summaryrefslogtreecommitdiff
path: root/graphics/circuit_macros/dpictools.pic
blob: c89f13d2939dda9c0b4c8a31afbd0279de6a96d9 (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
# dpictools.pic
# General-purpose pic macros. Input this file using the Circuit_macros
# m4 macro NeedDpicTools or the pic statement copy "HOMELIB_/dpictools.pic"
# when HOMELIB_ is defined or, generically, copy "<path>dpictools.pic"

# Circuit_macros Version 10.3, copyright (c) 2023 J. D. Aplevich under     #
# the LaTeX Project Public Licence in file Licence.txt. The files of       #
# this distribution may be redistributed or modified provided that this    #
# copyright notice is included and provided that modifications are clearly #
# marked to distinguish them from this distribution.  There is no warranty #
# whatsoever for these files.                                              #

#                   findroot(function,left bound,right bound,tolerance,var name)
#                   Solve function(x)=0 by the method of bisection
#                   e.g. define parabola { $2 = ($1)^2 - 1 }
#                   findroot( parabola, 0, 2, 1e-8, x )
define findroot {$5 = 0; [ x_m = $2; x_M = $3
  loop( $1(x_m,f_m);, abs(x_M-x_m)>$4,,
    x_c = (x_m+x_M)/2
    $1(x_c,f_c)
    if sign(f_c)==sign(f_m) then {x_m=x_c} else {x_M=x_c};)
  $5 := (x_m+x_M)/2 ] ; }

#                   bisect(function,left bound,right bound, tolerance, var name)
#                   Like findroot but uses recursion and without a [] box
define bisect { x_m_$1 = $2; x_M_$1 = $3
  x_c_$1 = (x_m_$1+x_M_$1)/2
  if (abs(x_m_$1-x_M_$1) <= $4) then { $5 = x_c_$1 } else {
     $1(x_m_$1,f_m_$1)
     $1(x_c_$1,f_c_$1)
     if (sign(f_c_$1)==sign(f_m_$1)) then { bisect($1,x_c_$1,x_M_$1,$4,$5) } \
     else { bisect($1,x_m_$1,x_c_$1,$4,$5) } } }

#                               case(i, alt1, alt2, ... ),
#                               Case statement: execute alternative i
#                               e.g., case(2, x=5, x=10, x=15) sets x to 10
define case { exec sprintf("$%g",floor($1+0.5)+1); }

#                               testexpr(i, expr1, expr2, ... )
#                               Set i to index of the first true alternative
#                               in a sequence of logical expressions, e.g.,
#                               testexpr(i, 1>2, 1<2 ) sets i to 2; to 0
#                               if no test is true.
define testexpr { $1 = 0; [for i_testexpr=2 to $+ do {
  exec sprintf("if $%g then {$1 := i_testexpr-1; i_testexpr=$+}",i_testexpr)
  }] ; }

#                               loop(initial,test,loopend,statements)
#                               C-like loop.  Commas in arg3 and arg4 must
#                               be in quotes or parentheses, e.g.,
#                               loop(i=1, i<=3, i+=1, print i) prints 1, 2, 3
define loop {ld__+=1
 $1
 for lx__[ld__]=0 to 1 do {
    if $2 then { lx__[ld__]=0; $4; $3; } else { lx__[ld__]=1 }}
 ld__-=1; }

#                               array(var,expr1,expr2,...)
#                               var[1]=expr1; var[2]=expr2,...
define array {
 for i_array=2 to $+ do { exec sprintf("$1[%g] = $%g",i_array-1,i_array); }}

#                               array2(var,expr1,expr2,...)
#                               var[expr1,1]=expr2; var[expr1,2]=expr3,...
define array2 { for i_array=3 to $+ do {
  exec sprintf("$1[%g,%g]=$%g",$2,i_array-2,i_array);}}

#                               posarray(Var,Position1,Position2,...)
#                               Var[1]:Position1; Var[2]:Position2,...
define posarray {
 for i_array=2 to $+ do { exec sprintf("$1[%g] : $%g",i_array-1,i_array); }}

#                               posarray2(Var,expr,position1,position2,...)
#                               Var[expr,1]:position1; Var[expr,2]:Position2,...
define posarray2 { for i_array=3 to $+ do {
  exec sprintf("$1[%g,%g] : $%g",$2,i_array-2,i_array); }}

#                               Operations on 3D vectors (could be generalized
#                               except for cross):
#                               $3 = $1 + $2
define sum3 {
 $3[1]=$1[1]+$2[1]
 $3[2]=$1[2]+$2[2]
 $3[3]=$1[3]+$2[3]}

#                               $3 = $1 - $2
define diff3 {
 $3[1]=$1[1]-$2[1]
 $3[2]=$1[2]-$2[2]
 $3[3]=$1[3]-$2[3]}

#                               $3 = $1 X $2
define cross3 {
 $3[1]=$1[2]*$2[3]-$1[3]*$2[2]
 $3[2]=$1[3]*$2[1]-$1[1]*$2[3]
 $3[3]=$1[1]*$2[2]-$1[2]*$2[1]}

#                               $1 . $2
define dot3 {($1[1]*$2[1]+$1[2]*$2[2]+$1[3]*$2[3])}

#                               $3 = $1 * $2
define sprod3 {
 $3[1]=($1)*$2[1]
 $3[2]=($1)*$2[2]
 $3[3]=($1)*$2[3]}

#                               |$1|
define length3 { sqrt($1[1]^2+$1[2]^2+$1[3]^2) }

#                               Expand a vector
define vec3 {$1[1],$1[2],$1[3]}

#                               $2 = $1
define copy3 {
  $2[1] = $1[1]
  $2[2] = $1[2]
  $2[3] = $1[3] }

#                               slantbox(wid,ht,xslant,yslant,attributes)
define slantbox { [
  if "$1"=="" then { w = boxwid } else { w = $1 }
  if "$2"=="" then { h = boxht } else { h = $2 }
  if "$3"=="" then { xs = 0 } else { xs = $3 }
  if "$4"=="" then { ys = 0 } else { ys = $4 }
  NE: (w+xs,h+ys)/2 ; SE: (w-xs,-h+ys)/2
  SW: (-w-xs,-h-ys)/2 ; NW: (-w+xs,h-ys)/2
  N: 0.5 between NW and NE ; E: 0.5 between NE and SE
  S: 0.5 between SE and SW ; W: 0.5 between SW and NW
  C: 0.5 between SW and NE
  line from N to NE then to SE then to SW then to NW then to N $5
  ] }
#                               arraymax( data array, n, index name, value)
#                               Find the index in array[1:n] of the first
#                               occurrence of the max value.  The value is
#                               assigned if arg4 is non-blank.  eg.,
#                               array(x,4,9,8,6); arraymax( x,4,i )
#                               assigns 2 to i, and arraymax( x,4,i,m )
#                               assigns 2 to i and 9 to m
define arraymax { { $3 = -1; if "$4" != "" then { $4 = 0 }; m_arrm = -1e25
 for i_arrm=1 to $2 do { if $1[i_arrm] > m_arrm then {
   $3 := i_arrm; m_arrm = $1[i_arrm] }}
 if "$4" != "" then { $4 := m_arrm } } }

#                               arraymin( data array, n, index name, value)
#                               Like arraymax
define arraymin { { $3 = -1; if "$4" != "" then { $4 = 0 }; m_arrm = 1e25
 for i_arrm=1 to $2 do { if $1[i_arrm] < m_arrm then {
   $3 := i_arrm; m_arrm = $1[i_arrm] }}
 if "$4" != "" then { $4 := m_arrm } } }

#                               copythru(macro_name,"datafile")
#                               See the GNU pic manual
#                               Implements "copy datafile thru macro_name"
#                               for data separated by comma, spaces, or tabs
define copythru {
 sh "sed -e 's/^[ 	]*/$1(/' -e 's/[ 	]*$/)/' -e 's/[, 	][ 	]*/,/g' $2 \
   > copythru_tmp__"
 copy "copythru_tmp__"
 sh "rm -f copythru_tmp__";}

#                               randn(array_name,n,mean,stddev)
#                               Assign n Gaussian random numbers
#                               in array_name[1] ... array_name[n]
define randn {
  if "$2"=="" then { n_randn = 1 } else { n_randn = $2 }
  if "$3"=="" then { m_randn = 0 } else { m_randn = $3 }
  if "$4"=="" then { s_randn = 1 } else { s_randn = $4 }
  for i_randn=1 to n_randn by 2 do {
    for done=0 to 1 do { u_randn=2*rand()-1; v_randn=2*rand()-1
      t_randn = u_randn^2+v_randn^2; done=(t_randn<1) }
    t_randn = sqrt( -2*loge(t_randn)/t_randn )
    $1[i_randn] = u_randn*t_randn*s_randn+m_randn
    if i_randn < n_randn then {
      $1[i_randn+1] = v_randn*t_randn*s_randn+m_randn }
    }
  }

#                               dfitpoints(V,n,m,P,mP) 
#                               Compute the controls in P[mP], P[mP+1]... for
#                               the spline passing throught points V[m]...V[n]
define dfitpoints {
  if "$3"=="" then { m_dfit=0 } else { m_dfit=$3 }
  if "$5"=="" then { mP_dfit=0 } else { mP_dfit=$5 }
  n_dfit = $2; np_dfit = n_dfit-m_dfit
  $4[mP_dfit]: $1[m_dfit]
  for i_dfit=m_dfit+1 to n_dfit-1 do {
    $4[mP_dfit+i_dfit-m_dfit]: $1[i_dfit]*(4/3) }
  $4[mP_dfit+np_dfit]: $1[n_dfit]
  $4[mP_dfit+1]: $4[mP_dfit+1]-$4[mP_dfit+0]/6    # forward substitution
  d_dfit[1] = 1
  for i_dfit = 2 to np_dfit-1 do { $4[mP_dfit+i_dfit]: \
    $4[mP_dfit+i_dfit]-$4[mP_dfit+i_dfit-1]/d_dfit[i_dfit-1]/6
    d_dfit[i_dfit] = 1-1/d_dfit[i_dfit-1]/36 }
  for i_dfit= np_dfit-1 to 1 by -1 do {    # backward substitution
    $4[mP_dfit+i_dfit]: \
    ($4[mP_dfit+i_dfit]-$4[mP_dfit+i_dfit+1]/6)/d_dfit[i_dfit] } }

#                               dfitcurve(V,n,linetype,m (default 0))
#                               Draw a spline through V[m],...V[n]
#                               linetype=eg dotted.  Works only with dpic.
#                               The calculated control points P[i] satisfy
#                               approximately:
#                               P[0] = V[0]
#                               P[i-1]/8 + P[i]*3/4 + P[i+1]/8 = V[i]
#                               P[n] = V[n]
#                               Like m4 macro fitcurve
define dfitcurve { if "$4"=="" then { m_dfit=0 } else { m_dfit=$4 }
  n_dfit = $2; np_dfit = n_dfit-m_dfit
  M4P_[0]: $1[m_dfit]
  case( min(max(np_dfit,-1),3)+1,
    spline 0.551784 $3 from M4P_[0] to M4P_[0],
    spline 0.551784 $3 from M4P_[0] to $1[n_dfit],
    M4P_[3]: $1[n_dfit]; Q_dfit: (M4P_[3]-M4P_[0])/4 
    M4P_[1]: $1[m_dfit+1]-Q_dfit; M4P_[2]: $1[m_dfit+1]+Q_dfit
    spline 0.551784 $3 from M4P_[0] to M4P_[1] then to M4P_[2] then to M4P_[3],
    dfitpoints($1,$2,$4,M4P_,0)  # draw using computed control points
    spline 0.551784 $3 from M4P_[0] to 11/32 between M4P_[0] and M4P_[1] \
       then to 5/32 between M4P_[1] and M4P_[2]
    for i_dfit=2 to np_dfit-2 do { continue to M4P_[i_dfit] }
    continue to 27/32 between M4P_[np_dfit-2] and M4P_[np_dfit-1] \
      then to 21/32 between M4P_[np_dfit-1] and M4P_[np_dfit] \
      then to M4P_[np_dfit]) } 

#                               histbins { data array name, n, [min], [max],
#                                          nbins, bin array name )
#                               Generate the distribution of n values in
#                               dataarray. If given, arg3 and arg4 specify
#                               maximum and minimum data values, otherwise they
#                               are calculated. Bins have index 0 to arg5-1
define histbins { # dataarray, n, [min], [max], nbins, binarray
{ if "$3" == "" then { arraymin($1,$2,mn_histb,n_histb)} else { n_histb = $3 }
  if "$4" == "" then { arraymax($1,$2,mx_histb,m_histb)} else { m_histb = $4 }
  f_histb = ($5-0.001)/(m_histb-n_histb)
  for i_histb=0 to $5-1 do { $6[i_histb] = 0 }
  for i_histb=1 to $2 do {
   x_histb = floor(($1[i_histb]-n_histb)*f_histb)
   if (x_histb >= 0) && (x_histb < $5) then { $6[x_histb] += 1 } }
} }

#                               dpquicksort(a,lo,hi,ix)
#                               Given array a[lo:hi] and index
#                               array ix[lo:hi] = lo,lo+1,lo+2,...hi,
#                               sort a[lo:hi] and do identical exchanges on ix
define dpquicksort { [ if $3 > $2 then {
  pivot = $1[($2+($3))/2]
  loop(lo = $2; hi = $3, lo <= hi,
    loop(,$1[lo] < pivot, lo += 1 )
    loop(,$1[hi] > pivot, hi -= 1 )
    if lo < hi then {
      tmp = $1[lo]; $1[lo] := $1[hi]; $1[hi] := tmp
      tmp = $4[lo]; $4[lo] := $4[hi]; $4[hi] := tmp }
    if lo <= hi then { lo += 1; hi -= 1 } )
  if hi > $2 then { exec sprintf("dpquicksort($1,%g,%g,$4)",$2,hi) }
  if lo < $3 then { exec sprintf("dpquicksort($1,%g,%g,$4)",lo,$3) }
  } ] }

#                               dprot(radians,x,y)
#                               Evaluates to a rotated pair (like m4 rot_ )
define dprot { cos($1)*($2)-sin($1)*($3),sin($1)*($2)+cos($1)*($3) }

#                               dprtext(degrees,text)
#                               Rotated pstricks or pgf text in a [] box
define dprtext {[ if "$1"=="" then { a = 90 } else { a = $1 }
  if dpicopt==optPSTricks then {
    sprintf("\rput[c]{%g}(0,0)",a)+"{$2}"} else {
  if dpicopt==optPGF then {
    sprintf("\pgftext[rotate=%g]",a)+"{$2}" } else { "$2" }}
    ]}

#                               rgbtohsv(r,g,b,h,s,v)
#                               rgb color triple to hsv with h range 0 to 360
define rgbtohsv { $4 = 0; $5 = 0; $6 = 0
 [r = $1; g = $2; b = $3
  maxc = max(max(r,g),b)
  minc = min(min(r,g),b)
  if maxc==minc then { $4 := 0 } \
  else {if maxc == r then {
    $4 := pmod(60*((g-b)/(maxc-minc)),360) } \
  else {if maxc == g then {
    $4 := 60*((b-r)/(maxc-minc)) + 120 } \
  else { $4 := 60*((r-g)/(maxc-minc)) + 240 }}}
  if maxc == 0 then { $5 := 0 } else { $5 := 1 - (minc/maxc) }
  $6 := maxc
  ] }

#                               hsvtorgb(h,s,v,r,g,b)
#                               hsv color triple to rgb, h has range 0 to 360
define hsvtorgb { $4 = 0; $5 = 0; $6 = 0
 [h = pmod($1,360)/60; s = $2; v = $3
  i = floor(h)
  f = h-i
  m = v*(1-s)
  n = v*(1-s*f)
  k = v*(1-s*(1-f))
  case(i+1,
    $4 := v; $5 := k; $6 := m,
    $4 := n; $5 := v; $6 := m,
    $4 := m; $5 := v; $6 := k,
    $4 := m; $5 := n; $6 := v,
    $4 := k; $5 := m; $6 := v,
    $4 := v; $5 := m; $6 := n)
  ] }

#                               cmyktorgb(c,m,y,k,r,g,b)
#                               cmyk colors in percent to rgb
define cmyktorgb {
  $5 = 1-min(1,($1+$4)/100)
  $6 = 1-min(1,($2+$4)/100)
  $7 = 1-min(1,($3+$4)/100)
  }

#                               rgbtocmyk(r,g,b,c,m,y,k)
#                               rgb to cmyk colors out of 100
define rgbtocmyk {
  $7 = min(1-$1,min(1-$2,1-$3))*100
  $4 = (1-$7-$1)/(1-$7)*100
  $5 = (1-$7-$2)/(1-$7)*100
  $6 = (1-$7-$3)/(1-$7)*100 }

#                               DefineRGBColor(colorname,r,g,b)
#                               Arguments are in the range 0 to 1
#                               Define dpic macro colorname according to the
#                               postprocessor specified by dpic command-line
#                               option; colorname then evaluates to a string
define DefineRGBColor {
case(abs(dpicopt),  # The order of the following is defined in dpic source:
# MFpic:
  command sprintf("\mfpdefinecolor{_$1__}{rgb}{%g,%g,%g}",$2,$3,$4)
  define $1 {"_$1__"} ,
# Mpost:
  define $1 {sprintf("(%g,%g,%g)",$2,$3,$4)} ,
# PDF:
  define $1 {sprintf("%g %g %g",$2,$3,$4)} ,
# PGF:
  command sprintf("\definecolor{_$1__}{rgb}{%g,%g,%g}",$2,$3,$4)
  define $1 {"_$1__"} ,
# Pict2e:
  command sprintf("\definecolor{_$1__}{rgb}{%g,%g,%g}",$2,$3,$4)
  define $1 {"_$1__"} ,
# PS:
  define $1 {sprintf("%g %g %g",$2,$3,$4)} ,
# PSfrag:
  define $1 {sprintf("%g %g %g",$2,$3,$4)} ,
# PSTricks:
  command sprintf("\definecolor{_$1__}{rgb}{%g,%g,%g}",$2,$3,$4)
  define $1 {"_$1__"} ,
# SVG:
  define $1 {sprintf("rgb(%g,%g,%g)",int($2*255),int($3*255),int($4*255))} ,
# TeX:
  command sprintf("\definecolor{_$1__}{rgb}{%g,%g,%g}",$2,$3,$4)
  define $1 {"_$1__"} ,
# tTeX:
  command sprintf("\definecolor{_$1__}{rgb}{%g,%g,%g}",$2,$3,$4)
  define $1 {"_$1__"} ,
# xfig:
  define $1 {"black"}
  ) }

#                               DefineHSVColor(colorname,h,s,v)
#                               Like DefineRGBColor but takes arguments
#                               h in [0,360], s in [0,1], and v in [0,1]
define DefineHSVColor { hsvtorgb($2,$3,$4,r_HSVRGB,g_HSVRGB,b_HSVRGB)
  DefineRGBColor($1,r_HSVRGB,g_HSVRGB,b_HSVRGB) }

#                               DefineCMYKColor(colorname,c,m,y,k)
#                               Like DefineRGBColor but arguments in percent
define DefineCMYKColor { cmyktorgb($2,$3,$4,r_CMYKRGB,g_CMYKRGB,b_CMYKRGB)
  DefineRGBColor($1,r_CMYKRGB,g_CMYKRGB,b_CMYKRGB) }

#                               ShadeObject(DrawRoutineName, n, colorseq)
#                               colorseq = 0,r0,g0,b0,
#                                      frac1,r1,g1,b1,
#                                      frac2,r2,g2,b2,
#                                          ...
#                                          1,rn,gn,bn
#                                 with 0 < frac1 < frac2 < ... < 1
#
#                               calls DrawRoutineName(frac,r,g,b)
#                                 n+1 times for frac = 0, 1/n, 2/n, ... 1
#                                 with rgb args interpolated (in hsv space)
#                                 between colorseq points
#
# eg B: box; define HorizShade { line right B.wid thick B.ht/100/(1bp__) \
#         from (0,-($1)*B.ht) outlined rgbstring($2,$3,$4) }
# ShadeObject(HorizShade, 100, 0,1,0,0, 1,0,0,1) at B
#
define ShadeObject { [ Origin: Here; nSteps = abs($2)
  nextP = $3; nextR = $4; nextG = $5; nextB = $6
  nextarg = 7
  thisP = nextP
#                               Creates [] wid 0 ht 0 at (0,0):
  if $2 < 0 then { rgbtohsv(nextR,nextG,nextB,nextH,nextS,nextV) } \
  else { rgbtohsv(nextR^2,nextG^2,nextB^2,nextH,nextS,nextV) }
  if nextP*nSteps >= 1 then { nextP = 0 }
  $1(nextP,nextR,nextG,nextB)
  for stepnum = 1 to nSteps do {
    if stepnum > nextP*nSteps then {
      thisP = nextP; thisH = nextH; thisS = nextS; thisV = nextV
      exec sprintf("nextP = $%g; nextR = $%g; nextG = $%g; nextB = $%g",\
        nextarg,nextarg+1,nextarg+2,nextarg+3);
      nextarg +=4 }
    if nextP != thisP then {
      rgbtohsv(nextR^2,nextG^2,nextB^2,nextH,nextS,nextV)
      if thisS == 0 then { thisH = nextH }
      if nextS == 0 then { nextH = thisH }
      if thisH-nextH > 180 then { nextH += 360 } \
      else { if nextH-thisH > 180 then { thisH +=360 } } }
    if nextP > thisP then {
      x = (stepnum/nSteps-thisP)/(nextP-thisP)
      currP = thisP*(1-x) + nextP*x
      currH = thisH*(1-x) + nextH*x
      currS = thisS*(1-x) + nextS*x
      currV = thisV*(1-x) + nextV*x
      hsvtorgb(currH,currS,currV,cRsq,cGsq,cBsq)
      if $2 < 0 then { $1(currP,cRsq,cGsq,cBsq) } \
      else { $1(currP,sqrt(cRsq),sqrt(cGsq),sqrt(cBsq)) } }
    }
  exec sprintf("$%g",nextarg)
  ] }

#                               Useful for debugging:
#                               Print Pos:(Pos.x,Pos.y)
define prpos { { print sprintf("$1:(%g,%g)",($1).x,($1).y) } }

define prval { print sprintf("$1=%g",$1) }
define prval2 { print sprintf("$1=%g, $2=%g",$1,$2) }
define prval3 { print sprintf("$1=%g, $2=%g, $3=%g",$1,$2,$3) }

#                               prow(array name,rowno,lo,hi)
#                               print array[rowno,lo:hi] as a row
#                               rowno can be omitted, e.g.,
#                               array(x,6,4,5); prow(x,1,3)
define prow {
  sh "echo -n \"print \\"\" > $1_prow"
  if ($+ < 4) || ("$2"=="") then {
    for i_prow=$2 to $3-1 do {
      sh sprintf("echo -n \"%g \" >> $1_prow", $1[i_prow]) }
    sh sprintf("echo \"%g\\"\" >> $1_prow", $1[$3])
    } \
  else {
    for i_prow=$2 to $3-1 do {
      sh sprintf("echo -n \"%g \" >> $1_prow", $1[($4,i_prow)]) }
    sh sprintf("echo \"%g\\"\" >> $1_prow", $1[($4,$3)])
    }
  copy "$1_prow"
  sh "rm $1_prow"
  }

define rnd {int($1+sign($1)/2)} # round function

#                               Operations on complex numbers (x,y)
define Zsum {($1+($2))}
define Zdiff{($1-($2))}
define Zprod {($1.x*$2.x-$1.y*$2.y,$1.y*$2.x+$1.x*$2.y)}
define Zinv {($1.x/($1.x^2+$1.y^2),-$1.y/($1.x^2+$1.y^2))}
define Zexp {((cos($1.y),sin($1.y))*expe($1.x))}
define Zcos {(cos($1.x)*cosh($1.y),-sin($1.x)*sinh($1.y))}
define Zsin {(sin($1.x)*cosh($1.y), cos(%1.x)*sinh($1.y))}
define zabs {sqrt($1.x^2+$1.y^2)}
define zarg {atan2($1.y,$1.x)}
#                               Trig functions if undefined
if "cosh"=="co"+"sh" then {
  define cosh {((expe($1) + expe(-($1)))/2)}
  define sinh {((expe($1) - expe(-($1)))/2)}
}

## dpic equivalents or almost equivalents to libgen.m4 routines ########
## Including them here has to be regarded as experimental for now ######

define cosd {cos(($1)*dtor_)}
define sind {sin(($1)*dtor_)}

define ceiling {(-floor(-($1)))}
define round_ {int($1+sign($1)/2)}

define bp__ {*(scale/72)}       # Absolute Adobe point
define pt__ {*(scale/72.27)}    # Absolute TeX point
define pc__ {*(12*scale/72.27)} # Absolute Pica
define in__ {*scale}            # Absolute inch
define cm__ {*(scale/2.54)}     # Absolute cm
define mm__ {*(scale/25.4)}     # Absolute mm
define lthick {(linethick bp__)}
if dpicopt==optSVG then { define px__ {*(scale/dpPPI)} } \
else { define px__ {*(scale/96)} } # Absolute pixels

define assign_dpicvars {
# print " *** dpic: dpictools.pic processed"
 define dpictools_ {1}
 ld__ = 0
 rtod_ = 57.295779513082323
 dtor_ = 0.017453292519943295
 twopi_ = 6.2831853071795862
 pi_ = twopi_/2
 $1
 }
#                               Polar to rectangular conversion
define Rect_ {($1)*cos(($2)*dtor_),($1)*sin(($2)*dtor_)}

#                               intersect_(Start1,End1,Start2,End2)
#                               Intersection of lines joining named positions
define intersect_ {((($3.x-$1.x)*($3.y-$4.y)-($3.y-$1.y)*($3.x-$4.x))/\
 (($2.x-$1.x)*($3.y-$4.y)-($2.y-$1.y)*($3.x-$4.x)) \
 between $1 and $2) }
#                               Intersect_(Name1,Name2)
#                               Intersection of named lines
define Intersect_ {intersect_($1.start,$1.end,$2.start,$2.end)}

#                               drawdir_(degrees)
#                               Nearest multiple of 90
define drawdir_ {(int(pmod($1+45,360)/90)*90)}

#                               vlength(x,y) 2-D length
define vlength {sqrt(abs(($1)^2+($2)^2))}

#                               distance(Pos1,Pos2) distance between positions
define distance {vlength(($1).x-($2).x,($1).y-($2).y)}

#                               linang(linear obj) angle of linear object
define linang {atan2($1.end.y-$1.start.y,$1.end.x-$1.start.x)}

#                               posang(Position) angle of position wrt (0,0)
define posang {atan2(($1).y,($1).x)}

#                               cangle(A,B,C) angle at B of line A to B to C
define cangle { (posang(($1-($2)))-posang(($3-($2)))) }

# For PGF, PSTricks, or SVG only:
define dpshade { beginshade($1); $2; endshade } # like libgen shade()

# beginshade
if dpicopt==optPGF then {
 define beginshade { if "$1"!="" then { dpshade_=$1 } else { dpshade_=0.5 }
  command "\global\let\dpicshdraw=\dpicdraw\global\def\dpicdraw{}"
  command "\global\def\dpicstop{--}"
  command sprintf("\dpicshdraw[fill=white!%g!black]",dpshade_*100) } } \
else { if dpicopt==optPSTricks then {
 define beginshade { if "$1"!="" then { dpshade_=$1 } else { dpshade_=0.5 }
  command sprintf("\newgray{m4fillv}{%g}",dpshade_)
  command sprintf("\pscustom[fillstyle=solid,fillcolor=m4fillv]{%%") } } \
else { if dpicopt==optSVG then {
 define beginshade { if "$1"!="" then { dpshade_=$1 } else { dpshade_=0.5 }
  command sprintf("<g fill=\"rgb(%g,%g,%g)\">",int(dpshade_*255+0.5),\
   int(dpshade_*255+0.5),int(dpshade_*255+0.5))} } }}

# endshade
if dpicopt==optPGF then {
 define endshade {command "cycle; \
  \global\let\dpicdraw=\dpicshdraw\global\def\dpicstop{;}"} } \
else { if dpicopt==optPSTricks then {
  define endshade {command "}%"} } \
else { if dpicopt==optSVG then {
 define endshade { command "</g>"} } }}

# rgbstring
if dpicopt==optPGF then {
 define rgbstring \
  {sprintf("{rgb,1:red,%7.5f;green,%7.5f;blue,%7.5f}",$1,$2,$3)} } \
else { if dpicopt==optPSTricks then {
 define rgbstring \
  {sprintf("{rgb,1:red,%7.5f;green,%7.5f;blue,%7.5f}",$1,$2,$3)} } \
else { if dpicopt==optSVG then {
 define rgbstring {sprintf("rgb(%g,%g,%g)",\
  int(($1)*255+0.5),int(($2)*255+0.5),int(($3)*255+0.5))} } }}

#######################################################################

assign_dpicvars()

# dpictools end