%    Copyright (C) 1991 Silvio Levy
%     
%    This file is free software: you can redistribute it and/or modify
%    it under the terms of the GNU General Public License as published by
%    the Free Software Foundation, either version 2 of the License, or
%    (at your option) any later version.
%
%    This file is distributed in the hope that it will be useful,
%    but WITHOUT ANY WARRANTY; without even the implied warranty of
%    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
%    GNU General Public License for more details.
%
%    You should have received a copy of the GNU General Public License
%    along with this program.  If not, see <http://www.gnu.org/licenses/>.
%
%    As a special exception, if you create a document which uses this font,
%    and embed this font or unaltered portions of this font into the
%    document, this font does not by itself cause the resulting document to
%    be covered by the GNU General Public License. This exception does not
%    however invalidate any other reasons why the document might be covered
%    by the GNU General Public License. If you modify this font, you may
%    extend this exception to your version of the font, but you are not
%    obligated to do so. If you do not wish to do so, delete this exception
%    statement from your version.

if unknown gen_sigma: readfrom("gen_sigma") fi
     
def dims = 8.5u#,asc_height#,0 enddef;
def ital = 0 enddef;
def fit_params = 0,0 enddef;
     
def gen_letter =
  pickup fine.nib;
  top y1r=vround(if not monowidth:.95 fi x_height+oo); x1r=.5w; %top of loop
  x5r=.5w; bot y5r=-oo;                                 %bottom of ditto
  lft x3r=w-rt x7r=hround(.75u); y3r=y7r=.5[y1r,y5r];   %left and right bulge
  filldraw stroke gr_arc.e(1,2,3)(vair,stem,.5otilt)    %three quadrants of loop
    & gr_arc.e(3,4,5)(vair,stem,.5otilt) & gr_arc.e(5,6,7)(vair,stem,.5otilt);
     
  %we now draw the hook z8..z9..z10.  It must satisfy the following constraints:
  %its outer contour is symmetric with respect to some axis containing z9l;
  %one end is known, the width there is thin_stem, and the width at z10
  %is, ideally, stem.  (But since we may have to change that we call it Stem.)
  z8l=z1l; numeric thin_stem, med_stem; thin_stem=.7[hair,Stem];
  %the aperture, measured perpendicular to the axis, equals Stem
  numeric apert; apert=2Stem+thin_stem-currentbreadth;  %apert=length(z10l-z8l);
  numeric left_goal; lft left_goal=vround(lft x3r+.5u); %leftmost tangent known
  numeric top_goal; top top_goal=h+oo;                  %highest tangent known
     
  %if by taking Stem=stem we got apert > top_goal-y1l, the problem might
  %not have a solution with a horizontal tangent; in that case the
  %constraint is on apert:
  if 2stem+.7[hair,stem]-currentbreadth>top_goal-y8l: apert=top_goal-y8l;
  else: Stem=stem; fi
     
  %we first estimate the slope of the axis by imagining that, in the vicinity
  %of z9l, the hook looks like a semicircle of diameter apert/2.
  %(this value is empiric, but reasonable because the tension is high)
  z0l=(left_goal+.25apert,top_goal-.25apert);           %center of semicircle
  numeric axis; axis=angle(z0l-z8l)+angle(length(z0l-z8l)+-+.5apert,.5apert);
  z9l=z0l+(.25apert,0)rotated(axis); z10l=z8l+(0,-apert)rotated(axis);
     
  %we now iterate, correcting z9l until the tangencies are satisfied
  path hook; numeric left_real; numeric top_real;
  forever:
     
    hook:=z8l{dir(axis)}..tension 1.5..z9l..tension 1.5..{-dir(axis)}z10l;
    if directiontime up of hook=-1:
      left_error:=0; message "hook has no vertical tangent!";
    else: left_error:=xpart directionpoint up of hook-left_goal; fi
    if directiontime right of hook=-1:
      top_error:=0; message "hook has no horizontal tangent!";
    else: top_error:=ypart directionpoint right of hook-top_goal; fi
     
%message "top_error:"; show top_error; message "left_error:"; show left_error;
     
    exitif (abs(left_error)<.05) and (abs(top_error)<.05);
    x9l:=x9l-left_error; y9l:=y9l-top_error;
    axis:=angle(z9l-z8l)+angle(length(z9l-z8l)+-+.5apert,.5apert);
    x10l:=x8l+apert*sind axis; y10l:=y8l-apert*cosd axis;
  endfor
     
  pos8(thin_stem,axis-90); pos10(Stem,axis+90); pos9(.3[hair,Stem],axis+180);
  filldraw stroke
    z7e{z7'e}..{dir axis}z8e..tension 1.5..z9e..tension 1.5..{-dir axis}z10e;
enddef;
     
cmchar "Lowercase delta";
beginchar("d",dims);
this_letter; penlabels(1,2,3,4,5,6,7,8,9,10); endchar;
     
if boolean barebones: picture savedpicture; endinput; fi
     
cmchar "Lowercase sigma followed by delta";
begindoublechar(oct"004",dim_sigma);
mid_sigma; middoublechar(dims); this_letter; endchar;
     
picture savedpicture;
