% \iffalse meta-comment
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%% File: l3coffins.dtx Copyright(C) 2010,2011 The LaTeX3 Project
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%
%<*driver|package>
\RequirePackage{expl3,graphicx,xcolor}
\GetIdInfo$Id: l3coffins.dtx 2488 2011-06-30 19:19:20Z joseph $
  {L3 Experimental coffins}
%</driver|package>
%<*driver>
\documentclass[full]{l3doc}
\begin{document}
  \DocInput{\jobname.dtx}
\end{document}
%</driver>
% \fi
% 
% \title{^^A
%   The \textsf{l3coffins} package\\ Coffins^^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.
%
% \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}
%<*package>
%    \end{macrocode}
%    
%    \begin{macrocode}
\ProvidesExplPackage
  {\ExplFileName}{\ExplFileDate}{\ExplFileVersion}{\ExplFileDescription}
%    \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_execute:Nn}
%   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_execute:Nn #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_execute:Nn #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_execute:Nn #1
      {
        \hbox_set:Nn #1 
          { 
            \group_begin:
              \set@color
              #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_execute:Nn #1
      {
        \vbox_set:Nn #1 
          {
            \dim_set:Nn \tex_hsize:D {#2}
            \group_begin:
              \set@color
              #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 }
        \dim_set:Nn \l_coffin_tmp_dim
          { \box_ht:N #1 - \box_ht:N \l_coffin_tmp_box }
        \coffin_set_pole:Nnx #1 { T }
          { { 0 pt } { \dim_use:N \l_coffin_tmp_dim } { 1000 pt } { 0 pt } }  
      }
  }
\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_execute:Nn #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:cnN { l_coffin_poles_ \int_value:w #1 _prop } {#2} #3
    \quark_if_no_value:NT #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_execute:Nn #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_execute:Nn #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 } }
    \dim_set:Nn \l_coffin_tmp_dim { - \dim_use:N \box_dp:N #1 }  
    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { bl } 
      { { 0 pt } { \dim_use:N \l_coffin_tmp_dim } }
    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } { br } 
      { { \dim_use:N \box_wd:N #1 } { \dim_use:N \l_coffin_tmp_dim } }
  }
%    \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
  {
    \dim_set:Nn \l_coffin_tmp_dim { 0.5 \box_wd:N #1 }
    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { hc } 
      { { \dim_use:N \l_coffin_tmp_dim } { 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 } }
    \dim_set:Nn \l_coffin_tmp_dim { ( \box_ht:N #1 - \box_dp:N #1 ) / 2 }
    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { vc } 
      { { 0 pt } { \dim_use:N \l_coffin_tmp_dim } { 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 } }
    \dim_set:Nn \l_coffin_tmp_dim { \box_dp:N #1 }
    \dim_compare:nNnF { \l_coffin_tmp_dim } = { \c_zero_dim }
      { \dim_set:Nn \l_coffin_tmp_dim { -\l_coffin_tmp_dim } }
    \prop_put:cnx { l_coffin_poles_ \int_value:w #1 _prop } { b } 
      { { 0 pt } { \dim_use:N \l_coffin_tmp_dim } { 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:
    \hbox_set:Nn #1 { \rotatebox {#2} { \box_use:N #1 } }
%    \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 { - \dim_use:N \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{Resizing coffins}
%
% \begin{variable}{\l_coffin_scale_x_fp}
% \begin{variable}{\l_coffin_scale_y_fp}
%   Storage for the scaling factors in $x$ and $y$, respectively.
%    \begin{macrocode}
\fp_new:N \l_coffin_scale_x_fp
\fp_new:N \l_coffin_scale_y_fp
%    \end{macrocode}
% \end{variable}
% \end{variable}
%
% \begin{variable}{\l_coffin_scaled_total_height_dim}
% \begin{variable}{\l_coffin_scaled_width_dim}
%   When scaling, the values given have to be turned into absolute values.
%    \begin{macrocode}
\dim_new:N \l_coffin_scaled_total_height_dim
\dim_new:N \l_coffin_scaled_width_dim
%    \end{macrocode}
% \end{variable}
% \end{variable}
%
% \begin{macro}{\coffin_resize:Nnn, \coffin_resize:cnn}
%   Resizing a coffin begins by setting up the user-friendly names for
%   the dimensions of the coffin box. The new sizes are then turned into
%   scale factor. This is the same operation as takes place for the 
%   underlying box, but that operation is grouped and so the same
%   calculation is done here.
%    \begin{macrocode}
\cs_new_protected_nopar:Npn \coffin_resize:Nnn #1#2#3
  {
    \coffin_set_user_dimensions:N #1
    \fp_set_from_dim:Nn \l_coffin_scale_x_fp {#2}
    \fp_set_from_dim:Nn \l_coffin_tmp_fp { \Width }
    \fp_div:Nn \l_coffin_scale_x_fp { \l_coffin_tmp_fp }
    \fp_set_from_dim:Nn \l_coffin_scale_y_fp {#3}
    \fp_set_from_dim:Nn \l_coffin_tmp_fp { \TotalHeight }
    \fp_div:Nn \l_coffin_scale_y_fp { \l_coffin_tmp_fp }
    \hbox_set:Nn #1 { \resizebox * {#2} {#3} { \box_use:N #1 } }
    \coffin_resize_common:Nnn #1 {#2} {#3}
  }
\cs_generate_variant:Nn \coffin_resize:Nnn { c }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\coffin_resize_common:Nnn}
%   The poles and corners of the coffin are scaled to the appropriate
%   places before actually resizing the underlying box.
%    \begin{macrocode}
\cs_new_protected_nopar:Npn \coffin_resize_common:Nnn #1#2#3
  {
    \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
      { \coffin_scale_corner:Nnnn #1 {##1} ##2 }
    \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
      { \coffin_scale_pole:Nnnnnn #1 {##1} ##2 }
%    \end{macrocode}
%   Negative $x$-scaling values will place the poles in the wrong
%   location: this is corrected here.
%    \begin{macrocode}
    \fp_compare:NNNT \l_coffin_scale_x_fp < \c_zero_fp
      {
        \prop_map_inline:cn { l_coffin_corners_ \int_value:w #1 _prop }
          { \coffin_x_shift_corner:Nnnn #1 {##1} ##2 }
        \prop_map_inline:cn { l_coffin_poles_ \int_value:w #1 _prop }
          { \coffin_x_shift_pole:Nnnnnn #1 {##1} ##2 }
      }  
    \coffin_end_user_dimensions:
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\coffin_scale:Nnn, \coffin_scale:cnn}
%   For scaling, the opposite calculation is done to find the new
%   dimensions for the coffin. Only the total height is needed, as this
%   is the shift required for corners and poles. The scaling is done
%   the \TeX{} way as this works properly with floating point values
%   without needing to use the \texttt{fp} module.
%    \begin{macrocode}
\cs_new_protected_nopar:Npn \coffin_scale:Nnn #1#2#3
  {
    \coffin_set_user_dimensions:N #1
    \fp_set:Nn \l_coffin_scale_x_fp {#2}
    \fp_set:Nn \l_coffin_scale_y_fp {#3}
    \fp_compare:NNNTF \l_coffin_scale_y_fp > \c_zero_fp
      { \l_coffin_scaled_total_height_dim #3 \TotalHeight }
      { \l_coffin_scaled_total_height_dim -#3 \TotalHeight }
    \fp_compare:NNNTF \l_coffin_scale_x_fp > \c_zero_fp
      { \l_coffin_scaled_width_dim -#2 \Width }
      { \l_coffin_scaled_width_dim #2 \Width }
    \hbox_set:Nn #1 { \scalebox  {#2} [#3] { \box_use:N #1 } }
    \coffin_resize_common:Nnn #1 
      { \l_coffin_scaled_width_dim } { \l_coffin_scaled_total_height_dim }
  }
\cs_generate_variant:Nn \coffin_scale:Nnn { c }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\coffin_scale_vector:nnNN}
%   This functions scales a vector from the origin using the pre-set scale
%   factors in $x$ and $y$. This is a much less complex operation
%   than rotation, and as a result the code is a lot clearer.
%    \begin{macrocode}
\cs_new_protected_nopar:Npn \coffin_scale_vector:nnNN #1#2#3#4
  {
    \fp_set_from_dim:Nn \l_coffin_tmp_fp {#1}
    \fp_mul:Nn \l_coffin_tmp_fp { \l_coffin_scale_x_fp }
    \dim_set:Nn #3 { \fp_to_dim:N \l_coffin_tmp_fp }
    \fp_set_from_dim:Nn \l_coffin_tmp_fp {#2}
    \fp_mul:Nn \l_coffin_tmp_fp { \l_coffin_scale_y_fp }
    \dim_set:Nn #4 { \fp_to_dim:N \l_coffin_tmp_fp }
  }
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\coffin_scale_corner:Nnnn}
% \begin{macro}{\coffin_scale_pole:Nnnnnn}
%   Scaling both corners and poles is a simple calculation using the 
%   preceding vector scaling.
%    \begin{macrocode}
\cs_new_protected_nopar:Npn \coffin_scale_corner:Nnnn #1#2#3#4
  {
    \coffin_scale_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 } }  
  }
\cs_new_protected_nopar:Npn \coffin_scale_pole:Nnnnnn #1#2#3#4#5#6
  {
    \coffin_scale_vector:nnNN {#3} {#4} \l_coffin_x_dim \l_coffin_y_dim
    \coffin_set_pole:Nnx #1 {#2}
      {
        { \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_x_shift_corner:Nnnn}
% \begin{macro}{\coffin_x_shift_pole:Nnnnnn}
%   These functions correct for the $x$ displacement that takes
%   place with a negative horizontal scaling.
%    \begin{macrocode}
\cs_new_protected_nopar:Npn \coffin_x_shift_corner:Nnnn #1#2#3#4
  {
    \prop_put:cnx { l_coffin_corners_ \int_value:w #1 _prop } {#2}
      { 
        { \dim_eval:n { #3 + \box_wd:N #1 } } {#4}
    }  
  }
\cs_new_protected_nopar:Npn \coffin_x_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 + \box_wd:N #1 } {#4} 
        {#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
\tl_set:Nn \l_coffin_display_font_tl { \sffamily \tiny }
%    \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
      {
        \color {#4} 
        \rule { 1 pt } { 1 pt } 
        \hbox:n { \tex_vrule:D width 1 pt height 1 pt \scan_stop: }
      }
    \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
      {
        \color {#4} 
        \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
      {
        \color {#2} 
        \rule { 1 pt } { 1 pt } 
      }
    \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
              {
                \color {#6} 
                \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}
%</package>
%    \end{macrocode}
%
% \end{implementation}
%
% \PrintIndex