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
|
%%%%
%%%% MF2PT1.MP, by Scott Pakin, scott+mf@pakin.org
%%%%
%%%% This file is used to dump a special version of MetaPost with:
%%%% mpost -progname=mpost -ini mf2pt1 \\dump
%%%%
%%%% To pretty-print this file, you'll need LaTeX and the mftinc package
%%%% (available from CTAN).
%%%%
%%%% ==================================================================== %%%%
%%%% mf2pt1 %%%%
%%%% Copyright (C) 2012 Scott Pakin %%%%
%%%% %%%%
%%%% This program may be distributed and/or modified under the conditions %%%%
%%%% of the LaTeX Project Public License, either version 1.3c of this %%%%
%%%% license or (at your option) any later version. %%%%
%%%% %%%%
%%%% The latest version of this license is in: %%%%
%%%% %%%%
%%%% http://www.latex-project.org/lppl.txt %%%%
%%%% %%%%
%%%% and version 1.3c or later is part of all distributions of LaTeX %%%%
%%%% version 2006/05/20 or later. %%%%
%%%% ==================================================================== %%%%
input mfplain;
%%% addto makepath makepen
%%% length clockwise counterclockwise
%%% scaled dashed withcolor
%% \begin{explaincode}
%% Enable a \MF\ file to determine if it's being built with
%% \texttt{mf2pt1}.
%% \end{explaincode}
newinternal ps_output;
ps_output := 1;
%% \begin{explaincode}
%% The following was taken right out of \texttt{mfplain.mp}. The \mfcomment
% |def| and the |special|s at the end
%% are the sole additions. Normally, MetaPost outputs a tight bounding
%% box around the character in its PostScript output. The purpose of the
%% first \mfcomment
% |special|
%% is to pass \texttt{mf2pt1} a bounding box that includes the proper
%% surrounding whitespace. The purpose of the second special is to
%% provide \texttt{mf2pt1} with a default PostScript font name.
%% \end{explaincode}
def beginchar(expr c,w_sharp,h_sharp,d_sharp) =
begingroup
charcode:=if known c: byte c else: 0 fi;
charwd:=w_sharp; charht:=h_sharp; chardp:=d_sharp;
w:=charwd*pt; h:=charht*pt; d:=chardp*pt;
charic:=0; clearxy; clearit; clearpen; scantokens extra_beginchar;
def to_bp (expr num) = decimal (ceiling (num*bp_per_pixel)) enddef;
special "% MF2PT1: glyph_dimensions 0 " & to_bp (-d) & " " & to_bp(w) & " " & to_bp(h);
special "% MF2PT1: font_size " & decimal designsize;
special "% MF2PT1: font_slant " & decimal font_slant_;
special "% MF2PT1: charwd " & decimal charwd; % Must come after the |font_size| |special|
for fvar = "font_identifier", "font_coding_scheme", "font_version",
"font_comment", "font_family", "font_weight", "font_unique_id",
"font_name":
if known scantokens (fvar & "_"):
special "% MF2PT1: " & fvar & " " & scantokens (fvar & "_");
fi;
endfor;
for fvar = "font_underline_position", "font_underline_thickness":
if known scantokens (fvar & "_"):
special "% MF2PT1: " & fvar & " " &
scantokens ("decimal " & fvar & "_");
fi;
endfor;
special "% MF2PT1: font_fixed_pitch " &
(if font_fixed_pitch_: "1" else: "0" fi);
enddef;
%% \begin{explaincode}
%% Enable a character to specify explicitly the PostScript glyph
%% name associated with it.
%% \end{explaincode}
def glyph_name expr name =
special "% MF2PT1: glyph_name " & name;
enddef;
%% \begin{explaincode}
%% Store the value of \mfcomment
% |font_slant_|, so we can recall it at each |beginchar|.
%% \end{explaincode}
font_slant_ := 0;
def font_slant expr x =
font_slant_ := x;
fontdimen 1: x
enddef;
%% \begin{explaincode}
%% Redefine \mfcomment
% |bpppix_|, the number of ``big'' points per pixel. \mfcomment
% This in turn redefines |mm|, |in|, |pt|, and other derived units.
%% \end{explaincode}
def bpppix expr x =
bpppix_ := x;
mm := 2.83464 / bpppix_;
pt := 0.99626 / bpppix_;
dd := 1.06601 / bpppix_;
bp := 1 / bpppix_;
cm := 28.34645 / bpppix_;
pc := 11.95517 / bpppix_;
cc := 12.79213 / bpppix_;
in := 72 / bpppix_;
hppp := pt;
vppp := pt;
enddef;
%% \begin{explaincode}
%% Define a bunch of PostScript font parameters to be used by
%% \texttt{mf2pt1.pl}. Default values are specified in
%% \texttt{mf2pt1.pl}, not here.
%% \end{explaincode}
forsuffixes fvar = font_version, font_comment, font_family, font_weight,
font_name, font_unique_id:
scantokens ("string " & str fvar & "_;");
scantokens ("def " & str fvar & " expr x = " & str fvar & "_ := x enddef;");
endfor;
forsuffixes fvar = font_underline_position, font_underline_thickness:
scantokens ("numeric " & str fvar & "_;");
scantokens ("def " & str fvar & " expr x = " & str fvar & "_ := x enddef;");
endfor;
boolean font_fixed_pitch_;
font_fixed_pitch_ := false;
def font_fixed_pitch expr x = font_fixed_pitch_ := x enddef;
%% \begin{explaincode}
%% We'd like to be able to use calligraphic pens. Normally, MetaPost's
%% output routine does all the work for us of converting these to filled
%% PostScript paths. The only exception occurs for paths drawn using a
%% pen that was transformed from \mfcomment
% |pencircle|. MetaPost outputs these paths as stroked PostScript
%% paths. The following code tricks MetaPost into using a filled path
%% for \mfcomment
% |pencircle| by replacing the primitive |pencircle| pen with a
%% non-primitive approximation. Note that we use a 20-gon for our circle
%% instead of a diamond, so we get better results from \mfcomment
% |draw|.
%% \end{explaincode}
pen fakepencircle, mfplain_pencircle;
mfplain_pencircle := pencircle;
fakepencircle := makepen (for deg=0 step 360/20 until 359:
(0.5 cosd deg, 0.5 sind deg)--
endfor cycle);
save pencircle;
pen pencircle;
pencircle := fakepencircle;
%% \begin{explaincode}
%% Return \mfcomment
% |true| if a path is cyclic, |false| otherwise.
%% \end{explaincode}
def is_cyclic expr cpath =
(point 0 of cpath = point (length cpath) of cpath)
enddef;
%% \begin{explaincode}
%% Determine the direction of a path which doesn't intersect
%% itself. \mfcomment
% Returns |true| if the curve is clockwise, |false| if
%% counterclockwise. For non-cyclic paths the result is not
%% predictable.
%% \bigskip
%%
%% The \mfcomment
% |crossproduct|, |makeline|, and |is_clockwise| functions were
%% provided by Werner Lemberg.
%% \bigskip
%%
%% The algorithm used is quite simple:
%%
%% \begin{itemize}
%% \item Find a point~$P$ on the path which has a non-zero direction,
%% and which is on a not-too-short path element.
%%
%% \item Construct a ray of ``infinite'' length, starting in the
%% vicinity of~$P$ which intersects the path at this point.
%%
%% \item Use \mfcomment
% |intersectiontimes| to find the intersection. If the direction of
%% the path at this point is (near) zero, or if we have a grazing
%% intersection or even a tangent, get a new ray.
%%
%% \item Shorten the ray so that it starts right after the
%% intersection. Repeat the previous step until no intersection is
%% found. Then go back to the last intersection and compare the path's
%% direction with the direction of the ray. According to the
%% \emph{nonzero winding number} rule we have found a clockwise
%% oriented path if it crosses the ray from left to right.
%% \end{itemize}
%%
%% This method completely avoids any problems with the geometry of
%% B\'{e}zier curves. If problems arise, a different ray is tried.
%% Since it isn't necessary to analyze the whole path it runs quite fast
%% in spite of using \mfcomment
% |intersectiontimes| which is a slow MetaPost command.
%% \end{explaincode}
vardef crossproduct (expr u, v) =
save u_, v_;
pair u_, v_;
u_ := unitvector u;
v_ := unitvector v;
abs (xpart u_ * ypart v_ - ypart u_ * xpart v_)
enddef;
vardef makeline primary p =
save start, bad_n, loop, distance, d, i, n;
pair start, d;
loop := 0;
bad_n := -1;
for i := 0 step 1 until length p - 1:
distance := length (point i of p - point (i + 1) of p);
if distance <> 0:
if distance < 1:
% In case we don't find something better.
bad_n := i;
else:
n := i;
loop := 1;
fi;
fi;
exitif loop = 1;
endfor;
if loop = 0:
if bad_n <> -1:
n := bad_n;
loop = 1;
fi;
fi;
% Add some randomness to get different lines for each function call.
n := n + uniformdeviate 0.8 + 0.1;
start := point n of p;
if loop = 0:
% Construct a line which misses the degenerated path.
start + (1, 0)
-- start + (1, 1)
else:
d := direction n of p;
% Again, some added randomness.
n := uniformdeviate 150 + 15;
d := unitvector (d rotated n);
% Construct a line which intersects the path at least once.
start - eps * d
-- infinity * d
fi
enddef;
vardef is_clockwise primary p =
save line, cut, cut_new, res, line_dir, tangent_dir;
path line;
pair cut, cut_new, line_dir, tangent_dir;
line := makeline p;
line_dir := direction 0 of line;
% Find the outermost intersection.
cut := (0, 0);
forever:
cut_new := line intersectiontimes p;
exitif cut_new = (-1, -1);
% Compute a new line if we have a strange intersection.
tangent_dir := direction (ypart cut_new) of p;
if abs tangent_dir < eps:
% The vector is zero or too small.
line := makeline p;
line_dir := direction 0 of line;
elseif abs (ypart cut_new - floor (ypart cut_new + 0.5)) < eps:
% Avoid possible tangent touching in a corner or cusp.
line := makeline p;
line_dir := direction 0 of line;
elseif crossproduct (tangent_dir, line_dir) < 0.2:
% Grazing intersection (arcsin 0.2 ~= 11.5 degrees).
line := makeline p;
line_dir := direction 0 of line;
else:
% Go ahead.
cut := cut_new;
line := subpath (xpart cut + eps, infinity) of line;
fi;
endfor;
tangent_dir := direction (ypart cut) of p;
if tangent_dir <> (0, 0):
res := (angle tangent_dir - angle line_dir + 180) mod 360 - 180;
res < 0
else:
false
fi
enddef;
%% \begin{explaincode}
%% Make a given path run clockwise or counterclockwise. \mfcomment
% (|counterclockwise| is defined by \texttt{mfplain} but we override
%% it here.)
%% \end{explaincode}
vardef counterclockwise primary c =
(if is_clockwise c: (reverse c) else: c fi)
enddef;
vardef clockwise primary c =
(if is_clockwise c: c else: (reverse c) fi)
enddef;
%% \begin{explaincode}
%% Redefine \mfcomment
% |fill| and |unfill| to ensure that filled paths run
%% counterclockwise and unfilled paths run clockwise, as is required
%% by PostScript Type~1 fonts.
%% \end{explaincode}
def fill expr c =
addto currentpicture contour counterclockwise c t_ pc_
enddef;
def unfill expr c =
addto currentpicture contour clockwise c t_ pc_ withcolor background
enddef;
%% \begin{explaincode}
%% Convert \mfcomment
% |filldraw| and |unfilldraw| to |fill| and |unfill|.
%% \end{explaincode}
let mfplain_filldraw := filldraw;
def filldraw expr c =
begingroup
message "! Warning: Replacing filldraw with fill.";
fill c
endgroup
enddef;
let mfplain_unfilldraw := unfilldraw;
def unfilldraw expr c =
begingroup
message "! Warning: Replacing unfilldraw with unfill.";
unfill c
endgroup
enddef;
%% \begin{explaincode}
%% Return \mfcomment
% |true| if |currentpen| looks like a |pencircle|.
%% \end{explaincode}
def using_pencircle =
begingroup
path qpath, circlepath;
qpath = makepath currentpen;
numeric circlediv;
circlepath = makepath pencircle;
circlediv = xpart (lrcorner circlepath);
(length qpath = length circlepath) and (pen_rt <> 0) and (pen_top <> 0)
for pp = 0 upto (length qpath)-1:
and ((xpart (point pp of qpath) / pen_rt,
ypart (point pp of qpath) / pen_top) =
point pp of circlepath / circlediv)
endfor
endgroup
enddef;
%% \begin{explaincode}
%% If the pen looks like a circular pen, draw a nice circle. Otherwise,
%% draw the pen as is.
%% \end{explaincode}
def drawdot expr z =
if using_pencircle:
begingroup
path cpath;
numeric clength;
cpath = makepath currentpen;
clength = length cpath;
fill ((point 0 of cpath)
..(point clength/4 of cpath)
..(point clength/2 of cpath)
..(point 3*clength/4 of cpath)
..cycle) shifted z t_
endgroup
else:
addto currentpicture contour makepath currentpen shifted z
t_ pc_
fi
enddef;
%% \begin{explaincode}
%% Do the same as the above, but unfill the current pen.
%% \end{explaincode}
def undrawdot expr z =
if using_pencircle:
begingroup
path cpath;
numeric clength;
cpath = makepath currentpen;
clength = length cpath;
unfill ((point 0 of cpath)
..(point clength/4 of cpath)
..(point clength/2 of cpath)
..(point 3*clength/4 of cpath)
..cycle) shifted z t_
endgroup
else:
unfill makepath currentpen shifted z t_
fi
enddef;
%% \begin{explaincode}
%% MetaPost renders \mfcomment
% |draw| with a filled curve.
%% Hence, we need to ensure the orientation is correct (i.e.,
%% counterclockwise). Unfortunately, we have no way to check for
%% overlap, and it's fairly common for MetaPost to output
%% self-overlapping curve outlines, even if the curve itself has no
%% overlap.
%% \end{explaincode}
def draw expr p =
addto currentpicture
if picture p:
also p
elseif is_cyclic p:
doublepath counterclockwise p t_ withpen currentpen
else:
if is_clockwise (p--cycle):
doublepath (reverse p) t_ withpen currentpen
else:
doublepath p t_ withpen currentpen
fi
fi
pc_
enddef;
def undraw expr p =
addto currentpicture
if picture p:
also p
elseif is_cyclic p:
doublepath clockwise p t_ withpen currentpen
else:
if is_clockwise (p--cycle):
doublepath p t_ withpen currentpen
else:
doublepath (reverse p) t_ withpen currentpen
fi
fi
pc_ withcolor background
enddef;
|