File size: 42,320 Bytes
b72ab63
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
1001
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
1038
1039
1040
1041
1042
1043
1044
1045
1046
1047
1048
1049
1050
1051
1052
1053
1054
1055
1056
1057
1058
1059
1060
1061
1062
1063
1064
1065
1066
1067
1068
1069
1070
1071
1072
1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
1103
1104
1105
1106
1107
1108
1109
1110
1111
1112
1113
1114
1115
1116
1117
1118
1119
1120
1121
1122
1123
1124
1125
1126
1127
1128
1129
1130
1131
1132
1133
"""
Tool to find wrong contour order between different masters, and
other interpolatability (or lack thereof) issues.

Call as:
$ fonttools varLib.interpolatable font1 font2 ...
"""

from .interpolatableHelpers import *
from .interpolatableTestContourOrder import test_contour_order
from .interpolatableTestStartingPoint import test_starting_point
from fontTools.pens.recordingPen import (
    RecordingPen,
    DecomposingRecordingPen,
    lerpRecordings,
)
from fontTools.pens.transformPen import TransformPen
from fontTools.pens.statisticsPen import StatisticsPen, StatisticsControlPen
from fontTools.pens.momentsPen import OpenContourError
from fontTools.varLib.models import piecewiseLinearMap, normalizeLocation
from fontTools.misc.fixedTools import floatToFixedToStr
from fontTools.misc.transform import Transform
from collections import defaultdict
from types import SimpleNamespace
from functools import wraps
from pprint import pformat
from math import sqrt, atan2, pi
import logging
import os

log = logging.getLogger("fontTools.varLib.interpolatable")

DEFAULT_TOLERANCE = 0.95
DEFAULT_KINKINESS = 0.5
DEFAULT_KINKINESS_LENGTH = 0.002  # ratio of UPEM
DEFAULT_UPEM = 1000


class Glyph:
    ITEMS = (
        "recordings",
        "greenStats",
        "controlStats",
        "greenVectors",
        "controlVectors",
        "nodeTypes",
        "isomorphisms",
        "points",
        "openContours",
    )

    def __init__(self, glyphname, glyphset):
        self.name = glyphname
        for item in self.ITEMS:
            setattr(self, item, [])
        self._populate(glyphset)

    def _fill_in(self, ix):
        for item in self.ITEMS:
            if len(getattr(self, item)) == ix:
                getattr(self, item).append(None)

    def _populate(self, glyphset):
        glyph = glyphset[self.name]
        self.doesnt_exist = glyph is None
        if self.doesnt_exist:
            return

        perContourPen = PerContourOrComponentPen(RecordingPen, glyphset=glyphset)
        try:
            glyph.draw(perContourPen, outputImpliedClosingLine=True)
        except TypeError:
            glyph.draw(perContourPen)
        self.recordings = perContourPen.value
        del perContourPen

        for ix, contour in enumerate(self.recordings):
            nodeTypes = [op for op, arg in contour.value]
            self.nodeTypes.append(nodeTypes)

            greenStats = StatisticsPen(glyphset=glyphset)
            controlStats = StatisticsControlPen(glyphset=glyphset)
            try:
                contour.replay(greenStats)
                contour.replay(controlStats)
                self.openContours.append(False)
            except OpenContourError as e:
                self.openContours.append(True)
                self._fill_in(ix)
                continue
            self.greenStats.append(greenStats)
            self.controlStats.append(controlStats)
            self.greenVectors.append(contour_vector_from_stats(greenStats))
            self.controlVectors.append(contour_vector_from_stats(controlStats))

            # Check starting point
            if nodeTypes[0] == "addComponent":
                self._fill_in(ix)
                continue

            assert nodeTypes[0] == "moveTo"
            assert nodeTypes[-1] in ("closePath", "endPath")
            points = SimpleRecordingPointPen()
            converter = SegmentToPointPen(points, False)
            contour.replay(converter)
            # points.value is a list of pt,bool where bool is true if on-curve and false if off-curve;
            # now check all rotations and mirror-rotations of the contour and build list of isomorphic
            # possible starting points.
            self.points.append(points.value)

            isomorphisms = []
            self.isomorphisms.append(isomorphisms)

            # Add rotations
            add_isomorphisms(points.value, isomorphisms, False)
            # Add mirrored rotations
            add_isomorphisms(points.value, isomorphisms, True)

    def draw(self, pen, countor_idx=None):
        if countor_idx is None:
            for contour in self.recordings:
                contour.draw(pen)
        else:
            self.recordings[countor_idx].draw(pen)


def test_gen(
    glyphsets,
    glyphs=None,
    names=None,
    ignore_missing=False,
    *,
    locations=None,
    tolerance=DEFAULT_TOLERANCE,
    kinkiness=DEFAULT_KINKINESS,
    upem=DEFAULT_UPEM,
    show_all=False,
):
    if tolerance >= 10:
        tolerance *= 0.01
    assert 0 <= tolerance <= 1
    if kinkiness >= 10:
        kinkiness *= 0.01
    assert 0 <= kinkiness

    names = names or [repr(g) for g in glyphsets]

    if glyphs is None:
        # `glyphs = glyphsets[0].keys()` is faster, certainly, but doesn't allow for sparse TTFs/OTFs given out of order
        # ... risks the sparse master being the first one, and only processing a subset of the glyphs
        glyphs = {g for glyphset in glyphsets for g in glyphset.keys()}

    parents, order = find_parents_and_order(glyphsets, locations)

    def grand_parent(i, glyphname):
        if i is None:
            return None
        i = parents[i]
        if i is None:
            return None
        while parents[i] is not None and glyphsets[i][glyphname] is None:
            i = parents[i]
        return i

    for glyph_name in glyphs:
        log.info("Testing glyph %s", glyph_name)
        allGlyphs = [Glyph(glyph_name, glyphset) for glyphset in glyphsets]
        if len([1 for glyph in allGlyphs if glyph is not None]) <= 1:
            continue
        for master_idx, (glyph, glyphset, name) in enumerate(
            zip(allGlyphs, glyphsets, names)
        ):
            if glyph.doesnt_exist:
                if not ignore_missing:
                    yield (
                        glyph_name,
                        {
                            "type": InterpolatableProblem.MISSING,
                            "master": name,
                            "master_idx": master_idx,
                        },
                    )
                continue

            has_open = False
            for ix, open in enumerate(glyph.openContours):
                if not open:
                    continue
                has_open = True
                yield (
                    glyph_name,
                    {
                        "type": InterpolatableProblem.OPEN_PATH,
                        "master": name,
                        "master_idx": master_idx,
                        "contour": ix,
                    },
                )
            if has_open:
                continue

        matchings = [None] * len(glyphsets)

        for m1idx in order:
            glyph1 = allGlyphs[m1idx]
            if glyph1 is None or not glyph1.nodeTypes:
                continue
            m0idx = grand_parent(m1idx, glyph_name)
            if m0idx is None:
                continue
            glyph0 = allGlyphs[m0idx]
            if glyph0 is None or not glyph0.nodeTypes:
                continue

            #
            # Basic compatibility checks
            #

            m1 = glyph0.nodeTypes
            m0 = glyph1.nodeTypes
            if len(m0) != len(m1):
                yield (
                    glyph_name,
                    {
                        "type": InterpolatableProblem.PATH_COUNT,
                        "master_1": names[m0idx],
                        "master_2": names[m1idx],
                        "master_1_idx": m0idx,
                        "master_2_idx": m1idx,
                        "value_1": len(m0),
                        "value_2": len(m1),
                    },
                )
                continue

            if m0 != m1:
                for pathIx, (nodes1, nodes2) in enumerate(zip(m0, m1)):
                    if nodes1 == nodes2:
                        continue
                    if len(nodes1) != len(nodes2):
                        yield (
                            glyph_name,
                            {
                                "type": InterpolatableProblem.NODE_COUNT,
                                "path": pathIx,
                                "master_1": names[m0idx],
                                "master_2": names[m1idx],
                                "master_1_idx": m0idx,
                                "master_2_idx": m1idx,
                                "value_1": len(nodes1),
                                "value_2": len(nodes2),
                            },
                        )
                        continue
                    for nodeIx, (n1, n2) in enumerate(zip(nodes1, nodes2)):
                        if n1 != n2:
                            yield (
                                glyph_name,
                                {
                                    "type": InterpolatableProblem.NODE_INCOMPATIBILITY,
                                    "path": pathIx,
                                    "node": nodeIx,
                                    "master_1": names[m0idx],
                                    "master_2": names[m1idx],
                                    "master_1_idx": m0idx,
                                    "master_2_idx": m1idx,
                                    "value_1": n1,
                                    "value_2": n2,
                                },
                            )
                            continue

            #
            # InterpolatableProblem.CONTOUR_ORDER check
            #

            this_tolerance, matching = test_contour_order(glyph0, glyph1)
            if this_tolerance < tolerance:
                yield (
                    glyph_name,
                    {
                        "type": InterpolatableProblem.CONTOUR_ORDER,
                        "master_1": names[m0idx],
                        "master_2": names[m1idx],
                        "master_1_idx": m0idx,
                        "master_2_idx": m1idx,
                        "value_1": list(range(len(matching))),
                        "value_2": matching,
                        "tolerance": this_tolerance,
                    },
                )
                matchings[m1idx] = matching

            #
            # wrong-start-point / weight check
            #

            m0Isomorphisms = glyph0.isomorphisms
            m1Isomorphisms = glyph1.isomorphisms
            m0Vectors = glyph0.greenVectors
            m1Vectors = glyph1.greenVectors
            recording0 = glyph0.recordings
            recording1 = glyph1.recordings

            # If contour-order is wrong, adjust it
            matching = matchings[m1idx]
            if (
                matching is not None and m1Isomorphisms
            ):  # m1 is empty for composite glyphs
                m1Isomorphisms = [m1Isomorphisms[i] for i in matching]
                m1Vectors = [m1Vectors[i] for i in matching]
                recording1 = [recording1[i] for i in matching]

            midRecording = []
            for c0, c1 in zip(recording0, recording1):
                try:
                    r = RecordingPen()
                    r.value = list(lerpRecordings(c0.value, c1.value))
                    midRecording.append(r)
                except ValueError:
                    # Mismatch because of the reordering above
                    midRecording.append(None)

            for ix, (contour0, contour1) in enumerate(
                zip(m0Isomorphisms, m1Isomorphisms)
            ):
                if (
                    contour0 is None
                    or contour1 is None
                    or len(contour0) == 0
                    or len(contour0) != len(contour1)
                ):
                    # We already reported this; or nothing to do; or not compatible
                    # after reordering above.
                    continue

                this_tolerance, proposed_point, reverse = test_starting_point(
                    glyph0, glyph1, ix, tolerance, matching
                )

                if this_tolerance < tolerance:
                    yield (
                        glyph_name,
                        {
                            "type": InterpolatableProblem.WRONG_START_POINT,
                            "contour": ix,
                            "master_1": names[m0idx],
                            "master_2": names[m1idx],
                            "master_1_idx": m0idx,
                            "master_2_idx": m1idx,
                            "value_1": 0,
                            "value_2": proposed_point,
                            "reversed": reverse,
                            "tolerance": this_tolerance,
                        },
                    )

                # Weight check.
                #
                # If contour could be mid-interpolated, and the two
                # contours have the same area sign, proceeed.
                #
                # The sign difference can happen if it's a weirdo
                # self-intersecting contour; ignore it.
                contour = midRecording[ix]

                if contour and (m0Vectors[ix][0] < 0) == (m1Vectors[ix][0] < 0):
                    midStats = StatisticsPen(glyphset=None)
                    contour.replay(midStats)

                    midVector = contour_vector_from_stats(midStats)

                    m0Vec = m0Vectors[ix]
                    m1Vec = m1Vectors[ix]
                    size0 = m0Vec[0] * m0Vec[0]
                    size1 = m1Vec[0] * m1Vec[0]
                    midSize = midVector[0] * midVector[0]

                    for overweight, problem_type in enumerate(
                        (
                            InterpolatableProblem.UNDERWEIGHT,
                            InterpolatableProblem.OVERWEIGHT,
                        )
                    ):
                        if overweight:
                            expectedSize = max(size0, size1)
                            continue
                        else:
                            expectedSize = sqrt(size0 * size1)

                        log.debug(
                            "%s: actual size %g; threshold size %g, master sizes: %g, %g",
                            problem_type,
                            midSize,
                            expectedSize,
                            size0,
                            size1,
                        )

                        if (
                            not overweight and expectedSize * tolerance > midSize + 1e-5
                        ) or (overweight and 1e-5 + expectedSize / tolerance < midSize):
                            try:
                                if overweight:
                                    this_tolerance = expectedSize / midSize
                                else:
                                    this_tolerance = midSize / expectedSize
                            except ZeroDivisionError:
                                this_tolerance = 0
                            log.debug("tolerance %g", this_tolerance)
                            yield (
                                glyph_name,
                                {
                                    "type": problem_type,
                                    "contour": ix,
                                    "master_1": names[m0idx],
                                    "master_2": names[m1idx],
                                    "master_1_idx": m0idx,
                                    "master_2_idx": m1idx,
                                    "tolerance": this_tolerance,
                                },
                            )

            #
            # "kink" detector
            #
            m0 = glyph0.points
            m1 = glyph1.points

            # If contour-order is wrong, adjust it
            if matchings[m1idx] is not None and m1:  # m1 is empty for composite glyphs
                m1 = [m1[i] for i in matchings[m1idx]]

            t = 0.1  # ~sin(radian(6)) for tolerance 0.95
            deviation_threshold = (
                upem * DEFAULT_KINKINESS_LENGTH * DEFAULT_KINKINESS / kinkiness
            )

            for ix, (contour0, contour1) in enumerate(zip(m0, m1)):
                if (
                    contour0 is None
                    or contour1 is None
                    or len(contour0) == 0
                    or len(contour0) != len(contour1)
                ):
                    # We already reported this; or nothing to do; or not compatible
                    # after reordering above.
                    continue

                # Walk the contour, keeping track of three consecutive points, with
                # middle one being an on-curve. If the three are co-linear then
                # check for kinky-ness.
                for i in range(len(contour0)):
                    pt0 = contour0[i]
                    pt1 = contour1[i]
                    if not pt0[1] or not pt1[1]:
                        # Skip off-curves
                        continue
                    pt0_prev = contour0[i - 1]
                    pt1_prev = contour1[i - 1]
                    pt0_next = contour0[(i + 1) % len(contour0)]
                    pt1_next = contour1[(i + 1) % len(contour1)]

                    if pt0_prev[1] and pt1_prev[1]:
                        # At least one off-curve is required
                        continue
                    if pt0_prev[1] and pt1_prev[1]:
                        # At least one off-curve is required
                        continue

                    pt0 = complex(*pt0[0])
                    pt1 = complex(*pt1[0])
                    pt0_prev = complex(*pt0_prev[0])
                    pt1_prev = complex(*pt1_prev[0])
                    pt0_next = complex(*pt0_next[0])
                    pt1_next = complex(*pt1_next[0])

                    # We have three consecutive points. Check whether
                    # they are colinear.
                    d0_prev = pt0 - pt0_prev
                    d0_next = pt0_next - pt0
                    d1_prev = pt1 - pt1_prev
                    d1_next = pt1_next - pt1

                    sin0 = d0_prev.real * d0_next.imag - d0_prev.imag * d0_next.real
                    sin1 = d1_prev.real * d1_next.imag - d1_prev.imag * d1_next.real
                    try:
                        sin0 /= abs(d0_prev) * abs(d0_next)
                        sin1 /= abs(d1_prev) * abs(d1_next)
                    except ZeroDivisionError:
                        continue

                    if abs(sin0) > t or abs(sin1) > t:
                        # Not colinear / not smooth.
                        continue

                    # Check the mid-point is actually, well, in the middle.
                    dot0 = d0_prev.real * d0_next.real + d0_prev.imag * d0_next.imag
                    dot1 = d1_prev.real * d1_next.real + d1_prev.imag * d1_next.imag
                    if dot0 < 0 or dot1 < 0:
                        # Sharp corner.
                        continue

                    # Fine, if handle ratios are similar...
                    r0 = abs(d0_prev) / (abs(d0_prev) + abs(d0_next))
                    r1 = abs(d1_prev) / (abs(d1_prev) + abs(d1_next))
                    r_diff = abs(r0 - r1)
                    if abs(r_diff) < t:
                        # Smooth enough.
                        continue

                    mid = (pt0 + pt1) / 2
                    mid_prev = (pt0_prev + pt1_prev) / 2
                    mid_next = (pt0_next + pt1_next) / 2

                    mid_d0 = mid - mid_prev
                    mid_d1 = mid_next - mid

                    sin_mid = mid_d0.real * mid_d1.imag - mid_d0.imag * mid_d1.real
                    try:
                        sin_mid /= abs(mid_d0) * abs(mid_d1)
                    except ZeroDivisionError:
                        continue

                    # ...or if the angles are similar.
                    if abs(sin_mid) * (tolerance * kinkiness) <= t:
                        # Smooth enough.
                        continue

                    # How visible is the kink?

                    cross = sin_mid * abs(mid_d0) * abs(mid_d1)
                    arc_len = abs(mid_d0 + mid_d1)
                    deviation = abs(cross / arc_len)
                    if deviation < deviation_threshold:
                        continue
                    deviation_ratio = deviation / arc_len
                    if deviation_ratio > t:
                        continue

                    this_tolerance = t / (abs(sin_mid) * kinkiness)

                    log.debug(
                        "kink: deviation %g; deviation_ratio %g; sin_mid %g; r_diff %g",
                        deviation,
                        deviation_ratio,
                        sin_mid,
                        r_diff,
                    )
                    log.debug("tolerance %g", this_tolerance)
                    yield (
                        glyph_name,
                        {
                            "type": InterpolatableProblem.KINK,
                            "contour": ix,
                            "master_1": names[m0idx],
                            "master_2": names[m1idx],
                            "master_1_idx": m0idx,
                            "master_2_idx": m1idx,
                            "value": i,
                            "tolerance": this_tolerance,
                        },
                    )

            #
            # --show-all
            #

            if show_all:
                yield (
                    glyph_name,
                    {
                        "type": InterpolatableProblem.NOTHING,
                        "master_1": names[m0idx],
                        "master_2": names[m1idx],
                        "master_1_idx": m0idx,
                        "master_2_idx": m1idx,
                    },
                )


@wraps(test_gen)
def test(*args, **kwargs):
    problems = defaultdict(list)
    for glyphname, problem in test_gen(*args, **kwargs):
        problems[glyphname].append(problem)
    return problems


def recursivelyAddGlyph(glyphname, glyphset, ttGlyphSet, glyf):
    if glyphname in glyphset:
        return
    glyphset[glyphname] = ttGlyphSet[glyphname]

    for component in getattr(glyf[glyphname], "components", []):
        recursivelyAddGlyph(component.glyphName, glyphset, ttGlyphSet, glyf)


def ensure_parent_dir(path):
    dirname = os.path.dirname(path)
    if dirname:
        os.makedirs(dirname, exist_ok=True)
    return path


def main(args=None):
    """Test for interpolatability issues between fonts"""
    import argparse
    import sys

    parser = argparse.ArgumentParser(
        "fonttools varLib.interpolatable",
        description=main.__doc__,
    )
    parser.add_argument(
        "--glyphs",
        action="store",
        help="Space-separate name of glyphs to check",
    )
    parser.add_argument(
        "--show-all",
        action="store_true",
        help="Show all glyph pairs, even if no problems are found",
    )
    parser.add_argument(
        "--tolerance",
        action="store",
        type=float,
        help="Error tolerance. Between 0 and 1. Default %s" % DEFAULT_TOLERANCE,
    )
    parser.add_argument(
        "--kinkiness",
        action="store",
        type=float,
        help="How aggressively report kinks. Default %s" % DEFAULT_KINKINESS,
    )
    parser.add_argument(
        "--json",
        action="store_true",
        help="Output report in JSON format",
    )
    parser.add_argument(
        "--pdf",
        action="store",
        help="Output report in PDF format",
    )
    parser.add_argument(
        "--ps",
        action="store",
        help="Output report in PostScript format",
    )
    parser.add_argument(
        "--html",
        action="store",
        help="Output report in HTML format",
    )
    parser.add_argument(
        "--quiet",
        action="store_true",
        help="Only exit with code 1 or 0, no output",
    )
    parser.add_argument(
        "--output",
        action="store",
        help="Output file for the problem report; Default: stdout",
    )
    parser.add_argument(
        "--ignore-missing",
        action="store_true",
        help="Will not report glyphs missing from sparse masters as errors",
    )
    parser.add_argument(
        "inputs",
        metavar="FILE",
        type=str,
        nargs="+",
        help="Input a single variable font / DesignSpace / Glyphs file, or multiple TTF/UFO files",
    )
    parser.add_argument(
        "--name",
        metavar="NAME",
        type=str,
        action="append",
        help="Name of the master to use in the report. If not provided, all are used.",
    )
    parser.add_argument("-v", "--verbose", action="store_true", help="Run verbosely.")
    parser.add_argument("--debug", action="store_true", help="Run with debug output.")

    args = parser.parse_args(args)

    from fontTools import configLogger

    configLogger(level=("INFO" if args.verbose else "ERROR"))
    if args.debug:
        configLogger(level="DEBUG")

    glyphs = args.glyphs.split() if args.glyphs else None

    from os.path import basename

    fonts = []
    names = []
    locations = []
    upem = DEFAULT_UPEM

    original_args_inputs = tuple(args.inputs)

    if len(args.inputs) == 1:
        designspace = None
        if args.inputs[0].endswith(".designspace"):
            from fontTools.designspaceLib import DesignSpaceDocument

            designspace = DesignSpaceDocument.fromfile(args.inputs[0])
            args.inputs = [master.path for master in designspace.sources]
            locations = [master.location for master in designspace.sources]
            axis_triples = {
                a.name: (a.minimum, a.default, a.maximum) for a in designspace.axes
            }
            axis_mappings = {a.name: a.map for a in designspace.axes}
            axis_triples = {
                k: tuple(piecewiseLinearMap(v, dict(axis_mappings[k])) for v in vv)
                for k, vv in axis_triples.items()
            }

        elif args.inputs[0].endswith((".glyphs", ".glyphspackage")):
            from glyphsLib import GSFont, to_designspace

            gsfont = GSFont(args.inputs[0])
            upem = gsfont.upm
            designspace = to_designspace(gsfont)
            fonts = [source.font for source in designspace.sources]
            names = ["%s-%s" % (f.info.familyName, f.info.styleName) for f in fonts]
            args.inputs = []
            locations = [master.location for master in designspace.sources]
            axis_triples = {
                a.name: (a.minimum, a.default, a.maximum) for a in designspace.axes
            }
            axis_mappings = {a.name: a.map for a in designspace.axes}
            axis_triples = {
                k: tuple(piecewiseLinearMap(v, dict(axis_mappings[k])) for v in vv)
                for k, vv in axis_triples.items()
            }

        elif args.inputs[0].endswith(".ttf"):
            from fontTools.ttLib import TTFont

            font = TTFont(args.inputs[0])
            upem = font["head"].unitsPerEm
            if "gvar" in font:
                # Is variable font

                fvar = font["fvar"]
                axisMapping = {}
                for axis in fvar.axes:
                    axisMapping[axis.axisTag] = {
                        -1: axis.minValue,
                        0: axis.defaultValue,
                        1: axis.maxValue,
                    }
                normalized = False
                if "avar" in font:
                    avar = font["avar"]
                    if getattr(avar.table, "VarStore", None):
                        axisMapping = {tag: {-1: -1, 0: 0, 1: 1} for tag in axisMapping}
                        normalized = True
                    else:
                        for axisTag, segments in avar.segments.items():
                            fvarMapping = axisMapping[axisTag].copy()
                            for location, value in segments.items():
                                axisMapping[axisTag][value] = piecewiseLinearMap(
                                    location, fvarMapping
                                )

                gvar = font["gvar"]
                glyf = font["glyf"]
                # Gather all glyphs at their "master" locations
                ttGlyphSets = {}
                glyphsets = defaultdict(dict)

                if glyphs is None:
                    glyphs = sorted(gvar.variations.keys())
                for glyphname in glyphs:
                    for var in gvar.variations[glyphname]:
                        locDict = {}
                        loc = []
                        for tag, val in sorted(var.axes.items()):
                            locDict[tag] = val[1]
                            loc.append((tag, val[1]))

                        locTuple = tuple(loc)
                        if locTuple not in ttGlyphSets:
                            ttGlyphSets[locTuple] = font.getGlyphSet(
                                location=locDict, normalized=True, recalcBounds=False
                            )

                        recursivelyAddGlyph(
                            glyphname, glyphsets[locTuple], ttGlyphSets[locTuple], glyf
                        )

                names = ["''"]
                fonts = [font.getGlyphSet()]
                locations = [{}]
                axis_triples = {a: (-1, 0, +1) for a in sorted(axisMapping.keys())}
                for locTuple in sorted(glyphsets.keys(), key=lambda v: (len(v), v)):
                    name = (
                        "'"
                        + " ".join(
                            "%s=%s"
                            % (
                                k,
                                floatToFixedToStr(
                                    piecewiseLinearMap(v, axisMapping[k]), 14
                                ),
                            )
                            for k, v in locTuple
                        )
                        + "'"
                    )
                    if normalized:
                        name += " (normalized)"
                    names.append(name)
                    fonts.append(glyphsets[locTuple])
                    locations.append(dict(locTuple))
                args.ignore_missing = True
                args.inputs = []

    if not locations:
        locations = [{} for _ in fonts]

    for filename in args.inputs:
        if filename.endswith(".ufo"):
            from fontTools.ufoLib import UFOReader

            font = UFOReader(filename)
            info = SimpleNamespace()
            font.readInfo(info)
            upem = info.unitsPerEm
            fonts.append(font)
        else:
            from fontTools.ttLib import TTFont

            font = TTFont(filename)
            upem = font["head"].unitsPerEm
            fonts.append(font)

        names.append(basename(filename).rsplit(".", 1)[0])

    glyphsets = []
    for font in fonts:
        if hasattr(font, "getGlyphSet"):
            glyphset = font.getGlyphSet()
        else:
            glyphset = font
        glyphsets.append({k: glyphset[k] for k in glyphset.keys()})

    if args.name:
        accepted_names = set(args.name)
        glyphsets = [
            glyphset
            for name, glyphset in zip(names, glyphsets)
            if name in accepted_names
        ]
        locations = [
            location
            for name, location in zip(names, locations)
            if name in accepted_names
        ]
        names = [name for name in names if name in accepted_names]

    if not glyphs:
        glyphs = sorted(set([gn for glyphset in glyphsets for gn in glyphset.keys()]))

    glyphsSet = set(glyphs)
    for glyphset in glyphsets:
        glyphSetGlyphNames = set(glyphset.keys())
        diff = glyphsSet - glyphSetGlyphNames
        if diff:
            for gn in diff:
                glyphset[gn] = None

    # Normalize locations
    locations = [normalizeLocation(loc, axis_triples) for loc in locations]
    tolerance = args.tolerance or DEFAULT_TOLERANCE
    kinkiness = args.kinkiness if args.kinkiness is not None else DEFAULT_KINKINESS

    try:
        log.info("Running on %d glyphsets", len(glyphsets))
        log.info("Locations: %s", pformat(locations))
        problems_gen = test_gen(
            glyphsets,
            glyphs=glyphs,
            names=names,
            locations=locations,
            upem=upem,
            ignore_missing=args.ignore_missing,
            tolerance=tolerance,
            kinkiness=kinkiness,
            show_all=args.show_all,
        )
        problems = defaultdict(list)

        f = (
            sys.stdout
            if args.output is None
            else open(ensure_parent_dir(args.output), "w")
        )

        if not args.quiet:
            if args.json:
                import json

                for glyphname, problem in problems_gen:
                    problems[glyphname].append(problem)

                print(json.dumps(problems), file=f)
            else:
                last_glyphname = None
                for glyphname, p in problems_gen:
                    problems[glyphname].append(p)

                    if glyphname != last_glyphname:
                        print(f"Glyph {glyphname} was not compatible:", file=f)
                        last_glyphname = glyphname
                        last_master_idxs = None

                    master_idxs = (
                        (p["master_idx"])
                        if "master_idx" in p
                        else (p["master_1_idx"], p["master_2_idx"])
                    )
                    if master_idxs != last_master_idxs:
                        master_names = (
                            (p["master"])
                            if "master" in p
                            else (p["master_1"], p["master_2"])
                        )
                        print(f"  Masters: %s:" % ", ".join(master_names), file=f)
                        last_master_idxs = master_idxs

                    if p["type"] == InterpolatableProblem.MISSING:
                        print(
                            "    Glyph was missing in master %s" % p["master"], file=f
                        )
                    elif p["type"] == InterpolatableProblem.OPEN_PATH:
                        print(
                            "    Glyph has an open path in master %s" % p["master"],
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.PATH_COUNT:
                        print(
                            "    Path count differs: %i in %s, %i in %s"
                            % (
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.NODE_COUNT:
                        print(
                            "    Node count differs in path %i: %i in %s, %i in %s"
                            % (
                                p["path"],
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.NODE_INCOMPATIBILITY:
                        print(
                            "    Node %o incompatible in path %i: %s in %s, %s in %s"
                            % (
                                p["node"],
                                p["path"],
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.CONTOUR_ORDER:
                        print(
                            "    Contour order differs: %s in %s, %s in %s"
                            % (
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.WRONG_START_POINT:
                        print(
                            "    Contour %d start point differs: %s in %s, %s in %s; reversed: %s"
                            % (
                                p["contour"],
                                p["value_1"],
                                p["master_1"],
                                p["value_2"],
                                p["master_2"],
                                p["reversed"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.UNDERWEIGHT:
                        print(
                            "    Contour %d interpolation is underweight: %s, %s"
                            % (
                                p["contour"],
                                p["master_1"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.OVERWEIGHT:
                        print(
                            "    Contour %d interpolation is overweight: %s, %s"
                            % (
                                p["contour"],
                                p["master_1"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.KINK:
                        print(
                            "    Contour %d has a kink at %s: %s, %s"
                            % (
                                p["contour"],
                                p["value"],
                                p["master_1"],
                                p["master_2"],
                            ),
                            file=f,
                        )
                    elif p["type"] == InterpolatableProblem.NOTHING:
                        print(
                            "    Showing %s and %s"
                            % (
                                p["master_1"],
                                p["master_2"],
                            ),
                            file=f,
                        )
        else:
            for glyphname, problem in problems_gen:
                problems[glyphname].append(problem)

        problems = sort_problems(problems)

        for p in "ps", "pdf":
            arg = getattr(args, p)
            if arg is None:
                continue
            log.info("Writing %s to %s", p.upper(), arg)
            from .interpolatablePlot import InterpolatablePS, InterpolatablePDF

            PlotterClass = InterpolatablePS if p == "ps" else InterpolatablePDF

            with PlotterClass(
                ensure_parent_dir(arg), glyphsets=glyphsets, names=names
            ) as doc:
                doc.add_title_page(
                    original_args_inputs, tolerance=tolerance, kinkiness=kinkiness
                )
                if problems:
                    doc.add_summary(problems)
                doc.add_problems(problems)
                if not problems and not args.quiet:
                    doc.draw_cupcake()
                if problems:
                    doc.add_index()
                    doc.add_table_of_contents()

        if args.html:
            log.info("Writing HTML to %s", args.html)
            from .interpolatablePlot import InterpolatableSVG

            svgs = []
            glyph_starts = {}
            with InterpolatableSVG(svgs, glyphsets=glyphsets, names=names) as svg:
                svg.add_title_page(
                    original_args_inputs,
                    show_tolerance=False,
                    tolerance=tolerance,
                    kinkiness=kinkiness,
                )
                for glyph, glyph_problems in problems.items():
                    glyph_starts[len(svgs)] = glyph
                    svg.add_problems(
                        {glyph: glyph_problems},
                        show_tolerance=False,
                        show_page_number=False,
                    )
                if not problems and not args.quiet:
                    svg.draw_cupcake()

            import base64

            with open(ensure_parent_dir(args.html), "wb") as f:
                f.write(b"<!DOCTYPE html>\n")
                f.write(
                    b'<html><body align="center" style="font-family: sans-serif; text-color: #222">\n'
                )
                f.write(b"<title>fonttools varLib.interpolatable report</title>\n")
                for i, svg in enumerate(svgs):
                    if i in glyph_starts:
                        f.write(f"<h1>Glyph {glyph_starts[i]}</h1>\n".encode("utf-8"))
                    f.write("<img src='data:image/svg+xml;base64,".encode("utf-8"))
                    f.write(base64.b64encode(svg))
                    f.write(b"' />\n")
                    f.write(b"<hr>\n")
                f.write(b"</body></html>\n")

    except Exception as e:
        e.args += original_args_inputs
        log.error(e)
        raise

    if problems:
        return problems


if __name__ == "__main__":
    import sys

    problems = main()
    sys.exit(int(bool(problems)))