⟦a82e92000⟧

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% EUBASE.MF                     June 1990
% This Metafont file is part of AMSFonts 2.0.
% Copyright (C) 1990, American Mathematical Society.
% All rights reserved.  Copying of this file is authorized only if either:
%   (1) you make absolutely no changes to your copy including filename; OR
%   (2) if you do make changes, you first rename it to some other filename.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% base file for Euler Fonts, by David Siegel and John Hobby

def define_euler_pixels(text t) =
 forsuffixes $=t: $=$.#*hppp; endfor enddef;



     pixperem = ptsize*pt;

h#=ptsize/programem;
v#=h#*aspect_ratio;
 define_euler_pixels(h,v);
v#:=h#; % DEK (I doubt if aspect_ratio<>1 will work, but this does help)
     define_pixels(leftside, rightside);
%     h = pixperem/programem;
%     v = pixperem/programem*aspect_ratio;

      dandch = 3.94h;          %     dandch = (pixperem/935);
      dandcv = 3.94v;         %     dandcv = (pixperem/935);

        nwdh#  = h#*programem/925;     % h*3.784
        nwdv#  = v#*programem/925;     % v*3.784
        nwdh   = h*programem/925;
        nwdv   = v*programem/925;
% dandc == dan mills and carol twombly; nwd == dave siegel -- DEK
     adjustx:=  3.92;
     adjusty:=  3.92;

save_leftside#:=leftside#; save_rightside#:=rightside#; % DEK
def more_side(expr s_sharp) =
 leftside#:=save_leftside#+s_sharp; rightside#:=save_rightside#+s_sharp;
 define_pixels(leftside,rightside);
enddef;
\f


% ----- Fontbegin, Charbegin -----------------------------------
% --------------------------------------------------------------

transform rot;

def charbegin(expr c,w_sharp,h_sharp,d_sharp) =
 begingroup
  charcode:=if known c: byte c else: 0 fi;
  W := w_sharp*pt;
  chardx:=round(W+leftside+rightside);     % desired width of character in pixels
  charwd:=w_sharp+leftside#+rightside#;    charht:=h_sharp;  chardp:=d_sharp;
% charic:=0; clearxy; clearit; clearpen; scantokens extra_beginchar;
% rot := identity;
  charic:=0; clearxy; clearit; clearpen; % DEK
  rot := identity; scantokens extra_beginchar;
  pair tiept[];
 enddef;

def endchar(expr addwidth_sharp) =
 scantokens extra_endchar;
%if proofing>0: makebox(proofrule); fi
 addwidth:=addwidth_sharp*pt;
%currentpicture := currentpicture shifted (leftside+addwidth,0);
xoffset:=leftside+addwidth;
H:=charht*pt; D:=chardp*pt;
if known nohashmarks:;
else:
 if proofing>0:
  for y=0,H,-D*pt:
    proofrule((-xoffset,y),(10-xoffset,y));
    proofrule((chardx-10-xoffset,y),(chardx-xoffset,y)); endfor % horizontals
  for x=-xoffset,chardx-xoffset:
    proofrule((x,10-D),(x,-D)); proofrule((x,H-10),(x,H)); endfor % verticals fi
 fi
fi
shipit;
%if displaying>0: makebox(screenrule); showit; fi
endgroup enddef;

def mathcorr(expr subwidth_sharp) = % DEK
 charic:=subwidth_sharp; charwd:=charwd-charic;
enddef;
\f


% -----     TeX Information: ----------------------------------------

     fontdimen 1:

     0,               % italic correction     degrees
     ptsize/3,          % default spacing (3em)     points
     0,               % stretch          "
     0,               % shrink          "
     (lcbody*v#),           % xheight          "
     ptsize,               % quad               "
     0,               % math space          
     (1400*v#),   % num1 baseline raise, for numerators, display style
     (1000*v#),   % num2 baseline raise, for numerators, non-atop
     (1100*v#),   % num3 baseline raise, for numerators, atop styles
     (1400*v#),     % denom1 amount to lower baselines in display style
     (600*v#),     % denom1 amount to lower baselines in non-display 
     (1500*v#),     % sup1
     (1400*v#),     % sup2 guess at superscript raising again
     (1200*v#),     % sup3
     (depthy*v#),     % sub1 subscripts with no super
     (900*v#),     % sub2 maybe this is off by a little.
     (1500*v#),     % supdrop how much to drop below a large box
     (100*v#),     % supdrop how much to raise above a large box
     2.2(programem*v#),     % size of \comb delimiters for display 
     (programem*v#),     % size of \comb delimiters for non-display 
     (950*v#);     % axisheight center for fraction line

font_size     ptsize;

\f


% Adjusting stems
% revised by DEK to allow highres adjustments, 11 Aug 87

vardef set_stem_round(expr slo,s,shi,clo,c,chi) =
 stem_lo:=slo*h; stem_hi:=shi*h; stem_norm:=s*h;
 curve_lo:=clo*h; curve_hi:=chi*h; curve_norm:=c*h;
  save a,b;
  a-b = round (stem_norm - curve_norm);
  a = round(.5(stem_norm + curve_norm + a - b));
  stem_norm_corr := a-stem_norm; % a is normal stem width in pixels
  curve_norm_corr := b-curve_norm; % b is normal curve width in pixels
enddef;

def no_stem_round = set_stem_round(-1,-1,-1,-1,-1,-1) enddef;
no_stem_round; % default is to do ordinary rounding

% The |stem_round| macro rounds its argument, forcing numbers that look like
% stem widths to round near to |stem_norm|, and similarly forcing vertical curve
% weights to round near to |curve_norm|.

def stem_round primary w = if w<0: -stem_rnd(-w) else: stem_rnd(w) fi enddef;

def stem_rnd(expr w) =
    round(w
    if (stem_lo<=w) and (w<=stem_hi): +stem_norm_corr
    elseif (curve_lo<=w) and (w<=curve_hi): +curve_norm_corr
    fi)
enddef;
\f


% Filling cyclic paths with step width adjustment and rounding

% Before calling the |adj_fill| macro, the user should set up an
% array |t[]| and a nonnegative integer |n| so that |t[1]| through |t[n]|
% are time values on some cyclic path |p|.  It should be true that |t[i]<t[j]|
% whenever |i<j|.  Also |t[n]-t[1]| should be less than the length of |p|.
% The |adj_fill| macro takes four lists of time values given as indices into
% the |t| array.  The avoids the necessity of writing \MF\ macros to sort
% the time values.
% Groups of paths are allowed to have points ``tied together.''  This is
% implemented by saving coordinates in a special array of type |pair|
% called |tiept|.  If a path contains a point that is tied to a point in
% an already computed path, then the adjusted coordinates of that point will
% be saved in the |tiept| array.  This array should be made unknown before
% starting a new group of paths; e.g., in |beginchar|.


% Make |y'a| and |y'b| rounded versions of |y.a| and |y.b|, so that
% |y'a-y'b| is as close as possible to |y.a-y.b|.
% If a time value is given as both fixed and vertical or horizontal then
% |y'a| or |y'b| or both may already be known.  Then we just round what
% we can.

vardef rnd_pr_y(suffix a, b) =
  if known y'a: if unknown y'b: y'b-y'a=round(y.b-y.a); fi
  elseif known y'b: y'b-y'a=round(y.b-y.a);
  else:
    y'a-y'b = round(y.a-y.b);
    y'a = round(.5(y.a + y.b + y'a - y'b));
  fi
enddef;

% Rounding |x| coordinates is similar except we use the special |stem_round|
% routine.

vardef rnd_pr_x(suffix a, b) =
% use the next line if you want to see what channel settings are reasonable
% (also set tracingtitles:=1 in such a case)
% message decimal t.a&","&decimal t.b&":"&decimal((x.b-x.a)/h);
  if known x'a: if unknown x'b: x'b-x'a=stem_round(x.b-x.a); fi
  elseif known x'b: x'b-x'a=stem_round(x.b-x.a);
  else:
    x'a-x'b = stem_round(x.a-x.b);
    x'a = round(.5(x.a + x.b + x'a - x'b));
  fi
enddef;



% Set up a transform |curtx=tx.a| that takes |x.a| into |x'a| and |x.b|
% into |x'b| without slanting or changing $y$-components.

vardef set_tx(suffix a,b) =
  save u,v;
  xypart tx.a = yxpart tx.a = 0;
  (x.a,0) transformed tx.a = (x'a,0);
  (u,v) = (x.b,1) transformed tx.a - (x'b,1);
  if known u: xxpart tx.a = yypart tx.a = 1;
        else: (u,v)=origin;
  fi
  curtx := tx.a
enddef;


% Set up a transform |curty=ty.a| that takes |y.a| into |y'a| and |y.b|
% into |y'b| without slanting or changing $x$-components.

vardef set_ty(suffix a,b) =
  save u,v;
  xypart ty.a = yxpart ty.a = 0;
  (0,y.a) transformed ty.a = (0,y'a);
  (u,v) = (1,y.b) transformed ty.a - (1,y'b);
  if known v: xxpart ty.a = yypart ty.a = 1;
        else: (u,v)=origin;
  fi
  curty := ty.a
enddef;


% The following macros ensure that |x'i| or |y'i| agree with the current
% transform.  It is important that this be done for all relevant |i| each
% time |set_tx| or |set_ty| is called.  Since some points may be tied to
% others, this can affect which |x'j| and |y'j| are known.  Future calls to
% |set_tx| and |set_ty| should be based on the most up to date possible
% information.

vardef yset@# = (0,y'@#) = (0,y@#) transformed curty; enddef;
vardef xset@# = (x'@#,0) = (x@#,0) transformed curtx; enddef;


% Apply |set_txy| to each pair indices |a,b| such that |xy'[a]| and |xy'[b]|
% are known, but |xy'[c] is unknown for all |c| between |a| and |b|.
% This leaves the appropriate initial transformation in |curtx| or |curty|.
% The |xyset| parameter is either |xset| or |yset| as explained above.

vardef set_trans(suffix xy, set_txy, xyset) =
  save previ, firsti;
  for i=1 upto n: if known xy'[i]:
      if known firsti:
     set_txy([previ], [i]);
     for j=previ+1 upto i-1: xyset[j]; endfor
      else: firsti = i;
      fi
      previ := i;
  fi endfor     
  if known firsti:
    for i=1 upto firsti: if known xy'[i]:
      set_txy([previ], [i]);
      if previ>=firsti:
     for j=previ+1 upto n: xyset[j]; endfor
     for j=1 upto i-1: xyset[j]; endfor
      else:
     for j=previ+1 upto i-1: xyset[j]; endfor
      fi
      previ:=i;
    fi endfor
  else:
    for i=1 upto n: xyset[i]; endfor
  fi
enddef;



% Return the transformed $i$th segement of |p_path| as defined by the time
% values in |t[]|, updating |curtx| and |curty| if appropriate.

vardef new_seg(expr i) =
  save p; path p;
  if known tx[i]: curtx:=tx[i]; fi
  if known ty[i]: curty:=ty[i]; fi
  p = subpath (t[i],t[i+1]) of p_path transformed (curtx transformed curty);
  p
enddef;



% The following macros are used only when |t| entries are readjusted:


% Find the first time on the path |p| where the direction is |dir| or |-dir|.

def extremetime expr dir of p =
  begingroup save a,b;
  a = directiontime dir of p; if a<0: a:=infinity; fi
  b = directiontime -dir of p; if b<0: b:=infinity; fi
  if a<b: a else: b fi
  endgroup
enddef;


% Adjust the time value |tt| to the nearest time when the direction of |p_path|
% is |dir| or |-dir|.

vardef adj_t(suffix tt)(expr dir) =
  save p, a, b; path p;
  p = subpath (tt,tt+nn) of p_path & cycle;
  a = extremetime dir of p;
  a := if a<1: a[tt,floor tt+1] else: a+floor tt fi;
  b = extremetime dir of reverse p;
  b := if b<1: b[tt,ceiling tt-1] else: ceiling tt - b fi;
  tt := if b+a>2tt: b else: a fi;
enddef;


% Issue an error message when |t[i]>t[i+1]| after the above adjustment process.

vardef bad_order(expr i) =
  initerim showstopping:=0;
  show t[i], t[i+1];
  errmessage "Adjusted t entries "&decimal i&" and "&decimal(i+1)
          &" are out of order. (See above)";
enddef;


% The |adj_fill| macro performs the entire adjustment and filling based on
% the following parameters: a list |tfx| of |t| indices for points whose
% $x$-coordinates should not be moved during the adjustment process, a similar
% list |tfy| for $y$-coordinates, a list of pairs $(i,j)$ where $i$ is a |t|
% index and |tiept[j]| is the corresponding tie point, lists |tv| and |th| of
% pairs of |t| indices that correspond to opposite sides of vertical and
% horizontal strokes, and finally a cyclic path |p|.  (Note the scaling by |h|
% and |v|.)

vardef adj_fill@#(text tfx, tfy, tie, tv, th)(expr p) =
% message str@#; % that's for use with the stem-round message above
  save p_path, nn, x, y, tx, ty, curtx, curty;
  path p_path, p_path';
  transform tx[], ty[], curtx, curty;
  p_path = p transformed (identity xscaled h yscaled v transformed rot);
  nn = length p_path;
  if proofing>1:
    makelabel(str @#, point 0 of p_path);
    for i=1 upto nn-1: makelabel(decimal i, point i of p_path); endfor
  fi
    forsuffixes i=tfx: x.fix.i=1; endfor          % Prepare for |adj_t| calls.
    forsuffixes i=tfy: y.fix.i=1; endfor
    for w=1 tv: if pair w: (x.fix[xpart w],x.fix[ypart w]) = (1,1); fi endfor
    for w=1 th: if pair w: (y.fix[xpart w],y.fix[ypart w]) = (1,1); fi endfor
    for i=1 upto n:
      if t[i]>floor t[i]:
     if unknown x.fix[i]: adj_t(t[i],right); fi
     if unknown y.fix[i]: adj_t(t[i],up); fi
      fi
    endfor
    t[n+1] := t1+nn;
    for i=1 upto n: if t[i]>t[i+1]: bad_order(i); fi endfor
  for i=1 upto n: z[i] = point t[i] of p_path; endfor
  forsuffixes i=tfx: x'i =x.i; endfor
  forsuffixes i=tfy: y'i =y.i; endfor
  for w=1 tie: if pair w: z'[xpart w] = tiept[ypart w]; fi endfor
  for w=1 tv: if pair w: rnd_pr_x([xpart w], [ypart w]); fi endfor
  for w=1 th: if pair w: rnd_pr_y([xpart w], [ypart w]); fi endfor
  curtx=curty=identity;
  set_trans(x, set_tx, xset);
  set_trans(y, set_ty, yset);
  p_path' = if n=0: p_path else:
              for i=1 upto n: new_seg(i)-- endfor cycle
         fi;
  interim autorounding := 0;
  interim smoothing := 0;
  if known fillwhite:
     draw p_path' withpen pencircle scaled 4;     % was scaled 2
  else:
    begingroup save pic;               % Now fill
    picture pic;
    pic=currentpicture;
    currentpicture:=nullpicture;
    interim turningcheck := 0;
    fill p_path';
    cull currentpicture dropping origin;
    addto currentpicture also pic;
    endgroup;
  fi
enddef;
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