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% Blackboard bold base file, containing lots of horrible hacks.
% Alan Jeffrey, 12--18 Dec 1989.

% DIGITIZATION

% I'm doing all my own digitization, so I don't need help from MF.
autorounding := 0;

% To get the unsharp version of x#, say unsharp x#.
def unsharp = hppp * enddef;

% The only pen I'm working with is of size pen_size.  This makes life
% rather easier.  To find the x-coordinate whose left-hand edge is
% at hround x, say leftround x, and similarly for rightround, 
% topround and bottomround.
def leftround expr x = hround x + 1/2 pen_size enddef;
def rightround expr x = hround x - 1/2 pen_size enddef;
def topround expr y = vround y - 1/2 pen_size enddef;
def bottomround expr y = vround y + 1/2 pen_size enddef;

% Using this, I can give the equivalent of define_whole_pixels...
def define_whole_top_pixels (text t) =
   forsuffixes $ = t:
      $ := topround unsharp $.#;
   endfor
enddef;

def define_whole_bottom_pixels (text t) =
   forsuffixes $ = t:
      $ := bottomround unsharp $.#;
   endfor
enddef;

% POINTS

% The point y~x is short for (x,y).  The reason for switching the
% points around is that I find it easier to say Top~Left than
% (Left, Top).
primarydef x ~ y = (y,x) enddef;

% To find the average of two points, say p -+- q.
primarydef x ~ y = (y,x) enddef;
tertiarydef x -+- y = .5[x,y] enddef;

% To get the point 1/2fatness above p, say above p.  This is useful
% for drawing lines fatness in width.  Similarly we have commands
% below, leftof and rightof.
def above secondary p = 
   p + 1/2fatness * up
enddef;

def below secondary p =
   p + 1/2fatness * down
enddef;

def leftof secondary p = 
   p + 1/2fatness * left
enddef;

def rightof secondary p =
   p + 1/2fatness * right
enddef;

% The command farleftof is equivalent to leftof leftof, and similarly
% farrightof.
def farleftof secondary p = 
   p + fatness * left
enddef;

def farrightof secondary p =
   p + fatness * right
enddef;

% To get curves with o-correction, we need to be able to move
% o pixels up or down.
def oabove secondary p =
   p + o * up
enddef;

def obelow secondary p =
   p + o * down
enddef;

% DECLARATIONS

% To declare a new variable foo of type T, say var (T) foo.
def var (text type) text declarations =
   save declarations;
   type declarations
enddef;

% PATHS

% Given a cyclic path p, outline p draws the path and fills the inside
% with white.  This is stolen from the MF book, exercise 13.11.
def outline expr c =
   begingroup
      picture region;
      region := nullpicture;
      interim turningcheck := 0;
      addto region contour c;
      cull region dropping (0,0);
      cullit;
      addto currentpicture also -region;
      cullit;
      draw c
   endgroup
enddef;

% Given a path p, leftside p is the path 1/2 fatness to its left,
% and similarly rightside.
def leftside primary apath =
   apath shifted (1/2fatness * left)
enddef;

def rightside primary apath =
   apath shifted (1/2fatness * right)
enddef;

% Given a path p, fatten p draws the leftside of p,
% the rightside of p, and joins them up with straight lines.
def fatten expr apath =
   leftside apath
      -- (reverse rightside apath)
      -- cycle
enddef;

% Given a point p, splodge p draws an o-corrected circle of radius
% fatness around p.
def splodge expr apoint =
   above apoint + o*up {right}
      .. rightof apoint + o*right {down}
      .. below apoint + o*down {left}
      .. leftof apoint + o*left {up}
      .. cycle
enddef;

% The command splodgel does the same, but doesn't close the cycle,
% and leaves the current point at the left of the circle.
def splodgel tertiary apoint =
   leftof apoint + o*left {up}
      .. above apoint + o*up {right}
      .. rightof apoint + o*right {down}
      .. below apoint + o*down {left}
      .. leftof apoint + o*left {up}
enddef;

% Similarly, splodger leaves the current point at the right of the
% circle.
def splodger tertiary apoint =
   rightof apoint + o*right {down}
      .. below apoint + o*down {left}
      .. leftof apoint + o*left {up}
      .. above apoint + o*up {right}
      .. rightof apoint + o*right {down}
enddef;

% CLIPPING

% sometime (p, q) gives the time along p when it intersects q.
def sometime (expr apath, bpath) =
   xpart (apath intersectiontimes bpath)
enddef;

% othertime (p, q) gives another time at which p intersects q.
def othertime (expr apath, bpath) =
   length apath - sometime (reverse apath) (reverse bpath)
enddef;

% firsttime (p, q) gives the smallest of sometime (p,q) and othertime (p,q).
def firsttime (expr apath, bpath) =
   min (sometime (apath) (bpath), othertime (apath) (bpath))
enddef;

% lasttime (p, q) gives the largest of the two times.
def lasttime (expr apath, bpath) =
   max (sometime (apath) (bpath), othertime (apath) (bpath))
enddef;

% We can then clip p with q by finding the subpath of p from 0 to 
% the time p intersects q.
def cliponce (expr apath, clippath) =
   subpath (0, sometime (apath) (clippath)) of apath
enddef;

% Similarly, if p intersects q twice, we can find the path between
% the two times it intersects with cliptwice.
def cliptwice (expr apath, clippath) =
   subpath 
      (firsttime (apath) (clippath), lasttime (apath) (clippath)) 
   of apath
enddef;

% Given a path p and two paths q and r which intersect p,
% we can find the path between when p crosses q and when p crosses r.
% someclipbetween (p, q, r) will always start at q and finish at r.
def someclipbetween (expr apath, firstclip, secondclip) =
   subpath 
      (sometime (apath) (firstclip),
       sometime (apath) (secondclip))
   of
      apath
enddef;

% firstclipbetween does the same, but if p intersects q and r more
% than once, it gives the first clipping.
def firstclipbetween (expr apath, firstclip, secondclip) =
   subpath 
      (firsttime (apath) (firstclip),
       firsttime (apath) (secondclip))
   of
      apath
enddef;

% lastclipbetween gives the last clipping.
def lastclipbetween (expr apath, firstclip, secondclip) =
   subpath 
      (lasttime (apath) (firstclip),
       lasttime (apath) (secondclip))
   of
      apath
enddef;

% We can join these together and clip fat lines.
def fatcliponce (expr apath, clippath) =
   cliponce (leftside apath) (clippath)
      -- someclipbetween (clippath) (leftside apath) (rightside apath)
      -- reverse cliponce (rightside apath) (clippath)
      -- cycle
enddef;

def fatcliptwice (expr apath, clippath) =
   cliptwice (leftside apath) (clippath)
      -- lastclipbetween (clippath) (leftside apath) (rightside apath)
      -- cliptwice (rightside apath) (reverse clippath)
      -- firstclipbetween (clippath) (rightside apath) (leftside apath)
      -- cycle
enddef;

% BBCHAR.

% bbchar (c) (l#, w#, r#) (t#, b#) begins a character at code c,
% of width w# with l# gap at the left and r# gap at the right.
% It's topmost point is at t# and its bottommost point at b#.
% From these parameters we calculate Width (the width of the character
% in whole pixels) and hardTop and hardBottom (the exact top and bottom
% of the character).  Top is then 1/2 pensize from the top of the character,
% and Bottom is 1/2 pensize from the bottom.  This means if we draw a line
% through top, the top of it will exactly touch the top.  We then calculate
% Left, Middle, and Right in the same way, using calculateLeftetc.

def bbchar 
   (expr code)
   (expr sharphardLeft, sharpWidth, sharprightgap)
   (expr sharphardTop, sharphardBottom) =

   beginchar 
      (code)
      (sharphardLeft + sharpWidth + sharprightgap)
      (max (sharphardTop, 0pt#))
      (max (-sharphardBottom, 0pt#)); 

      save Top, Bottom, Horizon, hardTop, hardBottom,
           Width, hardLeft, hardRight, Left, Right, Middle;

      hardTop# = sharphardTop;
      hardBottom# = sharphardBottom;
      Width# = sharpWidth;
      hardLeft# = sharphardLeft;
      hardRight# = sharphardLeft + sharpWidth;

      define_whole_pixels (Width);
      define_whole_vertical_pixels (hardTop, hardBottom);
      Top = topround hardTop;
      Bottom = bottomround hardBottom;

      Horizon = .5 [Top, Bottom];

      calculateLeftetc;

      pickup pencircle scaled pen_size;

enddef;

def calculateLeftetc =   
   hardLeft := floor (unsharp hardLeft#);
   hardRight := hardLeft + Width;
   
   Left := (hardLeft + 1/2pen_size);
   Middle := (hardLeft + 1/2Width);
   Right := (hardRight - 1/2pen_size);
enddef;

% bbcap is bbchar with the top at ATop# and the bottom at aBottom#.
def bbcap (expr code, leftgap, width, rightgap) =
   bbchar (code) (leftgap, width, rightgap) (ATop#, aBottom#);
enddef;

% bbnum is bbchar with the dimensions of a number hard-wired.
def bbnum (expr code) =
   bbchar (code) (medgap#, numeral#, medgap#) (oneTop#, aBottom#);
enddef;

% For characters such as < and > which appear a lot blacker than the
% others, we can surround the character by beginblacker n ... endblacker,
% which temporarily multiplies fatness by n.
def beginblacker expr blackness = 
   begingroup
      save oldfatness;
      oldfatness# := fatness#;
      save fatness;
      fatness# := oldfatness# * blackness;
      define_whole_pixels (fatness)
enddef;

let endblacker = endgroup;
   
% SYMMETRY

% To try to get characters symmetric, we need to round the width so there
% are the same number of characters on the left of the central vertical
% as there are on the right.  So if we are symmetrical around a pen of
% size 2n, we need to make the width even.  If we are symmetrical around
% a pen of size 2n+1 we need to make the width odd.  This is done with
% roundlike (x) y, which rounds y to be even iff x is even.

def roundlike (expr x) expr y =
   2 * (round (x -+- y)) - x
enddef;

% To make the character symmetric, we round Width like pen_size.
def symmetric =
   Width := roundlike (pen_size) unsharp Width#;
   calculateLeftetc
enddef;

% To make the character symmetric around a fat vertical, we round
% Width like fatness + pen_size.
def fatsymmetric =
   Width := roundlike (fatness + pen_size) unsharp Width#;
   calculateLeftetc
enddef;

% DRAWING THE CHARACTERS ON THE SCREEN

% makebox and maketicks nicked from cmbase, adjusted for this job.

def makebox(text rule) =
 for y=0, hardBottom, hardTop:
  rule((0,y)t_,(w,y)t_); endfor % horizontals
 for x=0,hardLeft,hardRight,w:
  rule((x,hardBottom)t_,(x,hardTop)t_); endfor % verticals
enddef;

def maketicks(text rule) =
 for y=0, hardBottom, hardTop:
  rule((-10,y)t_,(0,y)t_);  % horizontals at left
  rule((w,y)t_,(w+10,y)t_);  % horizontals at right
 endfor
 for x=0,hardLeft,hardRight,w:
  rule((x,hardBottom-10)t_,(x,hardBottom)t_); % verticals at bottom
  rule((x,hardTop)t_,(x,hardTop+10)t_);       % verticals at top
 endfor % verticals at top
enddef;

% HACKS TO MAKE CMR WORK

% Some parameters I never use, but are needed by the cmr parameter files.
boolean 
   square_dots, hefty, serifs, monospace, 
   variant_g, low_asterisk, math_fitting;

% And that's that.