summaryrefslogtreecommitdiffstats
path: root/src/helper/geom-pathstroke.cpp
blob: 228ea5c5dfa4bedd34efb883c7516e2ceea6ce86 (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
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
1134
1135
1136
1137
1138
1139
1140
1141
1142
1143
1144
1145
1146
1147
1148
1149
1150
1151
1152
1153
1154
1155
1156
1157
1158
// SPDX-License-Identifier: GPL-2.0-or-later
/* Authors:
 *   Liam P. White
 *   Tavmjong Bah
 *   Alexander Brock
 *
 * Copyright (C) 2014-2015 Authors
 *
 * Released under GNU GPL v2+, read the file 'COPYING' for more information.
 */

#include <iomanip>
#include <2geom/path-sink.h>
#include <2geom/sbasis-to-bezier.h> // cubicbezierpath_from_sbasis
#include <2geom/path-intersection.h>
#include <2geom/circle.h>

#include "helper/geom-pathstroke.h"

namespace Geom {

static Point intersection_point(Point origin_a, Point vector_a, Point origin_b, Point vector_b)
{
    Coord denom = cross(vector_a, vector_b);
    if (!are_near(denom,0.)) {
        Coord t = (cross(vector_b, origin_a) + cross(origin_b, vector_b)) / denom;
        return origin_a + vector_a*t;
    }
    return Point(infinity(), infinity());
}

/**
* Find circle that touches inside of the curve, with radius matching the curvature, at time value \c t.
* Because this method internally uses unitTangentAt, t should be smaller than 1.0 (see unitTangentAt).
*/
static Circle touching_circle( D2<SBasis> const &curve, double t, double tol=0.01 )
{
    D2<SBasis> dM=derivative(curve);
    if ( are_near(L2sq(dM(t)), tol) ) {
        dM=derivative(dM);
    }
    if ( are_near(L2sq(dM(t)), tol) ) {   // try second time
        dM=derivative(dM);
    }
    Piecewise<D2<SBasis> > unitv = unitVector(dM,tol);
    Piecewise<SBasis> dMlength = dot(Piecewise<D2<SBasis> >(dM),unitv);
    Piecewise<SBasis> k = cross(derivative(unitv),unitv);
    k = divide(k,dMlength,tol,3);
    double curv = k(t); // note that this value is signed

    Geom::Point normal = unitTangentAt(curve, t).cw();
    double radius = 1/curv;
    Geom::Point center = curve(t) + radius*normal;
    return Geom::Circle(center, fabs(radius));
}


// Area of triangle given three corner points
static double area( Geom::Point a, Geom::Point b, Geom::Point c ) {

    using Geom::X;
    using Geom::Y;
    return( 0.5 * fabs( ( a[X]*(b[Y]-c[Y]) + b[X]*(c[Y]-a[Y]) + c[X]*(a[Y]-b[Y]) ) ) );
}

// Alternative touching circle routine directly using Beziers. Works only at end points.
static Circle touching_circle( CubicBezier const &curve, bool start ) {

    double k = 0;
    Geom::Point p;
    Geom::Point normal;
    if ( start ) {
        double distance = Geom::distance( curve[1], curve[0] );
        k = 4.0/3.0 * area( curve[0], curve[1], curve[2] ) /
            (distance * distance * distance);
        if( Geom::cross(curve[0]-curve[1], curve[1]-curve[2]) < 0 ) {
            k = -k;
        }
        p = curve[0];
        normal = Geom::Point(curve[1] - curve[0]).cw();
        normal.normalize();
        // std::cout << "Start k: " << k << " d: " << distance << " normal: " << normal << std::endl;
    } else {
        double distance = Geom::distance( curve[3], curve[2] );
        k = 4.0/3.0 * area( curve[1], curve[2], curve[3] ) /
            (distance * distance * distance);
        if( Geom::cross(curve[1]-curve[2], curve[2]-curve[3]) < 0 ) {
            k = -k;
        }
        p = curve[3];
        normal = Geom::Point(curve[3] - curve[2]).cw();
        normal.normalize();
        // std::cout << "End   k: " << k << " d: " << distance << " normal: " << normal << std::endl;
    }
    if( k == 0 ) {
        return Geom::Circle( Geom::Point(0,std::numeric_limits<float>::infinity()),
                             std::numeric_limits<float>::infinity());
    } else {
        double radius = 1/k;
        Geom::Point center = p + normal * radius;
        return Geom::Circle( center, fabs(radius) );
    }
}
}

namespace {

// Internal data structure

struct join_data {
    join_data(Geom::Path &_res, Geom::Path const&_outgoing, Geom::Point _in_tang, Geom::Point _out_tang, double _miter, double _width)
        : res(_res), outgoing(_outgoing), in_tang(_in_tang), out_tang(_out_tang), miter(_miter), width(_width) {};

    // contains the current path that is being built on
    Geom::Path &res;

    // contains the next curve to append
    Geom::Path const& outgoing;

    // input tangents
    Geom::Point in_tang;
    Geom::Point out_tang;

    // line parameters
    double miter;
    double width; // half stroke width
};

// Join functions must append the outgoing path

typedef void join_func(join_data jd);

void bevel_join(join_data jd)
{
    jd.res.appendNew<Geom::LineSegment>(jd.outgoing.initialPoint());
    jd.res.append(jd.outgoing);
}

void round_join(join_data jd)
{
    jd.res.appendNew<Geom::EllipticalArc>(jd.width, jd.width, 0, false, jd.width <= 0, jd.outgoing.initialPoint());
    jd.res.append(jd.outgoing);
}

void miter_join_internal(join_data const &jd, bool clip)
{
    using namespace Geom;

    Curve const& incoming = jd.res.back();
    Curve const& outgoing = jd.outgoing.front();
    Path &res = jd.res;
    double width = jd.width, miter = jd.miter;

    Point tang1 = jd.in_tang;
    Point tang2 = jd.out_tang;
    Point p = intersection_point(incoming.finalPoint(), tang1, outgoing.initialPoint(), tang2);

    bool satisfied = false;
    bool inc_ls = res.back_open().degreesOfFreedom() <= 4;

    if (p.isFinite()) {
        // check size of miter
        Point point_on_path = incoming.finalPoint() + rot90(tang1)*width;
        // SVG defines miter length as distance between inner intersection and outer intersection,
        // which is twice the distance from p to point_on_path but width is half stroke width.
        satisfied = distance(p, point_on_path) <= miter * width; 
        if (satisfied) {
            // miter OK, check to see if we can do a relocation
            if (inc_ls) {
                res.setFinal(p);
            } else {
                res.appendNew<LineSegment>(p);
            }
        } else if (clip) {
            // std::cout << "  Clipping ------------ " << std::endl;
            // miter needs clipping, find two points
            Point bisector_versor = Line(point_on_path, p).versor();
            Point point_limit = point_on_path + miter * width * bisector_versor;
            // std::cout << "     bisector_versor: " << bisector_versor << std::endl;
            // std::cout << "     point_limit: " << point_limit << std::endl;
            Point p1 = intersection_point(incoming.finalPoint(), tang1, point_limit, bisector_versor.cw());
            Point p2 = intersection_point(outgoing.initialPoint(), tang2, point_limit, bisector_versor.cw());
            // std::cout << "     p1: " << p1 << std::endl;
            // std::cout << "     p2: " << p2 << std::endl;
            if (inc_ls) {
                res.setFinal(p1);
            } else {
                res.appendNew<LineSegment>(p1);
            }
            res.appendNew<LineSegment>(p2);
        }
    }

    res.appendNew<LineSegment>(outgoing.initialPoint());

    // check if we can do another relocation
    bool out_ls = outgoing.degreesOfFreedom() <= 4;

    if ((satisfied || clip) && out_ls) {
        res.setFinal(outgoing.finalPoint());
    } else {
        res.append(outgoing);
    }

    // either way, add the rest of the path
    res.insert(res.end(), ++jd.outgoing.begin(), jd.outgoing.end());
}

void miter_join(join_data jd) { miter_join_internal(jd, false); }
void miter_clip_join(join_data jd) { miter_join_internal(jd, true); }

Geom::Point pick_solution(std::vector<Geom::ShapeIntersection> points, Geom::Point tang2, Geom::Point endPt)
{
    assert(points.size() == 2);
    Geom::Point sol;
    if ( dot(tang2, points[0].point() - endPt) > 0 ) {
        // points[0] is bad, choose points[1]
        sol = points[1];
    } else if ( dot(tang2, points[1].point() - endPt) > 0 ) { // points[0] could be good, now check points[1]
        // points[1] is bad, choose points[0]
        sol = points[0];
    } else {
        // both points are good, choose nearest
        sol = ( distanceSq(endPt, points[0].point()) < distanceSq(endPt, points[1].point()) )
            ? points[0].point() : points[1].point();
    }
    return sol;
}

// Arcs line join. If two circles don't intersect, expand inner circle.
Geom::Point expand_circle( Geom::Circle &inner_circle, Geom::Circle const &outer_circle, Geom::Point const &start_pt, Geom::Point const &start_tangent ) {
    // std::cout << "expand_circle:" << std::endl;
    // std::cout << "  outer_circle: radius: " << outer_circle.radius() << "  center: " << outer_circle.center() << std::endl;
    // std::cout << "  start: point: " << start_pt << "  tangent: " << start_tangent << std::endl;

    if( !(outer_circle.contains(start_pt) ) ) {
        // std::cout << "  WARNING: Outer circle does not contain starting point!" << std::endl;
        return Geom::Point(0,0);
    }

    Geom::Line secant1(start_pt, start_pt + start_tangent);
    std::vector<Geom::ShapeIntersection> chord1_pts = outer_circle.intersect(secant1);
    // std::cout << "  chord1: " << chord1_pts[0].point() << ", " << chord1_pts[1].point() << std::endl;
    Geom::LineSegment chord1(chord1_pts[0].point(), chord1_pts[1].point());

    Geom::Line bisector = make_bisector_line( chord1 );
    std::vector<Geom::ShapeIntersection> chord2_pts = outer_circle.intersect(bisector);
    // std::cout << "  chord2: " << chord2_pts[0].point() << ", " << chord2_pts[1].point() << std::endl;
    Geom::LineSegment chord2(chord2_pts[0].point(), chord2_pts[1].point());

    // Find D, point on chord2 and on circle closest to start point
    Geom::Coord d0 = Geom::distance(chord2_pts[0].point(),start_pt);
    Geom::Coord d1 = Geom::distance(chord2_pts[1].point(),start_pt);
    // std::cout << "  d0: " << d0 << " d1: " << d1 << std::endl;
    Geom::Point d = (d0 < d1) ? chord2_pts[0].point() : chord2_pts[1].point();
    Geom::Line da(d,start_pt);

    // Chord through start point and point D
    std::vector<Geom::ShapeIntersection> chord3_pts =  outer_circle.intersect(da);
    // std::cout << "  chord3: " << chord3_pts[0].point() << ", " << chord3_pts[1].point() << std::endl;

    // Find farthest point on chord3 and on circle (could be more robust)
    Geom::Coord d2 = Geom::distance(chord3_pts[0].point(),d);
    Geom::Coord d3 = Geom::distance(chord3_pts[1].point(),d);
    // std::cout << "  d2: " << d2 << " d3: " << d3 << std::endl;

    // Find point P, the intersection of outer circle and new inner circle
    Geom::Point p = (d2 > d3) ? chord3_pts[0].point() : chord3_pts[1].point();

    // Find center of new circle: it is at the intersection of the bisector
    // of the chord defined by the start point and point P and a line through
    // the start point and parallel to the first bisector.
    Geom::LineSegment chord4(start_pt,p);
    Geom::Line bisector2 = make_bisector_line( chord4 );
    Geom::Line diameter = make_parallel_line( start_pt, bisector );
    std::vector<Geom::ShapeIntersection> center_new = bisector2.intersect( diameter );
    // std::cout << "  center_new: " << center_new[0].point() << std::endl;
    Geom::Coord r_new = Geom::distance( center_new[0].point(), start_pt );
    // std::cout << "  r_new: " << r_new << std::endl;

    inner_circle.setCenter( center_new[0].point() );
    inner_circle.setRadius( r_new );
    return p;
}

// Arcs line join. If two circles don't intersect, adjust both circles so they just touch.
// Increase (decrease) the radius of circle 1 and decrease (increase) of circle 2 by the same amount keeping the given points and tangents fixed.
Geom::Point adjust_circles( Geom::Circle &circle1, Geom::Circle &circle2, Geom::Point const &point1, Geom::Point const &point2, Geom::Point const &tan1, Geom::Point const &tan2 ) {

    Geom::Point n1 = (circle1.center() - point1).normalized(); // Always points towards center
    Geom::Point n2 = (circle2.center() - point2).normalized();
    Geom::Point sum_n = n1 + n2;

    double r1 = circle1.radius();
    double r2 = circle2.radius();
    double delta_r = r2 - r1;
    Geom::Point c1 = circle1.center();
    Geom::Point c2 = circle2.center();
    Geom::Point delta_c = c2 - c1;

    // std::cout << "adjust_circles:" << std::endl;
    // std::cout << "    norm: " << n1 << "; " << n2 << std::endl;
    // std::cout << "    sum_n: " << sum_n << std::endl;
    // std::cout << "    delta_r: " << delta_r << std::endl;
    // std::cout << "    delta_c: " << delta_c << std::endl;

    // Quadratic equation
    double A = 4 - sum_n.length() * sum_n.length();
    double B = 4.0 * delta_r - 2.0 * Geom::dot( delta_c, sum_n );
    double C = delta_r * delta_r - delta_c.length() * delta_c.length();

    double s1 = 0;
    double s2 = 0;

    if( fabs(A) < 0.01 ) {
        // std::cout << "    A near zero! $$$$$$$$$$$$$$$$$$" << std::endl;
        if( B != 0 ) {
            s1 = -C/B;
            s2 = -s1;
        }
    } else {
        s1 = (-B + sqrt(B*B - 4*A*C))/(2*A);
        s2 = (-B - sqrt(B*B - 4*A*C))/(2*A);
    }

    double dr = (fabs(s1)<=fabs(s2)?s1:s2);

    // std::cout << "    A: " << A << std::endl;
    // std::cout << "    B: " << B << std::endl;
    // std::cout << "    C: " << C << std::endl;
    // std::cout << "    s1: " << s1 << " s2: " << s2 << " dr: " << dr << std::endl;

    circle1 = Geom::Circle( c1 - dr*n1, r1-dr );
    circle2 = Geom::Circle( c2 + dr*n2, r2+dr );

    // std::cout << "    C1: " << circle1 << std::endl;
    // std::cout << "    C2: " << circle2 << std::endl;
    // std::cout << "    d': " << Geom::Point( circle1.center() - circle2.center() ).length() << std::endl;

    Geom::Line bisector( circle1.center(), circle2.center() );
    std::vector<Geom::ShapeIntersection> points = circle1.intersect( bisector );
    Geom::Point p0 = points[0].point();
    Geom::Point p1 = points[1].point();
    // std::cout << "    points: " << p0 << "; " << p1 << std::endl;
    if( std::abs( Geom::distance( p0, circle2.center() ) - circle2.radius() ) <
        std::abs( Geom::distance( p1, circle2.center() ) - circle2.radius() ) ) {
        return p0;
    } else {
        return p1;
    }
}

void extrapolate_join_internal(join_data const &jd, int alternative)
{
    // std::cout << "\nextrapolate_join: entrance: alternative: " << alternative << std::endl;
    using namespace Geom;

    Geom::Path &res = jd.res;
    Geom::Curve const& incoming = res.back();
    Geom::Curve const& outgoing = jd.outgoing.front();
    Geom::Point startPt = incoming.finalPoint();
    Geom::Point endPt = outgoing.initialPoint();
    Geom::Point tang1 = jd.in_tang;
    Geom::Point tang2 = jd.out_tang;
    // width is half stroke-width
    double width = jd.width, miter = jd.miter;

    // std::cout << "  startPt: " << startPt << "  endPt: " << endPt << std::endl;
    // std::cout << "  tang1: " << tang1 << "  tang2: " << tang2 <<  std::endl;
    // std::cout << "    dot product: " << Geom::dot( tang1, tang2 ) <<  std::endl;
    // std::cout << "  width: " << width << std::endl;

    // CIRCLE CALCULATION TESTING
    Geom::Circle circle1 = touching_circle(Geom::reverse(incoming.toSBasis()), 0.);
    Geom::Circle circle2 = touching_circle(outgoing.toSBasis(), 0);
    // std::cout << "  circle1: " << circle1 << std::endl;
    // std::cout << "  circle2: " << circle2 << std::endl;
    if( Geom::CubicBezier const * in_bezier = dynamic_cast<Geom::CubicBezier const*>(&incoming) ) {
        Geom::Circle circle_test1 = touching_circle(*in_bezier, false);
        if( !Geom::are_near( circle1, circle_test1, 0.01 ) ) {
            // std::cout << "  Circle 1 error!!!!!!!!!!!!!!!!!" << std::endl;
            // std::cout << "           " << circle_test1 << std::endl;
        }
    }
    if( Geom::CubicBezier const * out_bezier = dynamic_cast<Geom::CubicBezier const*>(&outgoing) ) {
        Geom::Circle circle_test2 = touching_circle(*out_bezier, true);
        if( !Geom::are_near( circle2, circle_test2, 0.01 ) ) {
            // std::cout << "  Circle 2 error!!!!!!!!!!!!!!!!!" << std::endl;
            // std::cout << "           " << circle_test2 << std::endl;
        }
    }
    // END TESTING

    Geom::Point center1 = circle1.center();
    double side1 = tang1[Geom::X]*(startPt[Geom::Y]-center1[Geom::Y]) - tang1[Geom::Y]*(startPt[Geom::X]-center1[Geom::X]);
    // std::cout << "  side1: " << side1 << std::endl;

    bool inc_ls = !circle1.center().isFinite();
    bool out_ls = !circle2.center().isFinite();

    std::vector<Geom::ShapeIntersection> points;

    Geom::EllipticalArc *arc1 = nullptr;
    Geom::EllipticalArc *arc2 = nullptr;
    Geom::LineSegment *seg1 = nullptr;
    Geom::LineSegment *seg2 = nullptr;
    Geom::Point sol;
    Geom::Point p1;
    Geom::Point p2;

    if (!inc_ls && !out_ls) {
        // std::cout << " two circles" << std::endl;

        // See if tangent is backwards (radius < width/2 and circle is inside stroke).
        Geom::Point node_on_path = startPt + Geom::rot90(tang1)*width;
        // std::cout << "  node_on_path: " << node_on_path << "  -------------- " << std::endl;
        bool b1 = false;
        bool b2 = false;
        if (circle1.radius() < width &&  distance( circle1.center(), node_on_path ) < width) {
            b1 = true;
        }
        if (circle2.radius() < width &&  distance( circle2.center(), node_on_path ) < width) {
            b2 = true;
        }
        // std::cout << "  b1: " << (b1?"true":"false")
        //           << "  b2: " << (b2?"true":"false") << std::endl;

        // Two circles
        points = circle1.intersect(circle2);

        if (points.size() != 2) {
            // std::cout << "   Circles do not intersect, do backup" << std::endl;
            switch (alternative) {
                case 1:
                {
                    // Fallback to round if one path has radius smaller than half line width.
                    if(b1 || b2) {
                        // std::cout << "At one least path has radius smaller than half line width." << std::endl;
                        return( round_join(jd) );
                    }

                    Point p;
                    if( circle2.contains( startPt ) && !circle1.contains( endPt ) ) {
                        // std::cout << "Expand circle1" << std::endl;
                        p = expand_circle( circle1, circle2, startPt, tang1 );
                        points.emplace_back( 0, 0, p );
                        points.emplace_back( 0, 0, p );
                    } else if( circle1.contains( endPt ) && !circle2.contains( startPt ) ) {
                        // std::cout << "Expand circle2" << std::endl;
                        p = expand_circle( circle2, circle1, endPt, tang2 );
                        points.emplace_back( 0, 0, p );
                        points.emplace_back( 0, 0, p );
                    } else {
                        // std::cout << "Either both points inside or both outside" << std::endl;
                        return( miter_clip_join(jd) );
                    }
                    break;
                    
                }
                case 2:
                {
                    // Fallback to round if one path has radius smaller than half line width.
                    if(b1 || b2) {
                        // std::cout << "At one least path has radius smaller than half line width." << std::endl;
                        return( round_join(jd) );
                    }

                    if( ( circle2.contains( startPt ) && !circle1.contains( endPt ) ) ||
                        ( circle1.contains( endPt ) && !circle2.contains( startPt ) ) ) {
                        
                        Geom::Point apex = adjust_circles( circle1, circle2, startPt, endPt, tang1, tang2 );
                        points.emplace_back( 0, 0, apex );
                        points.emplace_back( 0, 0, apex );
                    } else {
                        // std::cout << "Either both points inside or both outside" << std::endl;
                        return( miter_clip_join(jd) );
                    }
                        
                    break;
                }
                case 3:
                    if( side1 > 0 ) {
                        Geom::Line secant(startPt, startPt + tang1);
                        points = circle2.intersect(secant);
                        circle1.setRadius(std::numeric_limits<float>::infinity());
                        circle1.setCenter(Geom::Point(0,std::numeric_limits<float>::infinity()));
                    } else {
                        Geom::Line secant(endPt, endPt + tang2);
                        points = circle1.intersect(secant);
                        circle2.setRadius(std::numeric_limits<float>::infinity());
                        circle2.setCenter(Geom::Point(0,std::numeric_limits<float>::infinity()));
                    }
                    break;


                case 0:
                default:
                    // Do nothing
                    break;
            }
        }

        if (points.size() == 2) {
            sol = pick_solution(points, tang2, endPt);
            if( circle1.radius() != std::numeric_limits<float>::infinity() ) {
                arc1 = circle1.arc(startPt, 0.5*(startPt+sol), sol);
            } else {
                seg1 = new Geom::LineSegment(startPt, sol);
            }
            if( circle2.radius() != std::numeric_limits<float>::infinity() ) {
                arc2 = circle2.arc(sol, 0.5*(sol+endPt), endPt);
            } else {
                seg2 = new Geom::LineSegment(sol, endPt);
            }
        }
    } else if (inc_ls && !out_ls) {
        // Line and circle
        // std::cout << " line circle" << std::endl;
        points = circle2.intersect(Line(incoming.initialPoint(), incoming.finalPoint()));
        if (points.size() == 2) {
            sol = pick_solution(points, tang2, endPt);
            arc2 = circle2.arc(sol, 0.5*(sol+endPt), endPt);
        }
    } else if (!inc_ls && out_ls) {
        // Circle and line
        // std::cout << " circle line" << std::endl;
        points = circle1.intersect(Line(outgoing.initialPoint(), outgoing.finalPoint()));
        if (points.size() == 2) {
            sol = pick_solution(points, tang2, endPt);
            arc1 = circle1.arc(startPt, 0.5*(sol+startPt), sol);
        }
    }
    if (points.size() != 2) {
        // std::cout << " no solutions" << std::endl;
        // no solutions available, fall back to miter
        return miter_join(jd);
    }

    // We have a solution, thus sol is defined.
    p1 = sol;
    
    // See if we need to clip. Miter length is measured along a circular arc that is tangent to the
    // bisector of the incoming and out going angles and passes through the end point (sol) of the
    // line join.

    // Center of circle is intersection of a line orthogonal to bisector and a line bisecting
    // a chord connecting the path end point (point_on_path) and the join end point (sol).
    Geom::Point point_on_path = startPt + Geom::rot90(tang1)*width;
    Geom::Line bisector = make_angle_bisector_line(startPt, point_on_path, endPt);
    Geom::Line ortho = make_orthogonal_line(point_on_path, bisector); 

    Geom::LineSegment chord(point_on_path, sol);
    Geom::Line bisector_chord =  make_bisector_line(chord);

    Geom::Line limit_line;
    double miter_limit = width * miter;
    bool clipped = false;

    if (are_parallel(bisector_chord, ortho)) {
        // No intersection (can happen if curvatures are equal but opposite)
        if (Geom::distance(point_on_path, sol) > miter_limit) {
            clipped = true;
            Geom::Point temp = bisector.versor();
            Geom::Point limit_point = point_on_path + miter_limit * temp; 
            limit_line = make_parallel_line( limit_point, ortho );
        }
    } else {
        Geom::Point center =
            Geom::intersection_point( bisector_chord.pointAt(0), bisector_chord.versor(),
                                      ortho.pointAt(0),          ortho.versor() );
        Geom::Coord radius = distance(center, point_on_path);
        Geom::Circle circle_center(center, radius);

        double limit_angle = miter_limit / radius;

        Geom::Ray start_ray(center, point_on_path);
        Geom::Ray end_ray(center, sol);
        Geom::Line limit_line(center, 0); // Angle set below

        if (Geom::cross(start_ray.versor(), end_ray.versor()) < 0) {
            limit_line.setAngle(start_ray.angle() - limit_angle);
        } else {
            limit_line.setAngle(start_ray.angle() + limit_angle);
        }

        Geom::EllipticalArc *arc_center = circle_center.arc(point_on_path, 0.5*(point_on_path + sol), sol);
        if (arc_center && arc_center->sweepAngle() > limit_angle) {
            // We need to clip
            clipped = true;

            if (!inc_ls) {
                // Incoming circular
                points = circle1.intersect(limit_line);
                if (points.size() == 2) {
                    p1 = pick_solution(points, tang2, endPt);
                    delete arc1;
                    arc1 = circle1.arc(startPt, 0.5*(p1+startPt), p1);
                }
            } else {
                p1 = Geom::intersection_point(startPt, tang1, limit_line.pointAt(0), limit_line.versor());
            }

            if (!out_ls) {
                // Outgoing circular
                points = circle2.intersect(limit_line);
                if (points.size() == 2) {
                    p2 = pick_solution(points, tang1, endPt);
                    delete arc2;
                    arc2 = circle2.arc(p2, 0.5*(p2+endPt), endPt);
                }
            } else {
                p2 = Geom::intersection_point(endPt, tang2, limit_line.pointAt(0), limit_line.versor());
            }
        }
    }    

    // Add initial
    if (arc1) {
        res.append(*arc1);
    } else if (seg1 ) {
        res.append(*seg1);
    } else {
        // Straight line segment: move last point
        res.setFinal(p1);
    }

    if (clipped) {
        res.appendNew<Geom::LineSegment>(p2);
    }

    // Add outgoing
    if (arc2) {
        res.append(*arc2);
        res.append(outgoing);
    } else if (seg2 ) {
        res.append(*seg2);
        res.append(outgoing);
    } else {
        // Straight line segment:
        res.appendNew<Geom::LineSegment>(outgoing.finalPoint());
    }

    // add the rest of the path
    res.insert(res.end(), ++jd.outgoing.begin(), jd.outgoing.end());

    delete arc1;
    delete arc2;
    delete seg1;
    delete seg2;
}

void extrapolate_join(     join_data jd) { extrapolate_join_internal(jd, 0); }
void extrapolate_join_alt1(join_data jd) { extrapolate_join_internal(jd, 1); }
void extrapolate_join_alt2(join_data jd) { extrapolate_join_internal(jd, 2); }
void extrapolate_join_alt3(join_data jd) { extrapolate_join_internal(jd, 3); }


void tangents(Geom::Point tang[2], Geom::Curve const& incoming, Geom::Curve const& outgoing)
{
    Geom::Point tang1 = Geom::unitTangentAt(reverse(incoming.toSBasis()), 0.);
    Geom::Point tang2 = outgoing.unitTangentAt(0.);
    tang[0] = tang1, tang[1] = tang2;
}

// Offsetting a line segment is mathematically stable and quick to do
Geom::LineSegment offset_line(Geom::LineSegment const& l, double width)
{
    Geom::Point tang1 = Geom::rot90(l.unitTangentAt(0));
    Geom::Point tang2 = Geom::rot90(unitTangentAt(reverse(l.toSBasis()), 0.));

    Geom::Point start = l.initialPoint() + tang1 * width;
    Geom::Point end = l.finalPoint() - tang2 * width;
    
    return Geom::LineSegment(start, end);
}

void get_cubic_data(Geom::CubicBezier const& bez, double time, double& len, double& rad)
{
    // get derivatives
    std::vector<Geom::Point> derivs = bez.pointAndDerivatives(time, 3);

    Geom::Point der1 = derivs[1]; // first deriv (tangent vector)
    Geom::Point der2 = derivs[2]; // second deriv (tangent's tangent)
    double l = Geom::L2(der1); // length

    len = rad = 0;

    // TODO: we might want to consider using Geom::touching_circle to determine the
    // curvature radius here. Less code duplication, but slower

    if (Geom::are_near(l, 0, 1e-4)) {
        l = Geom::L2(der2);
        Geom::Point der3 = derivs.at(3); // try second time
        if (Geom::are_near(l, 0, 1e-4)) {
            l = Geom::L2(der3);
            if (Geom::are_near(l, 0)) {
                return; // this isn't a segment...
            }
        rad = 1e8;
        } else {
            rad = -l * (Geom::dot(der2, der2) / Geom::cross(der2, der3));
        }
    } else {
        rad = -l * (Geom::dot(der1, der1) / Geom::cross(der1, der2));
    }
    len = l;
}

double _offset_cubic_stable_sub(
        Geom::CubicBezier const& bez,
        Geom::CubicBezier& c,
        const Geom::Point& start_normal,
        const Geom::Point& end_normal,
        const Geom::Point& start_new,
        const Geom::Point& end_new,
        const double start_rad,
        const double end_rad,
        const double start_len,
        const double end_len,
        const double width,
        const double width_correction) {
    using Geom::X;
    using Geom::Y;

    double start_off = 1, end_off = 1;
    // correction of the lengths of the tangent to the offset
    if (!Geom::are_near(start_rad, 0))
        start_off += (width + width_correction) / start_rad;
    if (!Geom::are_near(end_rad, 0))
        end_off += (width + width_correction) / end_rad;

    // We don't change the direction of the control points
    if (start_off < 0) {
        start_off = 0;
    }
    if (end_off < 0) {
        end_off = 0;
    }
    start_off *= start_len;
    end_off *= end_len;
    // --------

    Geom::Point mid1_new = start_normal.ccw()*start_off;
    mid1_new = Geom::Point(start_new[X] + mid1_new[X]/3., start_new[Y] + mid1_new[Y]/3.);
    Geom::Point mid2_new = end_normal.ccw()*end_off;
    mid2_new = Geom::Point(end_new[X] - mid2_new[X]/3., end_new[Y] - mid2_new[Y]/3.);

    // create the estimate curve
    c = Geom::CubicBezier(start_new, mid1_new, mid2_new, end_new);

    // check the tolerance for our estimate to be a parallel curve

    double worst_residual = 0;
    for (size_t ii = 3; ii <= 7; ii+=2) {
        const double t = static_cast<double>(ii) / 10;
        const Geom::Point req = bez.pointAt(t);
        const Geom::Point chk = c.pointAt(c.nearestTime(req));
        const double current_residual = (chk-req).length() - std::abs(width);
        if (std::abs(current_residual) > std::abs(worst_residual)) {
            worst_residual = current_residual;
        }
    }
    return worst_residual;
}

void offset_cubic(Geom::Path& p, Geom::CubicBezier const& bez, double width, double tol, size_t levels)
{
    using Geom::X;
    using Geom::Y;

    const Geom::Point start_pos = bez.initialPoint();
    const Geom::Point end_pos = bez.finalPoint();

    const Geom::Point start_normal = Geom::rot90(bez.unitTangentAt(0));
    const Geom::Point end_normal = -Geom::rot90(Geom::unitTangentAt(Geom::reverse(bez.toSBasis()), 0.));

    // offset the start and end control points out by the width
    const Geom::Point start_new = start_pos + start_normal*width;
    const Geom::Point end_new = end_pos + end_normal*width;

    // --------
    double start_rad, end_rad;
    double start_len, end_len; // tangent lengths
    get_cubic_data(bez, 0, start_len, start_rad);
    get_cubic_data(bez, 1, end_len, end_rad);


    Geom::CubicBezier c;

    double best_width_correction = 0;
    double best_residual = _offset_cubic_stable_sub(
                bez, c,
                start_normal, end_normal,
                start_new, end_new,
                start_rad, end_rad,
                start_len, end_len,
                width, best_width_correction);
    double stepsize = std::abs(width)/2;
    bool seen_success = false;
    double stepsize_threshold = 0;
    // std::cout << "Residual from " << best_residual << " ";
    size_t ii = 0;
    for (; ii < 100 && stepsize > stepsize_threshold; ++ii) {
        bool success = false;
        const double width_correction = best_width_correction - (best_residual > 0 ? 1 : -1) * stepsize;
        Geom::CubicBezier current_curve;
        const double residual = _offset_cubic_stable_sub(
                    bez, current_curve,
                    start_normal, end_normal,
                    start_new, end_new,
                    start_rad, end_rad,
                    start_len, end_len,
                    width, width_correction);
        if (std::abs(residual) < std::abs(best_residual)) {
            best_residual = residual;
            best_width_correction = width_correction;
            c = current_curve;
            success = true;
            if (std::abs(best_residual) < tol/4) {
                break;
            }
        }

        if (success) {
            if (!seen_success) {
                seen_success = true;
                //std::cout << "Stepsize factor: " << std::abs(width) / stepsize << std::endl;
                stepsize_threshold = stepsize / 1000;
            }
        }
        else {
            stepsize /= 2;
        }
        if (std::abs(best_width_correction) >= std::abs(width)/2) {
            //break; // Seems to prevent some numerical instabilities, not clear if useful
        }
    }

    // reached maximum recursive depth
    // don't bother with any more correction
    if (levels == 0) {
        try {
            p.append(c);
        }
        catch (...) {
            if ((p.finalPoint() - c.initialPoint()).length() < 1e-6) {
                c.setInitial(p.finalPoint());
            }
            else {
                auto line = Geom::LineSegment(p.finalPoint(), c.initialPoint());
                p.append(line);
            }
            p.append(c);
        }

        return;
    }

    // We find the point on our new curve (c) for which the distance between
    // (c) and (bez) differs the most from the desired distance (width).
    double worst_err = std::abs(best_residual);
    double worst_time = .5;
    for (size_t ii = 1; ii <= 9; ++ii) {
        const double t = static_cast<double>(ii) / 10;
        const Geom::Point req = bez.pointAt(t);
        // We use the exact solution with nearestTime because it is numerically
        // much more stable than simply assuming that the point on (c) closest
        // to bez.pointAt(t) is given by c.pointAt(t)
        const Geom::Point chk = c.pointAt(c.nearestTime(req));

        Geom::Point const diff = req - chk;
        const double err = std::abs(diff.length() - std::abs(width));
        if (err > worst_err) {
            worst_err = err;
            worst_time = t;
        }
    }

    if (worst_err < tol) {
        if (Geom::are_near(start_new, p.finalPoint())) {
            p.setFinal(start_new); // if it isn't near, we throw
        }

        // we're good, curve is accurate enough
        p.append(c);
        return;
    } else {
        // split the curve in two
        std::pair<Geom::CubicBezier, Geom::CubicBezier> s = bez.subdivide(worst_time);
        offset_cubic(p, s.first, width, tol, levels - 1);
        offset_cubic(p, s.second, width, tol, levels - 1);
    }
}

void offset_quadratic(Geom::Path& p, Geom::QuadraticBezier const& bez, double width, double tol, size_t levels)
{
    // cheat
    // it's faster
    // seriously
    std::vector<Geom::Point> points = bez.controlPoints();
    Geom::Point b1 = points[0] + (2./3) * (points[1] - points[0]);
    Geom::Point b2 = b1 + (1./3) * (points[2] - points[0]);
    Geom::CubicBezier cub = Geom::CubicBezier(points[0], b1, b2, points[2]);
    offset_cubic(p, cub, width, tol, levels);
}

void offset_curve(Geom::Path& res, Geom::Curve const* current, double width, double tolerance)
{
    size_t levels = 8;

    if (current->isDegenerate()) return; // don't do anything

    // TODO: we can handle SVGEllipticalArc here as well, do that!

    if (Geom::BezierCurve const *b = dynamic_cast<Geom::BezierCurve const*>(current)) {
        size_t order = b->order();
        switch (order) {
            case 1:
                res.append(offset_line(static_cast<Geom::LineSegment const&>(*current), width));
                break;
            case 2: {
                Geom::QuadraticBezier const& q = static_cast<Geom::QuadraticBezier const&>(*current);
                offset_quadratic(res, q, width, tolerance, levels);
                break;
            }
            case 3: {
                Geom::CubicBezier const& cb = static_cast<Geom::CubicBezier const&>(*current);
                offset_cubic(res, cb, width, tolerance, levels);
                break;
            }
            default: {
                Geom::Path sbasis_path = Geom::cubicbezierpath_from_sbasis(current->toSBasis(), tolerance);
                for (const auto & i : sbasis_path)
                    offset_curve(res, &i, width, tolerance);
                break;
            }
        }
    } else {
        Geom::Path sbasis_path = Geom::cubicbezierpath_from_sbasis(current->toSBasis(), 0.1);
        for (const auto & i : sbasis_path)
            offset_curve(res, &i, width, tolerance);
    }
}

typedef void cap_func(Geom::PathBuilder& res, Geom::Path const& with_dir, Geom::Path const& against_dir, double width);

void flat_cap(Geom::PathBuilder& res, Geom::Path const&, Geom::Path const& against_dir, double)
{
    res.lineTo(against_dir.initialPoint());
}

void round_cap(Geom::PathBuilder& res, Geom::Path const&, Geom::Path const& against_dir, double width)
{
    res.arcTo(width / 2., width / 2., 0., true, false, against_dir.initialPoint());
}

void square_cap(Geom::PathBuilder& res, Geom::Path const& with_dir, Geom::Path const& against_dir, double width)
{
    width /= 2.;
    Geom::Point normal_1 = -Geom::unitTangentAt(Geom::reverse(with_dir.back().toSBasis()), 0.);
    Geom::Point normal_2 = -against_dir[0].unitTangentAt(0.);
    res.lineTo(with_dir.finalPoint() + normal_1*width);
    res.lineTo(against_dir.initialPoint() + normal_2*width);
    res.lineTo(against_dir.initialPoint());
}

void peak_cap(Geom::PathBuilder& res, Geom::Path const& with_dir, Geom::Path const& against_dir, double width)
{
    width /= 2.;
    Geom::Point normal_1 = -Geom::unitTangentAt(Geom::reverse(with_dir.back().toSBasis()), 0.);
    Geom::Point normal_2 = -against_dir[0].unitTangentAt(0.);
    Geom::Point midpoint = ((with_dir.finalPoint() + normal_1*width) + (against_dir.initialPoint() + normal_2*width)) * 0.5;
    res.lineTo(midpoint);
    res.lineTo(against_dir.initialPoint());
}

} // namespace

namespace Inkscape {

Geom::PathVector outline(
        Geom::Path const& input,
        double width,
        double miter,
        LineJoinType join,
        LineCapType butt,
        double tolerance)
{
    if (input.size() == 0) return Geom::PathVector(); // nope, don't even try

    Geom::PathBuilder res;
    Geom::Path with_dir = half_outline(input, width/2., miter, join, tolerance);
    Geom::Path against_dir = half_outline(input.reversed(), width/2., miter, join, tolerance);
    res.moveTo(with_dir[0].initialPoint());
    res.append(with_dir);

    cap_func *cf;
    switch (butt) {
        case BUTT_ROUND:
            cf = &round_cap;
            break;
        case BUTT_SQUARE:
            cf = &square_cap;
            break;
        case BUTT_PEAK:
            cf = &peak_cap;
            break;
        default:
            cf = &flat_cap;
    }

    // glue caps
    if (!input.closed()) {
        cf(res, with_dir, against_dir, width);
    } else {
        res.closePath();
        res.moveTo(against_dir.initialPoint());
    }

    res.append(against_dir);

    if (!input.closed()) {
        cf(res, against_dir, with_dir, width);
    }

    res.closePath();
    res.flush();
    return res.peek();
}

Geom::Path half_outline(
        Geom::Path const& input,
        double width,
        double miter,
        LineJoinType join,
        double tolerance)
{
    if (tolerance <= 0) {
        if (std::abs(width) > 0) {
            tolerance = 5.0 * (std::abs(width)/100);
        }
        else {
            tolerance = 1e-4;
        }
    }
    Geom::Path res;
    if (input.size() == 0) return res;

    Geom::Point tang1 = input[0].unitTangentAt(0);
    Geom::Point start = input.initialPoint() + tang1 * width;
    Geom::Path temp;
    Geom::Point tang[2];

    res.setStitching(true);
    temp.setStitching(true);

    res.start(start);

    // Do two curves at a time for efficiency, since the join function needs to know the outgoing curve as well
    const Geom::Curve &closingline = input.back_closed();
    const size_t k = (are_near(closingline.initialPoint(), closingline.finalPoint()) && input.closed() )
            ?input.size_open():input.size_default();
    
    for (size_t u = 0; u < k; u += 2) {
        temp.clear();

        offset_curve(temp, &input[u], width, tolerance);

        // on the first run through, there isn't a join
        if (u == 0) {
            res.append(temp);
        } else {
            tangents(tang, input[u-1], input[u]);
            outline_join(res, temp, tang[0], tang[1], width, miter, join);
        }

        // odd number of paths
        if (u < k - 1) {
            temp.clear();
            offset_curve(temp, &input[u+1], width, tolerance);
            tangents(tang, input[u], input[u+1]);
            outline_join(res, temp, tang[0], tang[1], width, miter, join);
        }
    }
    if (input.closed()) {
        Geom::Curve const &c1 = res.back();
        Geom::Curve const &c2 = res.front();
        temp.clear();
        temp.append(c1);
        Geom::Path temp2;
        temp2.append(c2);
        tangents(tang, input.back(), input.front());
        outline_join(temp, temp2, tang[0], tang[1], width, miter, join);
        res.erase(res.begin());
        res.erase_last();
        res.append(temp);
        res.close();
    }
    return res;
}

void outline_join(Geom::Path &res, Geom::Path const& temp, Geom::Point in_tang, Geom::Point out_tang, double width, double miter, Inkscape::LineJoinType join)
{
    if (res.size() == 0 || temp.size() == 0)
        return;
    Geom::Curve const& outgoing = temp.front();
    if (Geom::are_near(res.finalPoint(), outgoing.initialPoint(), 0.01)) {
        // if the points are /that/ close, just ignore this one
        res.setFinal(temp.initialPoint());
        res.append(temp);
        return;
    }

    join_data jd(res, temp, in_tang, out_tang, miter, width);
    if (!(Geom::cross(in_tang, out_tang) > 0)) {
        join = Inkscape::JOIN_BEVEL;
    }
    join_func *jf;
    switch (join) {
        case Inkscape::JOIN_BEVEL:
            jf = &bevel_join;
            break;
        case Inkscape::JOIN_ROUND:
            jf = &round_join;
            break;
        case Inkscape::JOIN_EXTRAPOLATE:
            jf = &extrapolate_join;
            break;
        case Inkscape::JOIN_EXTRAPOLATE1:
            jf = &extrapolate_join_alt1;
            break;
        case Inkscape::JOIN_EXTRAPOLATE2:
            jf = &extrapolate_join_alt2;
            break;
        case Inkscape::JOIN_EXTRAPOLATE3:
            jf = &extrapolate_join_alt3;
            break;
        case Inkscape::JOIN_MITER_CLIP:
            jf = &miter_clip_join;
            break;
        default:
            jf = &miter_join;
    }
    jf(jd);
 }

} // namespace Inkscape

/*
  Local Variables:
  mode:c++
  c-file-style:"stroustrup"
  c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
  indent-tabs-mode:nil
  fill-column:99
  End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8 :