mfpic 1.06 (21mar11)

git-svn-id: svn://tug.org/texlive/trunk@21800 c570f23f-e606-0410-a88d-b1316a301751

3 files changed, 324 insertions, 103 deletions

diff --git a/Master/texmf-dist/source/generic/mfpic/grafbase.dtx b/Master/texmf-dist/source/generic/mfpic/grafbase.dtx
index 32d14a5b676..a309f242f6e 100644
--- a/Master/texmf-dist/source/generic/mfpic/grafbase.dtx
+++ b/Master/texmf-dist/source/generic/mfpic/grafbase.dtx
@@ -1,10 +1,10 @@
 % \iffalse
-%%% File: grafbase.dtx
-%%% A part of mfpic 1.05 2010/06/10
-%%%
+% File: grafbase.dtx
+% A part of mfpic 1.06 2011/03/08
+%
 % -------------------------------------------------------------------
 %
-% Copyright 2002--2010, Daniel H. Luecking
+% Copyright 2002--2011, Daniel H. Luecking
 %
 % Mfpic may be distributed and/or modified under the conditions of the
 % LaTeX Project Public License, either version 1.3b of this license or (at
@@ -19,7 +19,7 @@
 %
 %<*driver>
 \ProvidesFile{grafbase.dtx}
-  [2010/06/10 v1.05. Metafont/post macros to interface with mfpic.]%
+  [2011/03/08 v1.06. Metafont/post macros to interface with mfpic.]%
 \documentclass{ltxdoc}
 \usepackage{docmfp}
 
@@ -113,7 +113,7 @@
 %</driver>
 %\fi
 %
-% \CheckSum{1453}
+% \CheckSum{1473}
 % \CharacterTable
 %  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
 %   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
@@ -187,7 +187,7 @@ fi
 boolean grafbase; grafbase := true;
 
 string fileversion, filedate;
-fileversion := "1.05";  filedate := "2010/06/10";
+fileversion := "1.06";  filedate := "2011/02/25";
 
 message " Loading grafbase macros, version " & fileversion & ", " &
   filedate & ".";
@@ -236,7 +236,7 @@ def checkversions (expr g)=
   fi
 enddef;
 
-checkversions (105);
+checkversions (106);
 
 %    \end{macrocode}
 %
@@ -672,11 +672,11 @@ vardef cmykgray (expr g) =  cmyk(0,0,0,1 - snapto g)  enddef;
 % with three-way booleans (often containing nested booleans).
 %
 % For all three engines we require a definition of the color functions
-% \gbc{gray(g)}, \gbc{rgb(r,g,b)}, and \gbc{cmyk(c,m,y,k)}, conversion
-% functions \gbc{makegray(x)}, \gbc{makergb(x)}, amd \gbc{makecmyk(x)},
-% and the boolean \gbc{iscolor clr}. The first three have to return
-% numerics for \MF{}, colors for early \MP{}, and the associated color
-% type for recent \MP{}.
+% \gbc{gray(g)}, \gbc{rgb(r,g,b)}, and \gbc{cmyk(c,m,y,k)}, as well as
+% conversion functions \gbc{makegray(x)}, \gbc{makergb(x)}, and
+% \gbc{makecmyk(x)}, and the boolean \gbc{iscolor clr}. The first three
+% have to return numerics for \MF{}, colors for early \MP{}, and the
+% associated color type for recent \MP{}.
 %    \begin{macrocode}
 %<*MP>
 if has_cmyk :
@@ -729,7 +729,8 @@ if has_cmyk :
   enddef;
   vardef makergb primary clr =
     colorchoice (clr)(rgbblack)(rgbgray(clr))(clr)
-    (cmyktorgb(cyanpart clr, magentapart clr, yellowpart clr, blackpart clr))
+    (cmyktorgb(cyanpart clr, magentapart clr, yellowpart clr,
+        blackpart clr))
   enddef;
   vardef makegray primary clr =
     colorchoice (clr)(grayscaleblack)(grayscalegray(clr))
@@ -4513,12 +4514,14 @@ enddef;
 % Once we know what segment we are in, we determine the time by linear
 % interpolation between the times corresponding to \gbc{ct} and
 % \gbc{ct+1}. Note: in the \mfc{forever} loop, the exit must come before
-% the increment.
+% the increment. The function \gbc{inrange} is defined in
+% section~\ref{axes}. It checks if the third argument is between the
+% first two, or equal to one of them.
 %    \begin{macrocode}
 vardef gettime (suffix arr, ct) (expr lngth) =
   setnumeric (_gtl) emax (arr[ct], emin (arr[arr], lngth));
   setsplit (_s) segment_split;
-  forever:  exitif ( (arr[ct] <= _gtl) and (_gtl <= arr[ct+1]) );
+  forever:  exitif inrange (arr[ct], arr[ct+1]) (_gtl);
     next ct;
   endfor
   if arr[ct] = arr[ct+1]:  ct
@@ -4987,17 +4990,48 @@ vardef axisline.t =  axisline.x shifted (0, yhigh)  enddef;
 
 vardef axis@# (expr len) =  headpath (len, 0, 0) axisline@#  enddef;
 
+%    \end{macrocode}
+%
+% \DescribeRoutine{borderrect}
+% These are mostly for the simplification of \mfpic{} and readability of
+% code. The command \gbc{borderrect} produces the border of the picture
+% in graph coordinates, taking into account the four margins.
+%
+% \DescribeRoutine{between}
+% The boolean \gbc{between} checks if the last argument is strictly
+% between the first two (which must be in order).
+%
+% \DescribeRoutine{inrange}
+% The boolean \gbc{inrange} checks if the last argument is in the closed
+% interval determined by the first two (which must be in order).
+%
+% \DescribeRoutine{inbounds}
+% The boolean \gbc{inbounds} checks if the argument (a pair) is in
+% the closed border rectangle (\gbc{borderrect}). It is not yet used in
+% \grafbase{}, though it would seem it ought to be useful.
+%    \begin{macrocode}
 vardef borderrect =
   rect((xlow,ylow),(xhigh,yhigh))
 enddef;
 
+vardef between (expr A, B, X) = (A <  X) and (X <  B)  enddef;
+vardef inrange (expr A, B, X) = (A <= X) and (X <= B)  enddef;
+
 vardef inbounds (expr Z) =
-  (xpart Z >= xlow ) and (ypart Z >= ylow ) and
-  (xpart Z <= xhigh) and (ypart Z <= yhigh)
+  inrange (xlow, xhigh) (xpart Z) and inrange (ylow, yhigh) (ypart Z)
 enddef;
 
 %    \end{macrocode}
 %
+% Possible binary relation versions. The last is just a reversal of the
+% order of the first. These are not yet used in \grafbase{}.
+%    \begin{macrocode}
+tertiarydef X isbetween P =  between (xpart P, ypart P, X)  enddef;
+tertiarydef X isinrange P =  inrange (xpart P, ypart P, X)  enddef;
+tertiarydef P contains X  =  between (xpart P, ypart P, X)  enddef;
+
+%    \end{macrocode}
+%
 % Tick marks can be on the inside or outside of a border axis,
 % above or below any horizontal axes, left or right of any vertical axis
 % or centered on any axis. The following numerics are merely used to
@@ -5216,7 +5250,7 @@ def plrvectorfield (expr len, rsp, tsp) (text fcn) (text cond) =
   vardef _vf (expr r,t) =  ((0,0)--(fcn)) shifted (r*dir t)  enddef;
   vardef _is_OK (expr r,t) =
     save _X, _Y;  _X := r*cosd t;  _Y := r*sind t;
-    (cond) and (_A < _X) and (_X < _B) and (_C < _Y) and (_Y < _D)
+    (cond) and between (_A, _B) (_X) and between (_C, _D) (_Y)
   enddef;
   mkplrvectorfield (len, rsp, tsp) (_vf, _is_OK);
 enddef;
@@ -5385,7 +5419,7 @@ def getpolarbounds =
 % \gbc{tmin}${} < \theta < {}$\gbc{tmax} includes the graph.
 %    \begin{macrocode}
     rmin := 0;
-    if (xneg < 0) and (xpos > 0) and (yneg < 0) and (ypos > 0):
+    if between (xneg, xpos) (0) and between (yneg, ypos) (0):
       tmin := 0;  tmax := 360;
     elseif (p0 = origin):  tmin :=    0;  tmax :=  90;
     elseif (p1 = origin):  tmin :=  -90;  tmax :=   0;
@@ -5406,9 +5440,9 @@ def getpolarbounds =
 % the following order: (1)~above or below, (2)~left or right, and (3)~one
 % of the four corner regions.
 %    \begin{macrocode}
-      if (xneg < 0) and (0 < xpos):
+      if between (xneg, xpos) (0):
         rmin := emin (abs(yneg), abs(ypos));
-      elseif (yneg < 0) and (0 < ypos):
+      elseif between (yneg, ypos) (0):
         rmin := emin (abs(xneg), abs(xpos));
       else:
         rmin := min (r0, r1, r2, r3);
@@ -5596,8 +5630,10 @@ vardef anglefromto (expr u, v) =
 enddef;
 
 vardef cornerangle (expr A, B, C) =
-  if (A = B) and (B = C) :  60
-  elseif (A=B) or (A=C) :  90
+  if (A = B) or (A = C) :
+    if (B = C) :  60
+    else:         90
+    fi
   else:  anglefromto (B - A, C - A)
   fi
 enddef;
@@ -6834,14 +6870,14 @@ vardef pshcircle (expr disk, ctr, rad) =
   if disk:
     if rad >= 1 :
       if rad > 1:
-        GBerrmsg ("Impossible pseudohyperbolic circle.")
+        GBerrmsg ("Impossible radius of pseudohyperbolic circle.")
           "The radius of a pseudohyperbolic circle can be at most 1.";
       fi
       circle ((0,0),1)
     elseif abs(ctr) >= 1 :
       if abs(ctr) > 1:
-        GBerrmsg ("Impossible pseudohyperbolic circle.")
-          "The center of a pseudohyperbolic circle must be in"
+        GBerrmsg ("Impossible center of pseudohyperbolic circle.")
+          "The center of a pseudohyperbolic circle must be in "
           & "the unit disk.";
       fi
       onepointpath (true,ctr)
@@ -6861,7 +6897,7 @@ vardef pshcircle (expr disk, ctr, rad) =
     elseif ypart ctr <= 0:
       if ypart ctr < 0:
         GBerrmsg ("Impossible pseudohyperbolic circle.")
-          "The center of a pseudohyperbolic circle must be in"
+          "The center of a pseudohyperbolic circle must be in "
           & "the upper half-plane.";
       fi
       onepointpath (true,ctr)
@@ -7112,8 +7148,7 @@ tolerancefactor := .02;
 vardef mklevelset (expr sm, tens, X, Y, t, a, b, c, d) =
   save _inside_;
   vardef _inside_ (expr U, V) =
-    inside_levelset (U, V) and (a < U) and (U < b)
-      and (c < V) and (V < d)
+    inside_levelset (U, V) and between (a, b) (U) and between (c, d) (V)
   enddef;
   if not _inside_ (X, Y):
     GBwarn "Invalid seed point for levelset.";
@@ -7175,6 +7210,104 @@ enddef;
 
 %    \end{macrocode}
 %
+% Our next set of macros produce approximations to the solutions of
+% differential equations. While we could have several different macros
+% each using a different method (Euler, two-step Runge-Kutta, four-step
+% Runge-Kutta, etc.), our point of view is that we just want to draw a
+% reasonably accurate solution, so we only utilize one method: four-step
+% Runge-Kutta. The variations we allow are the following:
+% \begin{enumerate}
+% \item Drawing the graph of a one-dimensional differential
+%       equation,
+%       \[ \frac{dy}{dx} = g(x,y)\,.\]
+%
+% \item Drawing the trajectory of a two-dimensional differential
+%       equation,
+%       \[ \left( \frac{dx}{dt},\frac{dy}{dt} \right) =
+%       (f(x,y,t), g(x,y,t))\,.\]
+% \end{enumerate}
+% The first of these is implemented using the second with $f(x,y,t) \equiv
+% 1$ and $g(x,y,t)$ not depending on $t$. The parameters passed include
+% the starting point, the step size, the number of steps and an expression
+% representing the right side of the equation.
+%
+% We do not use exactly the traditional Runge-Kutta method: we use the
+% Runge-Kutta algorithm, but with a variable step size. The time step
+% $\Delta t$ is chosen so that $|\mathbf{F}(x,y,t)|\Delta t$ equals the
+% given step size parameter, and thus the parameter passed is actually a
+% distance step. This makes drawing more stable, especially if the DE is
+% one that produces an infinite path in finite time.
+%
+% This modification is itself unstable if $|\mathbf{F}|$ is very
+% small (and impossible if it is zero), so we never use a $\Delta t$
+% larger than the given step size parameter $\Delta s$. That is, we
+% actually use $\Delta t = \Delta s/\max(1,|\mathbf{F}|)$.
+%
+% As with our other function-like paths, we offer two variants. The basic
+% version has a final text parameter which is the name of a pair-valued
+% function of a numeric (representing $t$) and a pair variable
+% (representing $x$ and $y$). The other version takes a text
+% parameter, which must be a pair-valued expression in \mfc{x}, \mfc{y}
+% and \mfc{t}. This parameter is copied into the definition text of a
+% function and then the first form is called with that function's name.
+%
+% Also like other function-like paths, we offer polygonal or smooth
+% versions controlled by a boolean argument, and the smooth versions make
+% use of a tension parameter.
+%    \begin{macrocode}
+def RKIV (expr sm) =  tRKIV (sm, default_tension)
+enddef;
+vardef tRKIV (expr sm, tens, zstart, ds, N) (text _RHS_) =
+  save _trj, _ztr, _dz, _ztmp, _ctm;
+  pair _trj[],          % The trajectory
+       _ztr,            % current point
+       _dz[],           % array[4] of displacements
+       _ztmp;           % current point for calculating velocity
+%
+  _trj := N+1;          % ultimate size of _trj array
+  _trj1 := _ztr := zstart;
+  save _tt,             % current time
+       _dt,             % current time step
+       _th;             % current time plus half a step
+  _tt := 0;
+  for _idx := 2 upto _trj:
+    _dt   := ds/emax(1,abs(_RHS_(_tt,_ztr)));
+    _th   := _tt + .5_dt;
+    _dz1  := _dt*_RHS_(_tt, _ztr);  % displacement based on current point
+    _ztmp := _ztr + .5_dz1;         % 1st midpoint
+  % use _th instead of twice calculating (_tt + .5_dt)
+    _dz2  := _dt*_RHS_(_th, _ztmp); % displacement based on 1st midpoint
+    _ztmp := _ztr + .5_dz2;         % 2nd midpoint
+    _dz3  := _dt*_RHS_(_th, _ztmp); % displacement based on 2nd midpoint
+    _ztmp := _ztr + _dz3;           % temporary end point
+  % get time for next loop now since we need it right away in next line:
+    _tt   := _tt + _dt;
+    _dz4  := _dt*_RHS_(_tt, _ztmp); % displacement based on end point
+  % get next point
+    _ztr  := _ztr + (_dz1 + 2_dz2 + 2_dz3 + _dz4)/6;
+    _trj[_idx] := _ztr;
+  endfor
+  mkpath (sm, tens, false, _trj)
+enddef;
+
+def xyRKIV (expr sm) = txyRKIV (sm, default_tension)
+enddef;
+vardef txyRKIV (expr sm, tens, zstart, ds, N) (text _RHS_) =
+  save _fgxy, __fgxy;
+  vardef __fgxy (expr t, x, y) =  _RHS_  enddef;
+  vardef _fgxy (expr t, Z) = __fgxy(t, xpart Z, ypart Z) enddef;
+  tRKIV (sm, tens, zstart, ds, N) (_fgxy)
+enddef;
+
+def odeRKIV (expr sm) = todeRKIV (sm, default_tension)
+enddef;
+vardef todeRKIV (expr sm, tens, xstart, ystart, ds, N)
+(text _fxy) =
+  txyRKIV (sm, tens, (xstart, ystart), ds, N) ((1, _fxy))
+enddef;
+
+%    \end{macrocode}
+%
 % \section{Modification of Paths}\label{modification}
 %
 % \subsection{Closing a path}\label{closing}
diff --git a/Master/texmf-dist/source/generic/mfpic/mfpic.dtx b/Master/texmf-dist/source/generic/mfpic/mfpic.dtx
index cc427bbf7f2..5da4b773a74 100644
--- a/Master/texmf-dist/source/generic/mfpic/mfpic.dtx
+++ b/Master/texmf-dist/source/generic/mfpic/mfpic.dtx
@@ -1,17 +1,17 @@
 % \iffalse
-%%% File: mfpic.dtx
-%%% A part of mfpic 1.05 2010/06/10
-%%%
+% File: mfpic.dtx
+% A part of mfpic 1.06 2011/03/08
+%
 % -------------------------------------------------------------------
 %
-% Copyright 2002--2010, Daniel H. Luecking
+% Copyright 2002--2011, Daniel H. Luecking
 %
 % Mfpic may be distributed and/or modified under the conditions of the
-% LaTeX Project Public License, either version 1.3b of this license or (at
+% LaTeX Project Public License, either version 1.3c of this license or (at
 % your option) any later version. The latest version of this license is in
 %    <http://www.latex-project.org/lppl.txt>
-% and version 1.3b or later is part of all distributions of LaTeX version
-% 2003/12/01 or later.
+% and version 1.3c or later is part of all distributions of LaTeX version
+% 2008/12/01 or later.
 %
 % Mfpic has maintenance status "author-maintained". The Current Maintainer
 % is Daniel H. Luecking. There are several Base Interpreters: plain TeX, LaTeX,
@@ -22,7 +22,7 @@
 %</driver>
 %<sty>\ProvidesPackage{mfpic}
 %<*sty>
-  [2010/06/10 v1.05. Macros for drawing with Metafont/MetaPost.]%
+  [2011/03/08 v1.06. Macros for drawing with Metafont/MetaPost.]%
 %</sty>
 %<*driver>
 \documentclass{ltxdoc}
@@ -106,7 +106,7 @@
 \end{document}
 %</driver>
 %\fi
-% \CheckSum{5119}
+% \CheckSum{5145}
 % \CharacterTable
 %  {Upper-case    \A\B\C\D\E\F\G\H\I\J\K\L\M\N\O\P\Q\R\S\T\U\V\W\X\Y\Z
 %   Lower-case    \a\b\c\d\e\f\g\h\i\j\k\l\m\n\o\p\q\r\s\t\u\v\w\x\y\z
@@ -134,9 +134,9 @@
 % produce the picture. The picture is then included on a second pass
 % through \TeX.
 %
-% This file documents the source code. See \file{mfpic-doc.pdf} (source
-% \file{mfpic.doc.tex} for the user documentation or \file{mfpguide.pdf}
-% (source \file{mfpguide.tex}) for an introductory guide.
+% This file documents the source code. See \file{mfpic-doc.pdf}/\file{tex}
+% for the user documentation, or \file{mfpguide.pdf}/\file{tex}) for an
+% introductory guide.
 % \end{abstract}
 %
 % \StopEventually{\PrintIndex}
@@ -170,9 +170,9 @@
 \ifx\mfpfileversion\UndEfInEd\else\expandafter\endinput\fi%
 {%
   \catcode\lq\.12 \catcode\lq\/12%
-  \gdef\mfpfileversion{1.05}%
-  \gdef\mfpfiledate{2010/06/10}%
-  \gdef\mfpicversion{105}%
+  \gdef\mfpfileversion{1.06}%
+  \gdef\mfpfiledate{2011/02/25}%
+  \gdef\mfpicversion{106}%
 }%
 %    \end{macrocode}
 %
@@ -335,18 +335,20 @@
 % The following might be useful in patching things or adding to
 % \cs{mfp@additions}.
 %    \begin{macrocode}
-\mfp@ifdefined\g@addto@macro{}{%
+\mfp@ifundefined\g@addto@macro
   \long\def\g@addto@macro#1#2{%
     \begingroup
       \toks@\@xp{#1#2}%
       \xdef#1{\the\toks@}%
-    \endgroup}}%
-\mfp@ifdefined\g@prependto@macro{}{%
+    \endgroup}%
+\mfp@enddef
+\mfp@ifundefined\g@prependto@macro
   \long\def\g@prependto@macro#1#2{%
     \begingroup
       \toks@{#2}\toks2\@xp{#1}%
       \xdef#1{\the\toks@\the\toks2}%
-    \endgroup}}%
+    \endgroup}%
+\mfp@enddef
 %    \end{macrocode}
 %
 % We test for LaTeX. We assume plain\TeX{}, or something compatible,
@@ -527,7 +529,7 @@
 \newdef\mfp@justify@error{%
     \mfp@errmsg{Invalid justification parameter for text label}%
      {The optional argument for an mfpic text label must be^^J%
-      one of B, b, c or t, followed by^^J
+      one of B, b, c or t, followed by^^J%
       one of l, r or c, optionally followed by an angle.}}%
 %    \end{macrocode}
 %
@@ -722,7 +724,7 @@
   \ifmfp@latex
     \ifmfp@centcapt \centering \else \raggedright \fi
   \else
-    \rightskip 0pt plus 1fil
+    \rightskip 0pt plus 1fil\relax
     \ifmfp@centcapt
       \leftskip 0pt plus 1fil
       \parfillskip 0pt plus 1fil\relax
@@ -1065,6 +1067,11 @@
     \let\Gread@parse@bb\mfp@parse@bb}%
   \global\let\setmfpicgraphic\includegraphics
   \gdef\getmfpicoffset##1{}}%
+%    \end{macrocode}
+%
+% The \LaTeX{} wrapper ends by inputing \file{mfpic.tex}.
+%    \begin{macrocode}
+\input mfpic.tex\relax
 %</sty>
 %    \end{macrocode}
 %
@@ -1214,11 +1221,16 @@
 % executed. When neither follows, nothing is removed and \arg3 is
 % executed. Normally, this last is the main command being applied to each
 % element of the list.
+%
+% We also define \LaTeX's \cs{@ifstar} for the few cases that require it.
 %    \begin{macrocode}
 \def\mfp@iftoken#1#2{\@ifnextchar#1{\@firstoftwo{#2}}}%
 \def\mfp@ifstar#1#2#3{\mfp@iftoken*{#1{#2}}{#1{#3}}}%
 \def\mfp@ifend{\mfp@iftoken\mfp@end}%
 \def\mfp@ifendorcomma#1#2#3{\mfp@ifend{#1}{\mfp@iftoken,{#2}{#3}}}%
+\mfp@ifundefined\@ifstar
+  \def\@ifstar#1{\@ifnextchar*{\@firstoftwo{#1}}}%
+\mfp@enddef
 %    \end{macrocode}
 %
 % I've taken to making an empty optional argument the default for a lot
@@ -1390,6 +1402,19 @@
 \newdef\mfp@wlist#1{\mfp@src\mflist{(#1);}}%
 %    \end{macrocode}
 %
+% If \prog{babel} is loaded with some options, certain punctuation will
+% be made active. These will then be expanded when written to the graph
+% file. \prog{Babel} provides a way to turn this off, but it would be an
+% error to run those commands if \prog{babel} is not loaded. Rather than
+% try to detect \prog{babel}, we run these commands only if they are
+% defined.
+%    \begin{macrocode}
+\def\mfp@safe@activestrue{%
+  \mfp@ifdefined\@safe@activestrue\@safe@activestrue{}}%
+\def\mfp@safe@activesfalse{%
+  \mfp@ifdefined\@safe@activesfalse\@safe@activesfalse{}}%
+%    \end{macrocode}
+%
 % \subsection{Initializing the output file}\label{output}
 %
 % Category 12 characters percent, sharp and backslash signs for the
@@ -1501,7 +1526,7 @@
 % \grafbase{} macros to be loaded.
 %    \begin{macrocode}
 \newdef\mfp@versioninfo{%
-  \mfp@p\space\mfp@filename.m\mfp@ifmpost{p}{f},
+  \mfp@p\space\mfp@filename.m\mfp@ifmpost{p}{f}, %
     generated by Mfpic, v\mfpfileversion\space\mfpfiledate,\@nl
   \mfp@p\space from TeX source "\jobname" on \mfp@now\@nl
   numeric mfpicversion; mfpicversion := \mfpicversion;\@nl}%
@@ -1654,7 +1679,7 @@
 %    \begin{macrocode}
   \mfp@ifopengraphsfile%
    {\Mfpic@warn
-     {\@nl An attempt has been made to open a graph file,
+     {\@nl An attempt has been made to open a graph file, %
       \mfp@sanitized\mfp@tempa\@msgbreak
       while another, \mfp@filename, is still open. \@msgbreak
       Closing \mfp@filename.}\mfp@closegraphsfile}%
@@ -1758,8 +1783,8 @@
   #1\edef#2{%
     \@ifundefined{\mfp@cmdname#2}{???}{\@nameuse{\mfp@cmdname#2}}}%
   \@ifundefined{\mfp@cmdname#2}%
-    {\mfp@msg{}\Mfpic@msg{No value for \string#2\ifin@mfpicenv\space in
-    mfpic figure \number\mfp@count\fi.\@nl}}%
+    {\mfp@msg{}\Mfpic@msg{No value for \string#2\ifin@mfpicenv\space
+    in mfpic figure \number\mfp@count\fi.\@nl}}%
     {}%
   \mfsrc{\@ifmplabels{\@nl verbatimtex #1\def\string#2{#2} etex;\@nl}{}%
     message "\string\mfpicvalue";\@nl
@@ -2674,7 +2699,7 @@
   \mfp@local\edef\tl@rot{#2}%
   \@ifmplabels{}%
    {\mfp@ifexist{#2}%
-     {\Mfpic@warn{Rotation of labels is not supported without the
+     {\Mfpic@warn{Rotation of labels is not supported without the %
         mplabels\@msgbreak option. Rotation setting\on@line\space
         may be ignored.}}%
    }}%
@@ -2888,7 +2913,7 @@
   \mfp@ifmpost
    {\mfp@local\mfp@linetype0
     \mfp@def\mfp@setstyle{\draw[getcolor \number\mfp@linetype]}}%
-   {\Mfpic@warn{You can't use \mfp@b coloredlines in
+   {\Mfpic@warn{You can't use \mfp@b coloredlines in %
       Metafont.\@msgbreak Using \dashedlines instead}%
     \dashedlines}}%
 %    \end{macrocode}
@@ -3669,6 +3694,68 @@
   \def\levelcurve{\mfp@fcn{levelset}p}%
 %    \end{macrocode}
 %
+% We now define two macros for depicting the solution of an
+% ordinary differential equation. THe first of these, \cs{DEgraph},
+% produces the graph of solutions of equations of the form
+% $$
+%  \frac{dy}{dx} = f(x,y),\quad y(x_0) = y_0.
+% $$
+% The data required are the \emph{initial values} (the two numbers $x_0$
+% and $y_0$), the formula $f(x,y)$ (an explicit \MF{} numerical expression
+% with literal variables \mfc{x} and \mfc{y} as the only unknowns. Since
+% the \MF{} and only handle paths connecting discrete points, also
+% required is a step size which, roughly speaking, is the distance between
+% points in graph coordinates, and the number of steps $N$ to use. The \MF{}
+% macros then calculate $N$ additional points (the first is $(x_0,y_0)$) and join
+% them together to produce the graph.
+%
+% The second macro, \cs{DEtrajectory}, draws the trajectory of a
+% two-dimentional differential equation of the form
+% $$
+%   \left( \frac{dx}{dt}, \frac{dy}{dt}\right) = (f(x,y,t),g(x,y,t)\,,
+%        \quad (x(0),y(0)) = (x\sb0,y\sb0)
+% $$
+% This is not, strictly speaking, a \emph{graph} since that would
+% require three dimensions to indicate the relation between $x$, $y$, and
+% $t$. Mathematicians call it a trajectory, and it only shows the
+% two-dimensional path followed by the moving object. The required data
+% are an initial point $(x_0,y_0)$, the formula for the right-hand side
+% (an explicit \MF{} pair-valued expression or a pair of numerical
+% expressions in parentheses, with literal variables \mfc{x}, \mfc{y} and
+% \mfc{t} as the only unknowns. Also required are a step size and the
+% number of steps, as in \cs{DEgraph}.
+%
+% The method used to calculate the points to connect is a modified version
+% of the four-step Runge-Kutta method. The modifications are intended to
+% avoid numerical overflow. That is, infinite blow-up in finite time. An
+% example is the simple equation
+% $$
+%    \frac{dy}{dx} = y^2 \quad y(0) = 1,
+% $$
+% whose solution is $y = 1/(1-x)$. The usual definition of
+% Runge-Kutta-IV would have one process equally spaced $x$-values. If a
+% user had no idea of the character of the solution, and asked for $N$
+% $x$-values with separation $h$ to get a graph on $0\le x \le Nh$, and if
+% $Nh > 1$, then the result would be either quite different from the actual
+% solution (especially around $x=1$), or would reach a point of numerical
+% overflow.
+%
+% Thus our macros require the user to supply a parameter that will be
+% interpreted as a distance step: if $h$ is this parameter, instead of
+% finding values of $y$ at $x_0$, $x_0+h$, $x_0+2h$, etc., it finds points
+% $(x_n,y_n)$ on the graph so that the two-dimensional distance from $(x_0,y_0)$
+% to $(x_1,y_1)$ is $h$, then the distance from $(x_1,y_1)$ to $(x_2,y_2)$
+% is also $h$, etc. The resulting graph therefore simply follow the graph
+% of $y = 1/(1-x)$ a distance roughly $Nh$ and numerical overflow is
+% impossible unless the value of $Nh$ exceeds \MF{}'s size limits.
+%
+% There is an optional smoothness parameter as in \cs{function}.
+%    \begin{macrocode}
+  \newdef\DEgraph{\mfp@fcn{odeRKIV}s}%
+  \newdef\DEtrajectory{\mfp@fcn{xyRKIV}s}%
+%    \end{macrocode}
+%
+%
 % \subsection{Plotting data from files}\label{datafiles}
 %
 % \DescribeMacro{\plotdata}
@@ -3944,7 +4031,7 @@
 % the tension value (empty if there is no tension option).
 %
 % \DescribeMacro{\sclosed}
-% The first, \cs{sclosed} closes smoothly in the same manner that
+% The first, \cs{sclosed}, closes smoothly in the same manner that
 % \cs{curve} creates a smooth path.
 % \DescribeMacro{\bclosed}
 % The second, \cs{bclosed}, uses an ordinary \MF{} B\'ezier. These two
@@ -4781,15 +4868,16 @@
   \mfp@listmac{\mfp@ifempty{#1}{fcncurve}{functioncurve (#1)}}}%
 %    \end{macrocode}
 %
-% \cs{mfp@fcn} is called by six commands: \cs{levelcurve},
-% \cs{plrregion}, \cs{belowfcn}, \cs{function}, \cs{plrfcn} and,
-% \cs{parafcn}. They have a common argument structure for both
-% the \mfpic{} and \grafbase{} command. \cs{mfp@fcn} calls
-% \cs{mfp@dotension} to parse the optional tension argument (the second
-% argument) leaving the results in the macros \cs{mfp@t} (a \texttt{t}
-% for command name if a tension value was present) and \cs{mfp@sval}
-% (\texttt{true} or \texttt{false} and the tension value if it was
-% present). The first argument is the base name of a \grafbase{} command.
+% \cs{mfp@fcn} is called by eight commands: \cs{levelcurve},
+% \cs{plrregion}, \cs{belowfcn}, \cs{function}, \cs{plrfcn},
+% \cs{parafcn}, \cs{DEgraph} and \cs{DEtrajectory}. They have a common
+% argument structure for both the \mfpic{} and \grafbase{} command.
+% \cs{mfp@fcn} calls \cs{mfp@dotension} to parse the optional tension
+% argument (the second argument) leaving the results in the macros
+% \cs{mfp@t} (a \texttt{t} for command name if a tension value was
+% present) and \cs{mfp@sval} (\texttt{true} or \texttt{false} and the
+% tension value if it was present). The first argument is the base name of
+% a \grafbase{} command.
 %
 % Ultimately, \cs{mfp@@fcn} is called, and only then the two mandatory
 % arguments of the calling command are read.
@@ -5035,15 +5123,15 @@
   \mfp@ifexist{#1}{\mfp@@arropt#1\mfp@end}\mfp@@arr}%
 \newdef\mfp@@arropt#1#2\mfp@end{%
   \mfp@ifempty{#2}%
-   {\Mfpic@warn{Arrow option #1 has no value\on@line;
+   {\Mfpic@warn{Arrow option #1 has no value\on@line; %
       it will be ignored.}}%
    {\@ifundefined{mfp@arr@#1}%
-     {\Mfpic@warn{Arrow option #1 invalid \on@line;
+     {\Mfpic@warn{Arrow option #1 invalid \on@line; %
         it will be ignored}}%
      {\@nameuse{mfp@arr@#1}{#2}}%
    }}%
 \newdef\mfp@doarrow{%
-  \mfp@addmac{\mfp@clropt{\mfp@hcolour}{\mfp@hcommand} (\mfp@hlength,
+  \mfp@addmac{\mfp@clropt{\mfp@hcolour}{\mfp@hcommand} (\mfp@hlength, %
     \mfp@hrotate, \mfp@hlocate)}}%
 %    \end{macrocode}
 %
@@ -5209,7 +5297,7 @@
   \save@mfpicdimens
   \begingroup % ended near end of \endmfpic
   \@mfpicunit\mfpicunit
-  \@nameuse{@safe@activestrue}%
+  \mfp@safe@activestrue
   \mfp@ifopengraphsfile{}%
    {\ifmfp@nowrite\else \mfp@nooutput@error\mfpic
       \def\mfp@src##1##2{\endgroup}%
@@ -5234,14 +5322,23 @@
 % We also define the coordinate conversion macros \cs{@xconv} and
 % \cs{@yconv} via \cs{mfp@setconv}. These are used to calculate the
 % nominal dimensions of the picture and to position \TeX{} labels.
+%
+% We make all the arguments of \cs{@mfpic} available to the user. Macro
+% \cs{mfp@setconv} now also makes use of them.
+% \begin{itemize}
+%   \item  the x-scaling factor.
 % \DescribeMacro{\xfactor}
+%   \item  the y-scaling factor.
 % \DescribeMacro{\yfactor}
+%   \item  the leftmost x-coordinate.
 % \DescribeMacro{\xmin}
+%   \item  the rightmost x-coordinate.
 % \DescribeMacro{\xmax}
+%   \item  the leftmost y-coordinate.
 % \DescribeMacro{\ymin}
+%   \item  the rightmost y-coordinate.
 % \DescribeMacro{\ymax}
-% We make all the arguments of \cs{@mfpic} available to the user. Macro
-% \cs{mfp@setconv} now also makes use of them.
+% \end{itemize}
 %
 % We are going to add all text labels to a box \cs{@alltlabels} and put
 % that whole box on top of the graph during \cs{endmfpic}.
@@ -5626,7 +5723,7 @@
 %    \begin{macrocode}
 \newdef\set@textbox#1{%
   \setbox\@textbox\vbox{\def\\{\cr}\mfp@restorepar
-    \@tcurr\@nameuse{@safe@activesfalse}\every@tlabel
+    \mfp@safe@activesfalse\@tcurr\every@tlabel
     \halign{##\hfil\cr#1\crcr}}}%
 %    \end{macrocode}
 %
@@ -5795,7 +5892,7 @@
 \newdef\tlabelpath@{\@ifmplabels{}{\measure@textbox{\the\mfp@toks}}%
   \mfp@setMPpos
   \mfcmd{text\mfp@name x (\mfp@MPpos)\@nl
-    (\@ifmplabels{origin, \mfp@btex{\the\mfp@toks}}{\tb@ll, \tb@ur},
+    (\@ifmplabels{origin, \mfp@btex{\the\mfp@toks}}{\tb@ll, \tb@ur}, %
       \mfp@param) (\tl@points)}%
   \ifmfp@switch\else \mfp@thelabel\fi \endgroup}%
 %    \end{macrocode}
@@ -5908,7 +6005,7 @@
   \def\mfp@docaption{%
     \setbox\@textbox
       \hbox{\def\\{\hskip\@M\p@\let\\\relax}\mfp@restorepar
-       \@nameuse{@safe@activesfalse}\@tcurr#3}%
+       \mfp@safe@activesfalse\@tcurr#3}%
 %    \end{macrocode}
 %
 % If the above \cs{hbox} is too wide, we re-assign \cs{@textbox} to a
@@ -5922,10 +6019,10 @@
       \hbox{%
         \vbox{%
           \hsize#2\mfp@scratch \mfp@restorepar
-          \leftskip0pt
-          \rightskip0pt
+          \leftskip0pt \rightskip0pt\relax
           \mfp@capsettings
-          \@nameuse{@safe@activesfalse}\noindent\@tcurr #3%
+          \mfp@safe@activesfalse
+          \noindent\@tcurr #3%
         }% End vbox.
       }% End hbox.
     \fi
@@ -5974,7 +6071,8 @@
 %    \begin{macrocode}
 \mfp@DBlog{Definition of closure of mfpic environment.}%
 \newdef\endmfpic{\every@endmfpic
-  \mfsrc{\mfp@ifmpost{\@nl verbatimtex \relax\egroup\space etex;}{}\@nl
+  \mfsrc{%
+    \mfp@ifmpost{\@nl verbatimtex \relax\egroup\space etex;}{}\@nl
     endmfpic; \mfp@p\space(\number\mfp@count) \mfp@lineno.\@nl
     \mfp@p\mfp@d\mfp@d\mfp@d\@nl}%
   \ifmfpicdebug\wlog{}\wlog{Mfpic: ENTERED endmfpic.}\wlog{}\fi
@@ -6056,7 +6154,7 @@
      {\@graphright\wd\@wholegraph
       \@graphtop\ht\@wholegraph}{}%
     \ifmfpicdebug
-      \wlog{Mfpic debug: Dimensions of wholegraph before labels
+      \wlog{Mfpic debug: Dimensions of wholegraph before labels %
         are added, and before truebbox adjustments:}%
       \wlog{Mfpic: graphleft  = \the\@graphleft}%
       \wlog{Mfpic: graphright = \the\@graphright}%
@@ -6081,7 +6179,7 @@
 % (or both) that is nonempty, so one of the box resets may be redundant.
 %    \begin{macrocode}
     \ifmfpicdebug
-      \wlog{Mfpic debug: Dimensions of alltlabels, before
+      \wlog{Mfpic debug: Dimensions of alltlabels, before %
         truebbox adjustments:}%
       \mfp@scratch\mfpicllx bp\relax
       \wlog{Mfpic: mfpicllx     = \the\mfp@scratch}%
@@ -6126,7 +6224,7 @@
 % detected by \TeX.
 %    \begin{macrocode}
     \ifmfpicdebug
-      \wlog{Mfpic debug: Dimensions of alltlabels after
+      \wlog{Mfpic debug: Dimensions of alltlabels after %
         truebbox adjustments:}%
       \wlog{Mfpic: tlabelsleft  = \the\@tlabelsleft}%
       \wlog{Mfpic: tlabelstop   = \the\@tlabelstop}%
@@ -6147,7 +6245,7 @@
 % graphht${}={}$graphtop${}-{}$graphbot, and graphdp${}= 0$.
 %    \begin{macrocode}
     \ifmfpicdebug
-      \wlog{Mfpic debug: Dimensions of wholegraph after
+      \wlog{Mfpic debug: Dimensions of wholegraph after %
         labels are added:}%
       \wlog{Mfpic: graphleft  = \the\@graphleft}%
       \wlog{Mfpic: graphright = \the\@graphright}%
@@ -6391,12 +6489,6 @@
 \mfpicnumber{1}%
 %    \end{macrocode}
 %
-% Create a system for adding patches in the file \file{mfppatch.tex},
-% and for user defaults in a file \file{mfpic.usr}.
-%    \begin{macrocode}
-\InputIfFileExists{mfppatch.tex}{}{}%
-%    \end{macrocode}
-%
 % Set the font for missing or draft mode figures (for the file name or
 % figure number). This will already have been defined if \file{mfpic.sty}
 % was used, so here we can probably assume \LaTeX{} wasn't used, and
@@ -6406,7 +6498,8 @@
 %    \end{macrocode}
 %
 % Restore the meaning of \cs{+}, and execute the command that restores all
-% the saved category codes and \cs{newlinechar}.
+% the saved category codes and \cs{newlinechar}. Input user defaults in
+% the file \file{mfpic.usr}.
 %    \begin{macrocode}
 \mfp@DBlog{Punctuation, etc., will revert to old catcodes now.}%
 \let\+\mfpsaveplus
@@ -6415,10 +6508,5 @@
 %</tex>
 %    \end{macrocode}
 %
-% The \LaTeX{} wrapper inputs \file{mfpic.tex}.
-%    \begin{macrocode}
-%<sty>\input mfpic.tex\relax
-%    \end{macrocode}
-%
 %\clearpage
 %\Finale
diff --git a/Master/texmf-dist/source/generic/mfpic/mfpic.ins b/Master/texmf-dist/source/generic/mfpic/mfpic.ins
index 5a528221027..4b04ba5007b 100644
--- a/Master/texmf-dist/source/generic/mfpic/mfpic.ins
+++ b/Master/texmf-dist/source/generic/mfpic/mfpic.ins
@@ -1,13 +1,13 @@
-%%% File: mfpic.ins
-%%% A part of mfpic 1.05 2010/06/10
-%%%
+% File: mfpic.ins
+% A part of mfpic 1.06 2011/03/08
+%
 \input docstrip
 \keepsilent
 \preamble
 
 -------------------------------------------------------------------
 
-Copyright 2002--2010, Daniel H. Luecking
+Copyright 2002--2011, Daniel H. Luecking
 
 Mfpic may be distributed and/or modified under the conditions of the
 LaTeX Project Public License, either version 1.3c of this license or (at
@@ -41,9 +41,9 @@ endinput.^^J%
 ^^J
 ^^J To finish the installation:
 ^^J
-^^J -- Copy the files mfpic.tex, mfpic.sty and mfppatch.tex to a
-\sJ    location where TeX and LaTeX will find them. For example, in a
-\sJ    TDS compliant system, the directory TEXMF/tex/generic/mfpic/ .
+^^J -- Copy the files mfpic.tex and mfpic.sty to a location where
+\sJ    TeX and LaTeX will find them. For example, in a TDS compliant
+\sJ    system, the directory TEXMF/tex/generic/mfpic/ .
 ^^J
 ^^J -- Copy the file grafbase.mf to a location where Metafont
 \sJ    will find it, for example TEXMF/metafont/mfpic/ .