+    \coffin_display_attach:Nnnnn
+      \l_coffin_display_coord_coffin {#1} {#2}
+      { #3 \l_coffin_display_offset_dim } 
+      { #4 \l_coffin_display_offset_dim }
+  }
+\cs_generate_variant:Nn \coffin_display_handles:Nn { c }
+%    \end{macrocode}
+%   This is a dedicated version of \cs{coffin_attach:NnnNnnnn} with
+%    a hard-wired first coffin. As the intersection is already known
+%   and stored for the display coffin the code simply uses it directly,
+%   with no calculation.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_display_attach:Nnnnn #1#2#3#4#5
+  {
+    \coffin_calculate_intersection:Nnn #1 {#2} {#3}
+    \dim_set:Nn \l_coffin_x_prime_dim { \l_coffin_x_dim }
+    \dim_set:Nn \l_coffin_y_prime_dim { \l_coffin_y_dim }
+    \dim_set:Nn \l_coffin_offset_x_dim
+      { \l_coffin_display_x_dim - \l_coffin_x_prime_dim + #4 }
+    \dim_set:Nn \l_coffin_offset_y_dim
+      { \l_coffin_display_y_dim - \l_coffin_y_prime_dim + #5 }
+    \hbox_set:Nn \l_coffin_aligned_coffin
+      {
+        \box_use:N \l_coffin_display_coffin
+        \tex_kern:D -\box_wd:N \l_coffin_display_coffin
+        \tex_kern:D \l_coffin_offset_x_dim
+        \box_move_up:nn { \l_coffin_offset_y_dim } { \box_use:N #1 }
+      }
+    \box_set_ht:Nn \l_coffin_aligned_coffin 
+      { \box_ht:N \l_coffin_display_coffin }
+    \box_set_dp:Nn \l_coffin_aligned_coffin 
+      { \box_dp:N \l_coffin_display_coffin }
+    \box_set_wd:Nn \l_coffin_aligned_coffin 
+      { \box_wd:N \l_coffin_display_coffin }
+    \box_set_eq:NN \l_coffin_display_coffin \l_coffin_aligned_coffin
+  }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \begin{macro}{\coffin_show_structure:N, \coffin_show_structure:c}
+% \begin{macro}[aux]{\coffin_show_aux:n}
+% \begin{macro}[aux]{\coffin_show_aux:w}
+%   For showing the various internal structures attached to a coffin in 
+%   a way that keeps things relatively readable. If there is no apparent
+%   structure then the code complains.
+%    \begin{macrocode}
+\cs_new_protected_nopar:Npn \coffin_show_structure:N #1
+  {
+    \cs_if_exist:cTF { l_coffin_poles_ \int_value:w #1 _prop }
+      {
+        \iow_term:x 
+          { 
+            \iow_newline:
+            Size~of~coffin~\token_to_str:N #1 : \iow_newline:
+            > ~ ht~=~\dim_use:N \box_ht:N #1 \iow_newline:
+            > ~ dp~=~\dim_use:N \box_dp:N #1 \iow_newline:
+            > ~ wd~=~\dim_use:N \box_wd:N #1 \iow_newline:
+          }
+        \iow_term:x { Poles~of~coffin~\token_to_str:N #1 : }
+        \tl_set:Nx \l_coffin_tmp_tl
+          {
+            \prop_map_function:cN
+              { l_coffin_poles_ \int_value:w #1 _prop }
+              \coffin_show_aux:nn
+          }
+        \etex_showtokens:D \exp_after:wN \exp_after:wN \exp_after:wN
+          { \exp_after:wN \coffin_show_aux:w \l_coffin_tmp_tl } 
+      }
+      { 
+        \iow_term:x { ---~No~poles~found~--- }
+        \tl_show:n { Is~this~really~a~coffin? }
+      }
+  }
+\cs_new:Npn \coffin_show_aux:nn #1#2
+  {
+    \iow_newline: > \c_space_tl \c_space_tl
+    #1 \c_space_tl \c_space_tl => \c_space_tl \c_space_tl \exp_not:n {#2}
+  }
+\cs_new_nopar:Npn \coffin_show_aux:w #1 > ~ { }
+\cs_generate_variant:Nn \coffin_show_structure:N { c }
+%    \end{macrocode}
+% \end{macro}
+% \end{macro}
+% \end{macro}
+%
+% \subsection{Messages}
+%
+%    \begin{macrocode}
+\msg_kernel_new:nnnn { coffin } { no-pole-intersection }
+  { No~intersection~between~coffin~poles. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~was~asked~to~find~the~intersection~between~two~poles,~
+    but~they~do~not~have~a~unique~meeting~point:~
+    the~value~(0~pt,~0~pt)~will~be~used.
+  }
+\msg_kernel_new:nnnn { coffin } { unknown-coffin }
+  { Unknown~coffin~'#1'. }
+  { The~coffin~'#1'~was~never~defined. }
+\msg_kernel_new:nnnn { coffin } { unknown-coffin-pole }
+  { Pole~'#1'~unknown~for~coffin~'#2'. }
+  {
+    \c_msg_coding_error_text_tl
+    LaTeX~was~asked~to~find~a~typesetting~pole~for~a~coffin,~
+    but~either~the~coffin~does~not~exist~or~the~pole~name~is~wrong.
+  }
+%    \end{macrocode}
+%
+%    \begin{macrocode}
+%</initex|package>
+%    \end{macrocode}
+%
+% \end{implementation}
+%
+% \PrintIndex
\ No newline at end of file