% This is the plain METAFONT base that's described in The METAFONTbook.
% N.B.: Please change "base_version" whenever this file is modified!
% And don't modify the file unless you change its name:
% Everybody's "plain.mf" file should be the same, worldwide.
% Unlimited copying and redistribution of this file are permitted as long
% as this file is not modified. Modifications are permitted, but only if
% the resulting file is not named plain.mf.
message "Preloading the plain base, version "&base_version&": preliminaries,";
delimiters (); % this makes parentheses behave like parentheses
def upto = step 1 until enddef; % syntactic sugar
def downto = step -1 until enddef;
def exitunless expr c = exitif not c enddef;
let relax = \; % ignore the word `relax', as in TeX
let \\ = \; % double relaxation is like single
def ]] = ] ] enddef; % right brackets should be loners
def -- = {curl 1}..{curl 1} enddef;
def --- = .. tension infinity .. enddef;
def ... = .. tension atleast 1 .. enddef;
def gobble primary g = enddef; def killtext text t = enddef;
primarydef g gobbled gg = enddef;
def hide(text t) = exitif numeric begingroup t;endgroup; enddef;
def ??? = hide(interim showstopping:=1; showdependencies) enddef;
def stop expr s = message s; gobble readstring enddef;
smoothing:=1; autorounding:=2; % this adjusts curves to the raster
turningcheck:=2; % this will warn about a "strange path"
granularity:=1; % this says that pixels are pixels
def interact = % sets up to make "show" commands stop
hide(showstopping:=1; tracingonline:=1) enddef;
def loggingall = % puts tracing info into the log
tracingcommands:=3; tracingedges:=2; tracingtitles:=1; tracingequations:=1;
tracingcapsules:=1; tracingspecs:=1; tracingpens:=1; tracingchoices:=1;
tracingstats:=1; tracingoutput:=1; tracingmacros:=1; tracingrestores:=1;
enddef;
def tracingall = % turns on every form of tracing
tracingonline:=1; showstopping:=1; loggingall enddef;
def tracingnone = % turns off every form of tracing
tracingcommands:=0; tracingonline:=0; showstopping:=0;
tracingedges:=0; tracingtitles:=0; tracingequations:=0;
tracingcapsules:=0; tracingspecs:=0; tracingpens:=0; tracingchoices:=0;
tracingstats:=0; tracingoutput:=0; tracingmacros:=0; tracingrestores:=0;
enddef;
message " basic constants and mathematical macros,";
% numeric constants
newinternal eps,epsilon,infinity,_;
eps := .00049; % this is a pretty small positive number
epsilon := 1/256/256; % but this is the smallest
infinity := 4095.99998; % and this is the largest
_ := -1; % internal constant to make macros unreadable but shorter
% pen constants
def capsule_def(suffix s) primary u = def s = u enddef enddef;
capsule_def(pensquare) makepen(unitsquare shifted -(.5,.5));
capsule_def(penrazor) makepen((-.5,0)--(.5,0)--cycle);
pen penspeck; penspeck=pensquare scaled eps;
% nullary operators
vardef whatever = save ?; ? enddef;
% unary operators
let abs = length;
vardef round primary u =
if numeric u: floor(u+.5)
elseif pair u: (hround xpart u, vround ypart u)
else: u fi enddef;
vardef hround primary x = floor(x+.5) enddef;
vardef vround primary y = floor(y.o_+.5)_o_ enddef;
vardef ceiling primary x = -floor(-x) enddef;
vardef byte primary s =
if string s: ASCII fi s enddef;
vardef dir primary d = right rotated d enddef;
vardef unitvector primary z = z/abs z enddef;
vardef inverse primary T =
transform T_; T_ transformed T = identity; T_ enddef;
vardef counterclockwise primary c =
if turningcheck>0:
interim autorounding:=0;
if turningnumber c <= 0: reverse fi fi c enddef;
vardef tensepath expr r =
for k=0 upto length r - 1: point k of r --- endfor
if cycle r: cycle else: point infinity of r fi enddef;
% binary operators
primarydef x mod y = (x-y*floor(x/y)) enddef;
primarydef x div y = floor(x/y) enddef;
primarydef w dotprod z = (xpart w * xpart z + ypart w * ypart z) enddef;
primarydef x**y = if y=2: x*x else: takepower y of x fi enddef;
def takepower expr y of x =
if x>0: mexp(y*mlog x)
elseif (x=0) and (y>0): 0
else: 1
if y=floor y:
if y>=0: for n=1 upto y: *x endfor
else: for n=_ downto y: /x endfor
fi
else: hide(errmessage "Undefined power: " & decimal x&"**"&decimal y)
fi fi enddef;
vardef direction expr t of p =
postcontrol t of p - precontrol t of p enddef;
vardef directionpoint expr z of p =
a_:=directiontime z of p;
if a_<0: errmessage("The direction doesn't occur"); fi
point a_ of p enddef;
secondarydef p intersectionpoint q =
begingroup save x_,y_; (x_,y_)=p intersectiontimes q;
if x_<0: errmessage("The paths don't intersect"); origin
else: .5[point x_ of p, point y_ of q] fi endgroup
enddef;
tertiarydef p softjoin q =
begingroup c_:=fullcircle scaled 2join_radius shifted point 0 of q;
a_:=ypart(c_ intersectiontimes p); b_:=ypart(c_ intersectiontimes q);
if a_<0:point 0 of p{direction 0 of p} else: subpath(0,a_) of p fi
... if b_<0:{direction infinity of q}point infinity of q
else: subpath(b_,infinity) of q fi endgroup enddef;
newinternal join_radius,a_,b_; path c_;
def reflectedabout(expr w,z) = % reflects about the line w..z
transformed
begingroup transform T_;
w transformed T_ = w; z transformed T_ = z;
xxpart T_ = -yypart T_; xypart T_ = yxpart T_; % T_ is a reflection
T_ endgroup enddef;
def rotatedaround(expr z, d) = % rotates d degrees around z
shifted -z rotated d shifted z enddef;
let rotatedabout = rotatedaround; % for roundabout people
vardef min(expr u)(text t) = % t is a list of numerics, pairs, or strings
save u_; setu_ u; for uu = t: if uu<u_: u_:=uu; fi endfor
u_ enddef;
vardef max(expr u)(text t) = % t is a list of numerics, pairs, or strings
save u_; setu_ u; for uu = t: if uu>u_: u_:=uu; fi endfor
u_ enddef;
def setu_ primary u =
if pair u: pair u_ elseif string u: string u_ fi;
u_=u enddef;
def flex(text t) = % t is a list of pairs
hide(n_:=0; for z=t: z_[incr n_]:=z; endfor
dz_:=z_[n_]-z_1)
z_1 for k=2 upto n_-1: ...z_[k]{dz_} endfor ...z_[n_] enddef;
newinternal n_; pair z_[],dz_;
vardef interpath(expr a,p,q) =
for t=0 upto length p-1: a[point t of p, point t of q]
..controls a[postcontrol t of p, postcontrol t of q]
and a[precontrol t+1 of p, precontrol t+1 of q] .. endfor
if cycle p: cycle
else: a[point infinity of p, point infinity of q] fi enddef;
vardef solve@#(expr true_x,false_x)= % @#(true_x)=true, @#(false_x)=false
tx_:=true_x; fx_:=false_x;
forever: x_:=.5[tx_,fx_]; exitif abs(tx_-fx_)<=tolerance;
if @#(x_): tx_ else: fx_ fi :=x_; endfor
x_ enddef; % now x_ is near where @# changes from true to false
newinternal tolerance, tx_,fx_,x_; tolerance:=.1;
message " macros for converting from device-independent units to pixels,";
def fix_units = % define the conversion factors, given pixels_per_inch
mm:=pixels_per_inch/25.4; cm:=pixels_per_inch/2.54;
pt:=pixels_per_inch/72.27; pc:=pixels_per_inch/6.0225;
dd:=1238/1157pt; cc:=12dd;
bp:=pixels_per_inch/72; in:=pixels_per_inch;
hppp:=pt; % horizontal pixels per point
vppp:=aspect_ratio*hppp; % vertical pixels per point
enddef;
def lowres_fix(text t) expr ratio =
begingroup save min,max,first;
forsuffixes $=t: if unknown min: min=max=first=$; min#=max#=$.#;
elseif $.#<min#: min:=$; min#:=$.#;
elseif $.#>max#: max:=$; max#:=$.#; fi endfor
if max/min>ratio*max#/min#: forsuffixes $=t: $:=first; endfor fi
endgroup enddef;
message " macros and tables for various modes of operation,";
def mode_setup =
warningcheck:=0;
if unknown mode: mode=proof; fi
numeric aspect_ratio; transform currenttransform;
scantokens if string mode:("input "&mode) else: mode_name[mode] fi;
if unknown mag: mag=1; fi
if unknown aspect_ratio: aspect_ratio=1; fi
displaying:=proofing;
pixels_per_inch:=pixels_per_inch*mag;
if aspect_ratio=1: let o_=\; let _o_=\
else: def o_=*aspect_ratio enddef; def _o_=/aspect_ratio enddef fi;
fix_units;
scantokens extra_setup; % the user's special last-minute adjustments
currenttransform:=
if unknown currenttransform: identity else: currenttransform fi
yscaled aspect_ratio;
clearit;
pickup pencircle scaled (.4pt+blacker);
warningcheck:=1; enddef;
def smode = string mode; mode enddef;
string extra_setup, mode_name[];
extra_setup=""; % usually there's nothing special to do
newinternal displaying; % if positive, endchar will `showit'
vardef magstep primary m = mexp(46.67432m) enddef;
% proof mode: for initial design of characters
mode_def proof =
proofing:=2; % yes, we're making full proofs
fontmaking:=0; % no, we're not making a font
tracingtitles:=1; % yes, show titles online
pixels_per_inch:=2601.72; % that's 36 pixels per pt
blacker:=0; % no additional blackness
fillin:=0; % no compensation for fillin
o_correction:=1; % no reduction in overshoot
enddef;
% smoke mode: for label-free proofs to mount on the wall
mode_def smoke =
proof_; % same as proof mode, except:
proofing:=1; % yes, we're making unlabeled proofs
extra_setup:=extra_setup&"grayfont black"; % with solid black pixels
let makebox=maketicks; % make the boxes less obtrusive
enddef;
% lowres mode: for certain devices that print 200 pixels per inch
mode_def lowres =
proofing:=0; % no, we're not making proofs
fontmaking:=1; % yes, we are making a font
tracingtitles:=0; % no, don't show titles at all
pixels_per_inch:=200; % that's the meaning of lowres
blacker:=.65; % make pens a bit blacker
fillin:=.2; % compensate for diagonal fillin
o_correction:=.4; % but don't overshoot as much
enddef;
localfont:=lowres; % the mode most commonly used to make fonts
% It is customary to input another file to supplement the PLAIN base.
% This supplementary file adds analogous modes, corresponding to
% local output devices, and it redefines `localfont' as appropriate.
% The values of screen_rows and screen_cols should also be updated.
% The auxiliary file should set base_version:=base_version&"/localname".
% Remember that the present file PLAIN.MF should not be changed;
% all local changes should be confined to a separate file.
def fill expr c = addto_currentpicture contour c.t_ enddef;
def addto_currentpicture = addto currentpicture enddef;
def draw expr p =
addto_currentpicture doublepath p.t_ withpen currentpen enddef;
def filldraw expr c = fill counterclockwise c withpen currentpen enddef;
def drawdot expr z = if unknown currentpen_path: def_pen_path_ fi
addto_currentpicture contour
currentpen_path shifted (z.t_) withpen penspeck enddef;
def def_pen_path_ =
hide(currentpen_path=tensepath makepath currentpen) enddef;
def unfill expr c = fill c withweight _ enddef;
def undraw expr p = draw p withweight _ enddef;
def unfilldraw expr c = filldraw c withweight _ enddef;
def undrawdot expr z = drawdot z withweight _ enddef;
def erase text t = begingroup interim default_wt_:=_;
cullit; t withweight _; cullit; endgroup enddef;
newinternal default_wt_; default_wt_:=1;
def cutdraw expr p = % caution: you may need autorounding=0
cutoff(point 0 of p, 180+angle direction 0 of p);
cutoff(point infinity of p, angle direction infinity of p);
culldraw p enddef;
def culldraw expr p = addto pic_ doublepath p.t_ withpen currentpen;
cull pic_ dropping(-infinity,0) withweight default_wt_;
addto_currentpicture also pic_; pic_:=nullpicture; killtext enddef;
vardef cutoff(expr z,theta) =
interim autorounding := 0; interim smoothing := 0;
addto pic_ doublepath z.t_ withpen currentpen;
addto pic_ contour
(cut_ scaled (1+max(-pen_lft,pen_rt,pen_top,-pen_bot))
rotated theta shifted z)t_;
cull pic_ keeping (2,2) withweight -default_wt_;
addto currentpicture also pic_;
pic_:=nullpicture enddef;
picture pic_; pic_:=nullpicture;
path cut_; cut_ = ((0,_)--(1,_)--(1,1)--(0,1)--cycle) scaled 1.42;
def pickup secondary q =
if numeric q: numeric_pickup_ else: pen_pickup_ fi q enddef;
def numeric_pickup_ primary q =
if unknown pen_[q]: errmessage "Unknown pen"; clearpen
else: currentpen:=pen_[q];
pen_lft:=pen_lft_[q];
pen_rt:=pen_rt_[q];
pen_top:=pen_top_[q];
pen_bot:=pen_bot_[q];
currentpen_path:=pen_path_[q] fi; enddef;
def pen_pickup_ primary q =
currentpen:=q yscaled aspect_ratio;
pen_lft:=xpart penoffset down of currentpen;
pen_rt:=xpart penoffset up of currentpen;
pen_top:=(ypart penoffset left of currentpen)_o_;
pen_bot:=(ypart penoffset right of currentpen)_o_;
path currentpen_path; enddef;
newinternal pen_lft,pen_rt,pen_top,pen_bot,pen_count_;
vardef lft primary x = x + if pair x: (pen_lft,0) else: pen_lft fi enddef;
vardef rt primary x = x + if pair x: (pen_rt,0) else: pen_rt fi enddef;
vardef top primary y = y + if pair y: (0,pen_top) else: pen_top fi enddef;
vardef bot primary y = y + if pair y: (0,pen_bot) else: pen_bot fi enddef;
vardef good.x primary x = hround(x+pen_lft)-pen_lft enddef;
vardef good.y primary y = vround(y+pen_top)-pen_top enddef;
vardef good.lft primary z = save z_; pair z_;
(z_+(pen_lft,0))t_=round((z+(pen_lft,0))t_); z_ enddef;
vardef good.rt primary z = save z_; pair z_;
(z_+(pen_rt,0))t_=round((z+(pen_rt,0))t_); z_ enddef;
vardef good.top primary z = save z_; pair z_;
(z_+(0,pen_top))t_=round((z+(0,pen_top))t_); z_ enddef;
vardef good.bot primary z = save z_; pair z_;
(z_+(0,pen_bot))t_=round((z+(0,pen_bot))t_); z_ enddef;
def italcorr expr x_sharp = if x_sharp>0: charic:=x_sharp fi enddef;
def change_width =
w:=w if w>charwd*hppp:- else:+ fi 1 enddef;
def endchar =
scantokens extra_endchar;
if proofing>0: makebox(proofrule); fi
chardx:=w; % desired width of the character in pixels
shipit;
if displaying>0: makebox(screenrule); showit; fi
endgroup enddef;
def makebox(text r) =
for y=0,h.o_,-d.o_: r((0,y),(w,y)); endfor % horizontals
for x=0,w: r((x,-d.o_),(x,h.o_)); endfor % verticals
if charic<>0: r((w+charic*hppp,h.o_),(w+charic*hppp,.5h.o_)); fi
enddef;
def maketicks(text r) =
for y=0,h.o_,-d.o_: r((0,y),(10,y)); r((w-10,y),(w,y)); endfor
for x=0,w: r((x,10-d.o_),(x,-d.o_)); r((x,h.o_-10),(x,h.o_)); endfor
if charic<>0: r((w+charic*hppp,h.o_-10),(w+charic*hppp,h.o_)); fi
enddef;
def font_size expr x = designsize:=x enddef;
def font_slant expr x = fontdimen 1: x enddef;
def font_normal_space expr x = fontdimen 2: x enddef;
def font_normal_stretch expr x = fontdimen 3: x enddef;
def font_normal_shrink expr x = fontdimen 4: x enddef;
def font_x_height expr x = fontdimen 5: x enddef;
def font_quad expr x = fontdimen 6: x enddef;
def font_extra_space expr x = fontdimen 7: x enddef;
def font_identifier expr x = font_identifier_:=x enddef;
def font_coding_scheme expr x = font_coding_scheme_:=x enddef;
string font_identifier_, font_coding_scheme_;
font_identifier_=font_coding_scheme_="UNSPECIFIED";
message "and a few last-minute items.";
vardef z@#=(x@#,y@#) enddef;
newinternal screen_rows, screen_cols, currentwindow;
screen_rows:=400; % these values should be corrected,
screen_cols:=500; % by reading in a separate file after PLAIN.MF
def openit = openwindow currentwindow
from origin to (screen_rows,screen_cols) at (-50,300) enddef;
def showit = openit; let showit=showit_; showit enddef; % first time only
def showit_ = display currentpicture inwindow currentwindow enddef;
def screenchars = % endchar should `showit'
extra_endchar:=extra_endchar&"showit;" enddef;
def screenstrokes = % every stroke should `showit'
def addto_currentpicture text t=
addto currentpicture t; showit enddef; enddef;
def imagerules = % a box should be part of the character image
extra_beginchar:=extra_beginchar & "makebox(screenrule);" enddef;
def gfcorners = % `maketicks' should send rules to the GF file
extra_setup:=extra_setup & "let makebox=maketicks;proofing:=1;" enddef;
def nodisplays = % endchar shouldn't `showit'
extra_setup:=extra_setup & "displaying:=0;" enddef;
def notransforms = % currenttransform should not be used
let t_ = \ enddef;
let bye = end; outer end,bye;
clear_pen_memory; % initialize the `savepen' mechanism
mode_setup; % establish proof mode as the default
numeric mode,mag; % but leave mode and mag undefined