summaryrefslogtreecommitdiff
path: root/fonts/mathabx/source/mathbase.mf
blob: 03619996ddc58027c930da042252b8859f657dc9 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
% mathematical symbols by Anthony Phan.
% file: mathbase.mf (base file)
% last modification: May 16, 2005.

mathbase := 1; % when |mathbase| is known, this file has been input

newinternal slant, currentbreadth, math_spread, superness, stress;
slant := 0; superness := 1/sqrt 2; stress := 0.5;

string main_name_string, tmp_string, 
extra_beginchar_save, extra_endchar_save;

picture tmp_picture;
path tmp_path, tmpp_path;

boolean true_size, tmp_boolean, dagesh;
true_size := false;% see mathhbrw.mf

pair both; both = (1, 1);

def autorounded = interim autorounding := 2 enddef;

def localtransform = save currenttransform;
  transform currenttransform; currenttransform
enddef;

numeric currentlocation_;

vardef currentlocation = 
  currentlocation_ := currentlocation_+1;
  currentlocation_-1
enddef;

def main_name_with(suffix $) = 
  scantokens(main_name_string & str$)
enddef;

def math_setup = 
  autorounding := 0; smoothing := 0;
  appr# := u#+letter_fit#; Appr# := 1.5u#+letter_fit#;
  numeric paren_depth#, asc_depth#, body_depth#;
  0.5[body_height#, -paren_depth#] = math_axis#;
  0.5[asc_height#, -asc_depth#] = math_axis#;
  body_depth# := desc_depth#+body_height#-asc_height#;
  %
  define_pixels(u, dh, dish, stem_corr, vair_corr);
  define_whole_blacker_pixels(hair, stem, curve, 
    cap_hair, cap_stem, cap_curve, dtsz, ast_curve, ast_stem);
  define_whole_vertical_blacker_pixels(vair, slab);% cap_bar...
  define_whole_vertical_pixels(body_height, asc_height, 
    cap_height, fig_height, x_height, desc_depth, 
    asc_depth, body_depth, paren_depth);
  define_whole_pixels(letter_fit, appr, Appr, 
    crisp, tiny, fine, ast_size);
  define_corrected_pixels(o);
  define_horizontal_corrected_pixels(ho);
  lowres_fix(stem, curve) 1.2;
  lowres_fix(cap_stem, cap_curve) 1.2;
  lowres_fix(hair, cap_hair) 1.2;
  oo := vround(0.5o#*hppp*o_correction)+eps;
  dw := (curve#-stem#)*hppp; bold := curve#*hppp+blacker;
  vair' := vround(vair+vair_corr);
  % 
  % usual pens.
  %
  clear_pen_memory;
  if fine = 0: fine := 1; fi
  null := 0;
  forsuffixes $ = null, crisp, tiny, fine:
    $.breadth := $;
    pickup if $ = 0: nullpen else: pencircle scaled $ fi;
    $ := $-eps; $.nib := savepen; breadth_[$.nib] := $;
  endfor
  $ := 0;
  forever:
    exitif unknown rth[$].#;
    rth[$] := ceiling(rth[$].#*hppp);
    pickup pencircle scaled rth[$];
    rule.nib[$] := savepen;
    $ := $+1;
  endfor
  %
  % spreads
  %
  for $ = 0 upto 10:
    if known spread[$].#:
      spread[$] := 2ceiling(0.5spread[$].#*hppp);
    fi
  endfor
  %
  % current transform (slant is not taken into account)
  %
  currenttransform = identity
  yscaled aspect_ratio scaled granularity;
  %
  % proofing
  %
  standard_proofing;
  use_rule1;
enddef;

% The following environment enables people to draw a picture
% almost like drawing a character. The resulting picture is
% stored in $_picture and then it can be used in at any
% place later.

def beginpicture(suffix $)(expr w_sharp, h_sharp, d_sharp) = 
  begingroup
    save picturename;
    w := hround(w_sharp*hppp); h := vround(h_sharp*hppp);
    d := vround(d_sharp*hppp); clearxy; clearit; clearpen;
    string picturename; picturename = str $ &"_picture";
  enddef;

  def endpicture = 
    expandafter picture scantokens picturename;
    scantokens picturename = currentpicture;
  endgroup
enddef;

vardef use_rule@# = 
  rth := rth@#; rth# := rth@#.#;
  rule.nib := rule.nib@#;
  math_axis := vround(math_axis#*hppp-0.5rth)+0.5rth;
enddef;

def numeric_pickup_ primary q = 
  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];
  if known breadth_[q]: currentbreadth := breadth_[q]; fi
enddef;

%def compute_spread(expr normal_spread, big_spread) = 
% spread# := math_spread[normal_spread, big_spread];
% spread := 2ceiling((spread#)*hppp/2)
%enddef;

def v_center(expr h_sharp) = 
  .5h_sharp+math_axis#, .5h_sharp-math_axis#
enddef;

def ensure_centering_of(expr stem) = 
  if hround 0.5(w-hround stem)+0.5hround stem<> 0.5w:
    change_width; fi
enddef;

vardef v_adjust(suffix $, $$)(expr middle, height) = 
  top y$-middle = middle-bot y$$ = vround 0.5(height-rth)+0.5rth
enddef;

def arithmetic_bounds = 
  12u#+2appr#, math_axis#+6u#, 6u#-math_axis#
enddef;

def padded expr del_sharp = 
  charht := charht+del_sharp; chardp := chardp+del_sharp
enddef;

%vardef pos@#(expr b, d) = 
% if known b: if b <= currentbreadth: errmessage "bad pos"; fi fi
% save d_; pair d_; d_ = dir d;
% z@#r-z@#l+penoffset d_ of currentpen+penoffset -d_ of currentpen = b*d_;
% x@# = .5(x@#l+x@#r); y@# = .5(y@#l+y@#r) enddef;

vardef pos@#(expr b, d) = 
  if known b: if b <= currentbreadth: errmessage "bad pos"; fi fi
  (x@#r-x@#l, y@#r-y@#l) = (b-currentbreadth, 0) rotated d;
  x@# = .5(x@#l+x@#r); y@# = .5(y@#l+y@#r) enddef;

vardef stroke text t = 
  forsuffixes e = l, r: path_.e := t;endfor
  if cycle path_.l:
    errmessage "Beware: `stroke' doesn't work with cycles";
  fi
  path_.l -- reverse path_.r -- cycle
enddef;

% DIAGONALS

def diag_width(expr $, $$) = 
  $/abs sind angle $$
enddef;

%vardef diag_height(expr $, $$) = 
% $/abs cosd angle $$
%enddef;

% $ <---> $$$; $$ <---> $$$$. sign = +1 for \, -1 for /.

vardef adjust_slanted_bar(suffix $, $$, $$$, $$$$)(expr thickness, sign) = 
  save a, b;
  if abs(y$$-y$) = thickness:
    (a1, a2) = (z$$-z$);
    if a1 = 0: b = 0;% b should then be infinite.
    else: b = if sign<0: - fi (a1++a2)*((a1++a2)/2a1);
    fi
  else:
    a = angle(z$$-z$);
    b = (cosd(a)/sind(a) if sign<0: - else: + fi
      (((y$$-y$)/(thickness)/sind(a))+-+1))
    /(((y$$-y$)/(thickness))**2-1)*(y$$-y$);
  fi
  z$$$ = (x$-b, y$); z$$$$ = (x$$+b, y$$)
enddef;

% supplementary points for diagonal strokes
% as in cm's \#. (see MetaFontbook, p. 200--201)
% Well, ...

vardef diag_stroke.@#(suffix $, $$, s)(text y_list) = 
  z$.@#--for y_ = y_list:
    (good.x(((x$.s-x$$.s)/(y$.s-y$$.s))*(y_-y$$r)+x$$.s), y_)
    +z$.@#-z$.s
    --endfor z$$.@#
enddef;

% CIRCLES, ELLIPSES AND RELATED THINGS

primarydef w up_to_right z = 
  w{0, ypart(z-w)}
  ...(superness[xpart z, xpart w], 
    superness[ypart w, ypart z]){z-w}
  ...{xpart(z-w), 0}z
enddef;

let up_to_left = up_to_right;
let down_to_right = up_to_right;
let down_to_left = up_to_right;

primarydef w right_to_up z = 
  w{xpart(z-w), 0}
  ...(superness[xpart w, xpart z], 
    superness[ypart z, ypart w]){z-w}
  ...{0, ypart(z-w)}z
enddef;

let right_to_down = right_to_up;
let left_to_up = right_to_up;
let left_to_down = right_to_up;

def ellipse_set(suffix $, @, @@, $$) = 
  alpha_ := slope*(x@-x$); beta_ := y$$-y$-slope*(x$$-x$);
  gamma_ := alpha_/beta_;
  y@-y$ = .5(beta_-alpha_*gamma_);
  x@@-x$ = -2gamma_*(x@-x$)/(1+gamma_*gamma_);
  y@@-y$$ = slope*(x@@-x$$)
enddef;

def hellipse_set(suffix $, @, @@, $$) = 
  alpha_ := (y@-y$)/slope; beta_ := x$$-x$-(y$$-y$)/slope;
  gamma_ := alpha_/beta_;
  x@-x$ = .5(beta_-alpha_*gamma_);
  y@@-y$ = -2gamma_*(y@-y$)/(1+gamma_*gamma_);
  x@@-x$$ = (y@@-y$$)/slope
enddef;

vardef adjust_elliptic_arc(suffix $, $$, $$$) = 
  save a, b;
  if known (y$$$-y$): a = (1+-+((y$$$-y$)/(y$$-y$)));
    x$$-x$ = (x$$$-x$)/(1+a); b = (1+-+((x$$$-x$$)/(x$$-x$)));
  else: b = (1+-+((x$$$-x$$)/(x$$-x$)));
    y$$$-y$ = (y$$-y$)*b; a = (1+-+((y$$$-y$)/(y$$-y$)));
  fi
  y$$$' = y$$; x$$$' = (((1-b)/a)*(b/a))[x$$$, x$$];
enddef;

def flatcup(expr zi, zii, ziii) = 
  zi..controls (xpart zi, flatness[ypart zi, ypart zii])
  and (xpart zi, ypart zii)
  ..zii..controls (xpart ziii, ypart zii)
  and (xpart ziii, flatness[ypart ziii, ypart zii])..ziii
enddef;

% DOTS

boolean full_dot; full_dot := true;

def dot(suffix $, $$) = 
  autorounded;
  if full_dot: filldraw else: draw fi
  dot_path($, $$); full_dot := true;
enddef;

def dot_path(suffix $, $$) = 
  (x$, 0.5[y$, y$$]) down_to_right (0.5[x$, x$$], y$) right_to_up
  (x$$, 0.5[y$, y$$]) up_to_left (0.5[x$, x$$], y$$) left_to_down
  (x$, 0.5[y$, y$$])...cycle
enddef;

vardef adjust_dot@#(expr center, diameter, h_fit, v_fit) = 
  if v_fit: save y_min, y_max;
    bot y_min = vround(ypart center-0.5diameter)-eps;
    top y_max = vround(ypart center+0.5diameter)+eps;
    y@#'-ypart center = ypart center-y@#
    = max(y_max-ypart center, ypart center-y_min);
  else:
    bot y@# = vround(ypart center-0.5diameter)-eps;
    top y@#'-bot y@# = vround diameter+2eps; fi
  if h_fit: save x_min, x_max;
    lft x_min = hround(xpart center-0.5diameter)-eps;
    rt x_max = hround(xpart center+0.5diameter)+eps;
    x@#'-xpart center = xpart center-x@#
    = max(x_max-xpart center, xpart center-x_min);
  else: 
    lft x@# = vround(xpart center-0.5diameter)-eps;
    rt x@#'-lft x@# = hround(diameter)+2eps; fi
  labels(@#, @#');
enddef;

% VERY DESIGN DEPENDENT MACROS

% DAGGERS AND ASTERISKS

vardef dagger_stroke@#(expr height, curve, stem, u_) = 
  save alpha, a, b, c, R;
  alpha = angle u_-90; R = 0.5(curve-currentbreadth);
  a = stress*(height-curve+0.5currentbreadth)+R;
  b = 0.5(stem-currentbreadth);
  c = (a*R-b*sqrt(a**2+b**2-R**2))/(a**2+b**2);
  z@#c-z@# = (height-0.5currentbreadth)*u_;
  z@#c-z@#b = R*u_; z@#d-z@#b = -a*u_; z@#a = (c*(R/a))[z@#b, z@#d];
  penpos@#(2b, alpha); penpos@#d(2b, alpha);
  penpos@#a(2R*(1+-+c), alpha); penpos@#b(2R, alpha);
  penlabels(@#a, @#b, @#c, @#d, @#);
  z@#r{u_}...z@#a.r{z@#a.r-z@#d.r}...z@#b.r{u_}...
  (superness[z@#b, z@#b.r]+superness[z@#b, z@#c]-z@#b){z@#c-z@#b.r}
  ...z@#c{z@#b.l-z@#b.r}...
  (superness[z@#b, z@#b.l]+superness[z@#b, z@#c]-z@#b){z@#b.l-z@#c}
  ...z@#b.l{-u_}...z@#a.l{z@#d.l-z@#a.l}...{-u_}z@#l
enddef;

% ARROWS

numeric arrow_height, arrow_width, arrow_breadth, arrow_stress, 
arrow_tense[], arrow_time, double_arrow_height, double_arrow_width, 
double_arrow_tense, double_arrow_flatness;

boolean arrow_head_fitting;
arrow_head_fitting := false;

vardef arrow_head@#(expr p, side) = 
  save a, t; numeric a[];
  a1 = angle direction infinity of p; pos@#a(rth, a1-90);
  z@#a = point infinity of p
  if arrow_head_fitting: -0.5currentbreadth*dir a1 fi;
  t := xpart(p intersectiontimes (halfcircle rotated(a1+90)
      scaled (2arrow_stress*arrow_height-currentbreadth)
      shifted z@#a));
  a2 := angle direction t of p; arrow_time := t;
  z@# = point t of p; pos@#(rth, a2-90);
  z@#-z@#c = (1-arrow_stress)*arrow_height*dir a2;
  z@#c.r-z@#c = z@#c-z@#c.l = 0.5(arrow_width-currentbreadth)*dir(a2-90);
  z@#b.r-z@#c.r = z@#b.l-z@#c.l = max(arrow_breadth-currentbreadth, 0)*dir a2;
  z@#b = p intersectionpoint (z@#b.r..z@#b.l);
  t := xpart(p intersectiontimes (halfcircle rotated(a1+90)
      scaled (2arrow_tense2[1, arrow_stress]*arrow_height-currentbreadth)
      shifted z@#a));
  a3 = angle direction t of p; z@#' = point t of p; pos@#'(rth, a3-90);
  z@#a' = if arrow_tense1<1:
    p intersectionpoint (halfcircle rotated(a1+90)
      scaled(arrow_tense1[length(z@#b-z@#a), 0]*2) shifted z@#a);
  else: z@#a; fi
  filldraw
  if side = right: z@#a.l{-dir a1}...{-dir a2}z@#l
  else: z@#a...{z@#b.l-z@#a'}z@#b.l--z@#c.l{z@#'l-z@#c.l}...z@#l
  fi --
  if side = left: z@#r{dir a2}...z@#a.r{dir a1}
  else: z@#r...{z@#c.r-z@#'r}z@#c.r--z@#b.r{z@#a'-z@#b.r}...z@#a
  fi -- cycle;
  labels(@#a'); penlabels(@#', @#a, @#b, @#c);
  arrow_head_fitting := false;
enddef;

vardef double_arrow_head@#(expr head, vect) = 
  save a, b, u_, v_; pair u_, v_;
  u_ = unitvector vect; v_ = u_ rotated 90;
  z@# = z@#' = head;
  z@#-z@#m = double_arrow_height*u_;
  pos@#'(rth, angle u_-90);
  pos@#m(rth, angle u_-90);
  z@#-z@#b.r = z@#m-z@#m.b = 0.5rth*double_arrow_flatness*v_;
  a = angle(-double_arrow_height, 0.5double_arrow_width);
  b = (cosd(a)/sind(a)+
    ((0.5double_arrow_width/rth/sind(a))+-+1))
  /((0.5double_arrow_width/rth)**2-1)
  *0.5double_arrow_width;
  z@#c.l = double_arrow_tense[z@#m.b, z@#b.r-b*u_];
  z@#m-z@#a.l = 0.5double_arrow_width*v_;
  b := rth/abs sind(angle(z@#a.l-z@#c.l)-angle(-u_));
  z@#a.r-z@#a.l = z@#c.r-z@#c.l = b*u_;
  z@#ab = 0.5[z@#a.r, z@#c.r];
  penpos@#b(rth, angle(z@#b.r-z@#ab)-90);
   %
  save p, t; path p[]; numeric t[];
  z@#a = 0.5[z@#a.r, z@#a.l];
  p1 = z@#a{z@#ab-z@#a.r}...{z@#b.r-z@#ab}z@#b;
  p3 = z@#a.r{z@#ab-z@#a.r}...{z@#b.r-z@#ab}z@#b.r;
  p5 = if (z@#b.l-z@#) dotprod v_<0:
    z@#'l+(u_ dotprod (z@#b.l-z@#))*u_-- fi
  z@#b.l{z@#ab-z@#b.r}...{z@#a.r-z@#ab}z@#a.l;
  p2 = reverse p1 reflectedabout (z@#, z@#m);
  p4 = reverse p3 reflectedabout (z@#, z@#m);
  p6 = reverse p5 reflectedabout (z@#, z@#m);
  t5 = xpart(p5 intersectiontimes (z@#+eps*v_ .. z@#m+eps*v_));
  t6 = xpart(p6 intersectiontimes (z@#-eps*v_ .. z@#m-eps*v_));
  fill p3--z@#+eps*v_--subpath (t5, length p5) of p5--cycle;
  fill z@#-eps*v_--p4--subpath (0, t6) of p6--cycle;
  forsuffixes $ = l, , r:
    z@#r$ = p1 intersectionpoint
    ((z@#'$..z@#m$) shifted (-0.5spread1*v_));
    z@#l$ = p2 intersectionpoint
    ((z@#'$..z@#m$) shifted (0.5spread1*v_));
  endfor
  penlabels(@#, @#', @#a, @#b, @#c, @#r, @#l, @#m); labels(@#ab, @#m.b);
enddef;

% ARM, BEAK and SERIFS (personal taste)

% vardef arm@#(expr beak, beak_jut, breadth, darkness, orientation, x_limit) = 
%  save a; a = 90;
%  if orientation = up: y@#a = min(y@#l, y@#r); y@#d = max(y@#l, y@#r);
%   y@#b-y@#d = vround beak; a := -a;
%  else: y@#a = max(y@#l, y@#r); y@#d = min(y@#l, y@#r);
%   y@#b-y@#d = -vround beak; fi
%  if x_limit>x@#: rt x@#b = hround x_limit; x@#b-x@#a = hround beak_jut;
%  else: lft x@#b = hround x_limit; x@#b-x@#a = -hround beak_jut; a := -a; fi
%  z@#c-z@#b = max(0, breadth-currentbreadth)
%  *unitvector(z@#a-z@#b)rotated a;
%  z@#d-z@#c = whatever*(z@#a-z@#b);
%  filldraw z@#c{z@#d-z@#c}...
%  if y@#l = y@#.d: darkness[z@#d, 0.5[z@#c, z@#l]]{z@#l-z@#c}
%   ...z@#l{z@#l-z@#d}--z@#r
%  else: darkness[z@#d, 0.5[z@#c, z@#r]]{z@#r-z@#c}
%   ...z@#r{z@#r-z@#d}--z@#l fi
%  --z@#a--z@#b--cycle;
%  labels(@#a, @#b, @#c, @#d);
% enddef;

vardef arm@#(expr beak, beak_jut, hair, darkness, direction, limit) = 
  y@#d = y@#r; y@#a = y@#b = y@#r if ypart direction > 0: + else: - fi vround beak;
  y@#c = y@#l;
  rt x@#b = hround limit; lft x@#a = hround(limit-hair);
  x@#b-x@#c = hround beak_jut; z@#d-z@#a = whatever*(z@#c-z@#b);
  filldraw z@#r{z@#d-z@#r}...darkness[z@#d, 0.5[z@#r, z@#a]]...
  z@#a{z@#a-z@#d}--z@#b--z@#c--z@#l--cycle;
  labels(@#a, @#b, @#c, @#d);
enddef;

vardef serif(suffix $, $$)
  (expr bracket, left_jut, left_slab, dished_left, left_dish, 
    right_jut, right_slab, dished_right, right_dish) = 
  save a, b; b = cosd angle(z$$-z$);
  a = max(0.5left_jut, 0.5right_jut, bracket);
  if y$<y$$: top y$b = bot y$+vround left_slab;
    top y$g = bot y$+vround right_slab;
    y$a-y$b = y$h-y$g = bracket;
    top y$c-bot y$d = left_slab+left_dish;
    top y$f-bot y$e = right_slab+right_dish;
  else: bot y$b = top y$-vround left_slab;
    bot y$g = top y$-vround right_slab;
    y$a-y$b = y$h-y$g = -bracket;
    bot y$c-top y$d = -left_slab-left_dish;
    bot y$f-top y$e = -right_slab-right_dish;
  fi
  if dished_left: y$c = y$b; else: y$d = y$; fi
  if dished_right: y$f = y$g; else: y$e = y$; fi
  if x$l<x$r: z$a = whatever[z$l, z$$l];
    z$h = whatever[z$r, z$$r];
    x$c = x$d = x$l-hround(left_jut-b*abs(y$b-y$));
    x$e = x$f = x$r+hround(right_jut+b*abs(y$g-y$));
    x$l-x$b = min(left_jut, a);
    x$g-x$r = min(right_jut, a);
  else: z$a = whatever[z$r, z$$r];
    z$h = whatever[z$l, z$$l];
    x$c = x$d = x$r-hround(left_jut-b*abs(y$b-y$));
    x$e = x$f = x$l+hround(right_jut+b*abs(y$g-y$));
    x$r-x$b = min(left_jut, a);
    x$g-x$l = min(right_jut, a);
  fi
  filldraw z$a{z$-z$$}...z$b{left}...z$c--z$d...z${right}
  ...z$e--z$f...z$g{left}...{z$$-z$}z$h--cycle;
  labels($a, $b, $c, $d, $e, $f, $g, $h);
enddef;

% SIM: drawn once, used many times

def make_sim_picture = 
  if unknown sim_picture:
    beginpicture(sim, 12u#+2appr#, v_center(spread1#+rth#));
    pickup tiny.nib;
    save a, b;
    a = angle(1, 1.25(h+d)/u);
    b = angle(1, -(h+d)/4.5u);
    pos1(hair, a+90); pos9(hair, a+90); pos5(stem, b+90);
    bot y7l = -d-eps; top y3r = h+eps;
    y1l = good.y 0.225[y7l, y3r]; y3r-y9r = y1l-y7l;
    top y3r-bot y3l = top y7r-bot y7l = vround 0.5[hair, stem];
    lft x1r = Appr-eps; rt x9l = w-Appr+eps;
    z5 = 0.5[z1, z9];
    forsuffixes $ = r, l: y2$ = y3$ = y4$; y6$ = y7$ = y8$;
      z2$-z1$ = whatever*dir a; z8$-z9$ = whatever*dir a;
      z4$-z5$ = whatever*dir b; z6$-z5$ = whatever*dir b;
      x3$ = 0.6525[x2$, x4$]; x7$ = 0.6525[x8$, x6$];
    endfor
    filldraw stroke z1e..controls 0.66[z1e, z2e] and 0.66[z3e, z2e]
    ..z3e..controls 0.4[z3e, z4e] and 1[z5e, z4e]% 1 for inflexion point
    ..z5e..controls 1[z5e, z6e] and 0.4[z7e, z6e]
    ..z7e..controls 0.66[z7e, z8e] and 0.66[z9e, z8e]..z9e;
   %penlabels(1, 2, 3, 4, 5, 6, 7, 8, 9);
    endpicture;
  fi
enddef;

% TRIANGLES

% makes an equilateral triangle optionally fully centered.

numeric triangle_foot;

vardef set_triangle@#(expr orientation, a, rth, centered, fit_bounds) = 
  if orientation = left:
    rt x1@#r = rt x3@#r = if centered:
      hround(0.5w+0.5a/sqrt3);
    else: hround triangle_foot; fi
    x1@#r-x2@#r = hround(0.5a*sqrt(3)-currentbreadth)+eps;
    y2@#r = good.y 0.5[-d, h];
    y3@#r-y2@#r = y2@#r-y1@#r = vround(0.5(a-currentbreadth))+eps;
  elseif orientation = right:
    lft x1@#r = lft x3@#r = if centered:
      hround(0.5w-0.5a/sqrt3);
    else: hround triangle_foot; fi
    x2@#r-x1@#r = hround(0.5a*sqrt(3)-currentbreadth)+eps;
    y2@#r = good.y 0.5[-d, h];
    y2@#r-y3@#r = y1@#r-y2@#r = vround(0.5(a-currentbreadth))+eps;
  elseif orientation = down:
    top y1@#r = top y3@#r = if centered:
      vround(math_axis+0.5a/sqrt3);
    else: vround triangle_foot; fi
    y1@#r-y2@#r = hround(0.5a*sqrt(3)-currentbreadth)+eps;
    x2@#r = good.x 0.5w;
    x1@#r-x2@#r = x2@#r-x3@#r
    = hround 0.5min(a-currentbreadth, w-2appr-currentbreadth+2ho)+eps;
  else:
    bot y1@#r = bot y3@#r = if centered:
      vround(math_axis-0.5a/sqrt3);
    else: vround triangle_foot; fi
    y2@#r-y1@#r = hround(0.5a*sqrt(3)-currentbreadth)+eps;
    x2@#r = good.x 0.5w;
    x3@#r-x2@#r = x2@#r-x1@#r
    = hround 0.5min(a-currentbreadth, w-2appr-currentbreadth+2ho)+eps;
  fi
  z1@#l-z1@#r = (rth-currentbreadth)/sind(60)
  *(unitvector(z3@#r-z1@#r)+unitvector(z2@#r-z1@#r));
  z2@#l-z2@#r = (rth-currentbreadth)/sind(60)
  *(unitvector(z3@#r-z2@#r)+unitvector(z1@#r-z2@#r));
  z3@#l-z3@#r = (rth-currentbreadth)/sind(60)
  *(unitvector(z1@#r-z3@#r)+unitvector(z2@#r-z3@#r)); 
  penlabels(1@#, 2@#, 3@#);
enddef;

% It's buggy
vardef draw_star@#(expr center, n_edges, radius, tense, angle_init, void) = 
  save a, b, theta; theta = 360/n_edges;
  x@# = good.x xpart center; y@# = good.y ypart center;
  % external points
  a = radius-0.5currentbreadth;
  b = (1-tense)*a*cosd theta/cosd(theta/2);
  for $ = 1 upto n_edges:
    z@#[2$-1]l = z@#+round(a*dir(($-1)*theta+angle_init));
    z@#[2$]l = z@#+round(b*dir(($-0.5)*theta+angle_init));
    labels(@#[2$-1]l, @#[2$]l);
  endfor
  if void:
  % internal points
    a := (rth-currentbreadth)/
    abs sind(angle(z@#[1]l-z@#[2]l)-angle(z@#[1]l-z@#));
    b := (rth-currentbreadth)/
    abs sind(angle(z@#[2]l-z@#[1]l)-angle(z@#[2]l-z@#));
    for $ = 1 upto n_edges:
      z@#[2$-1]l-z@#[2$-1]r = a*dir(($-1)*theta+angle_init);
      z@#[2$]l-z@#[2$]r = b*dir(($-0.5)*theta+angle_init);
      labels(@#[2$-1]r, @#[2$]r);
    endfor
    filldraw stroke for $ = 1 upto 2n_edges: z@#[$]e--endfor z@#[1]e;
  else:
    filldraw for $ = 1 upto 2n_edges: z@#[$]l--endfor cycle;
  fi
enddef;

% ADMINISTRATION

% PROOFING

def horizontal_rules_list = 
  -body_depth, -desc_depth, x_height, cap_height, asc_height, body_height
enddef;

def makebox(text rule) = 
  for y = -d.o_, 0, h.o_:
    rule((-xoffset, y), (w-xoffset, y)); endfor
  for y = horizontal_rules_list:
    rule((appr-xoffset, y), (w-appr-xoffset, y));
  endfor
  for x = -xoffset, appr-xoffset, w-appr-xoffset, w-xoffset:
    rule((x, -d.o_), (x, h.o_)); endfor
  for x = appr+u-xoffset step u until w-appr-1.5-xoffset:
    rule((x, -d.o_), (x, h.o_)); endfor
  if charic<>0:
    rule((w-xoffset+charic*hppp, h.o_), 
      (w-xoffset+charic*hppp, .5[h, -d].o_)); fi
enddef;

def accents_proofing = 
  for $ = 0 upto 19:
    makelabel("", (0.5w-xoffset, 0.5x_height)
      +(4u*cosd($*360/20), 0.5x_height*sind($*360/20)));
  endfor
enddef;

def diacritics_proofing = 
  if proofing>0: extra_endchar := extra_endchar&"accents_proofing;"; fi
enddef;

def standard_proofing = 
  if proofing>0: extra_endchar := "additions_to_proof;"; fi
enddef;

def additions_to_proof = 
  makelabel.lft("baseline", (-xoffset, 0));
  if h>math_axis: makelabel.lft("math axis", (-xoffset, math_axis)); fi
enddef;

% `iff' CONSTRUCTION

let semi_ = ;; let colon_ = :; let endchar_ = endchar;
def iff expr b = if b:let next_ = use_it else:let next_ = lose_it fi; next_ enddef;
def use_it = let : = restore_colon; enddef;
def restore_colon = let : = colon_; enddef;
def lose_it = let endchar = fi;
let ; = fix_ semi_ if false enddef;
def fix_ = let ; = semi_; let endchar = endchar_;
enddef;
def always_iff = let : = endgroup; killboolean enddef;
def killboolean text t = use_it enddef;

% Not the fastest solution
def beginchar(expr c, w_sharp, h_sharp, d_sharp) = 
    iff known c:
    begingroup
      charcode := byte c;
      charwd := w_sharp;
      charht := h_sharp;
      chardp := d_sharp;
      w := hround(charwd*hppp);
      h := vround(charht*hppp);
      d := vround(chardp*hppp);
      charic := 0; clearxy; clearit;
      clearpen;
      scantokens extra_beginchar;
    enddef;

    endinput;