Source

VectorBoolean / VectorBoolean / FBBezierGraph.m

Full commit
   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
//
//  FBBezierGraph.m
//  VectorBoolean
//
//  Created by Andrew Finnell on 6/15/11.
//  Copyright 2011 Fortunate Bear, LLC. All rights reserved.
//

#import "FBBezierGraph.h"
#import "FBBezierCurve.h"
#import "NSBezierPath+Utilities.h"
#import "FBBezierContour.h"
#import "FBContourEdge.h"
#import "FBBezierIntersection.h"
#import "FBEdgeCrossing.h"
#import "FBDebug.h"
#import "Geometry.h"
#import <math.h>

static const CGFloat FB2PI = 2.0 * M_PI;

static CGFloat NormalizeAngle(CGFloat value)
{
    while ( value < 0.0 )
        value += FB2PI;
    while ( value >= FB2PI )
        value -= FB2PI;
    return value;
}

static CGFloat PolarAngle(NSPoint point)
{
    CGFloat value = 0.0;
    if ( point.x > 0.0 )
        value = atanf(point.y / point.x);
    else if ( point.x < 0.0 ) {
        if ( point.y >= 0.0 )
            value = atanf(point.y / point.x) + M_PI;
        else
            value = atanf(point.y / point.x) - M_PI;
    } else {
        if ( point.y > 0.0 )
            value =  M_PI_2;
        else if ( point.y < 0.0 )
            value =  -M_PI_2;
        else
            value = 0.0;
    }
    return NormalizeAngle(value);
}

typedef struct FBAngleRange {
    CGFloat minimum;
    CGFloat maximum;
} FBAngleRange;

static FBAngleRange FBAngleRangeMake(CGFloat minimum, CGFloat maximum)
{
    FBAngleRange range = { minimum, maximum };
    return range;
}

static BOOL FBAngleRangeContainsAngle(FBAngleRange range, CGFloat angle)
{
    if ( range.minimum <= range.maximum )
        return angle > range.minimum && angle < range.maximum;
    
    // The range wraps around 0. See if the angle falls in the first half
    if ( angle > range.minimum && angle <= FB2PI )
        return YES;
    
    return angle >= 0.0 && angle < range.maximum;
}

@interface FBBezierGraph ()

- (NSUInteger) numberOfCrossings;
- (void) removeDuplicateCrossings;
- (BOOL) doesEdge:(FBContourEdge *)edge1 crossEdge:(FBContourEdge *)edge2 atIntersection:(FBBezierIntersection *)intersection;
- (BOOL) insertCrossingsWithBezierGraph:(FBBezierGraph *)other;
- (BOOL) containsPoint:(NSPoint)point;
- (FBEdgeCrossing *) firstUnprocessedCrossing;
- (void) markCrossingsAsEntryOrExitWithBezierGraph:(FBBezierGraph *)otherGraph markInside:(BOOL)markInside;
- (FBBezierGraph *) bezierGraphFromIntersections;
- (void) removeCrossings;

- (void) addContour:(FBBezierContour *)contour;
- (void) addBezierGraph:(FBBezierGraph *)graph;
- (void) round;
- (FBContourInside) contourInsides:(FBBezierContour *)contour;

- (void) markCrossingsAsEntryOrExitWithBezierGraphForUnion:(FBBezierGraph *)otherGraph;
- (void) markCrossingsAsEntryOrExitWithBezierGraphForIntersect:(FBBezierGraph *)otherGraph;
- (void) markCrossingsAsEntryOrExitWithBezierGraphForDifference:(FBBezierGraph *)otherGraph markInside:(BOOL)markInside;

- (NSArray *) nonintersectingContours;
- (BOOL) containsContour:(FBBezierContour *)contour;
- (FBBezierContour *) containerForContour:(FBBezierContour *)testContour;
- (BOOL) eliminateContainers:(NSMutableArray *)containers thatDontContainContour:(FBBezierContour *)testContour usingRay:(FBBezierCurve *)ray;
- (BOOL) findBoundsOfContour:(FBBezierContour *)testContour onRay:(FBBezierCurve *)ray minimum:(NSPoint *)testMinimum maximum:(NSPoint *)testMaximum;
- (void) removeContoursThatDontContain:(NSMutableArray *)crossings;
- (BOOL) findCrossingsOnContainers:(NSArray *)containers onRay:(FBBezierCurve *)ray beforeMinimum:(NSPoint)testMinimum afterMaximum:(NSPoint)testMaximum crossingsBefore:(NSMutableArray *)crossingsBeforeMinimum crossingsAfter:(NSMutableArray *)crossingsAfterMaximum;
- (void) removeCrossings:(NSMutableArray *)crossings forContours:(NSArray *)containersToRemove;
- (void) removeContourCrossings:(NSMutableArray *)crossings1 thatDontAppearIn:(NSMutableArray *)crossings2;
- (NSArray *) minimumCrossings:(NSArray *)crossings onRay:(FBBezierCurve *)ray;
- (NSArray *) maximumCrossings:(NSArray *)crossings onRay:(FBBezierCurve *)ray;
- (NSArray *) contoursFromCrossings:(NSArray *)crossings;
- (NSUInteger) numberOfTimesContour:(FBBezierContour *)contour appearsInCrossings:(NSArray *)crossings;

@property (readonly) NSArray *contours;
@property (readonly) NSRect bounds;
@property (readonly) NSPoint testPoint;

@end

@implementation FBBezierGraph

@synthesize contours=_contours;

+ (id) bezierGraphWithBezierPath:(NSBezierPath *)path
{
    return [[[FBBezierGraph alloc] initWithBezierPath:path] autorelease];
}

+ (id) bezierGraph
{
    return [[[FBBezierGraph alloc] init] autorelease];
}

- (id) initWithBezierPath:(NSBezierPath *)path
{
    self = [super init];
    
    if ( self != nil ) {
        NSPoint lastPoint = NSZeroPoint;
        _contours = [[NSMutableArray alloc] initWithCapacity:2];
            
        FBBezierContour *contour = nil;
        for (NSUInteger i = 0; i < [path elementCount]; i++) {
            NSBezierElement element = [path fb_elementAtIndex:i];
            
            switch (element.kind) {
                case NSMoveToBezierPathElement:
                    // Start a new contour
                    contour = [[[FBBezierContour alloc] init] autorelease];
                    [self addContour:contour];
                    
                    lastPoint = element.point;
                    break;
                    
                case NSLineToBezierPathElement: {
                    // Convert lines to bezier curves as well. Just set control point to be in the line formed
                    //  by the end points
                    [contour addCurve:[FBBezierCurve bezierCurveWithLineStartPoint:lastPoint endPoint:element.point]];
                    
                    lastPoint = element.point;
                    break;
                }
                    
                case NSCurveToBezierPathElement:
                    [contour addCurve:[FBBezierCurve bezierCurveWithEndPoint1:lastPoint controlPoint1:element.controlPoints[0] controlPoint2:element.controlPoints[1] endPoint2:element.point]];
                    
                    lastPoint = element.point;
                    break;
                    
                case NSClosePathBezierPathElement:
                    lastPoint = NSZeroPoint;
                    break;
            }
        }
        
        for (contour in _contours)
            contour.inside = [self contourInsides:contour];
    }
    
    return self;
}

- (id) init
{
    self = [super init];
    
    if ( self != nil ) {
        _contours = [[NSMutableArray alloc] initWithCapacity:2];
    }
    
    return self;
}

- (void)dealloc
{
    [_contours release];
    
    [super dealloc];
}

- (FBBezierGraph *) unionWithBezierGraph:(FBBezierGraph *)graph
{
    [self insertCrossingsWithBezierGraph:graph];
    
    [self markCrossingsAsEntryOrExitWithBezierGraphForUnion:graph];
    [graph markCrossingsAsEntryOrExitWithBezierGraphForUnion:self];

    FBBezierGraph *result = [self bezierGraphFromIntersections];
    [result round];
    
    NSArray *ourNonintersectingContours = [self nonintersectingContours];
    NSArray *theirNonintersectinContours = [graph nonintersectingContours];
    NSMutableArray *finalNonintersectingContours = [[ourNonintersectingContours mutableCopy] autorelease];
    [finalNonintersectingContours addObjectsFromArray:theirNonintersectinContours];
    // There are no crossings, which means one contains the other, or they're completely disjoint 
    for (FBBezierContour *ourContour in ourNonintersectingContours) {
        BOOL clipContainsSubject = [graph containsContour:ourContour];
        if ( clipContainsSubject )
            [finalNonintersectingContours removeObject:ourContour];
    }
    for (FBBezierContour *theirContour in theirNonintersectinContours) {
        BOOL subjectContainsClip = [self containsContour:theirContour];
        if ( subjectContainsClip )
            [finalNonintersectingContours removeObject:theirContour];
    }

    // Append the final nonintersecting contours
    for (FBBezierContour *contour in finalNonintersectingContours)
        [result addContour:contour];
    
    // Clean up crossings so the graphs can be reused
    [self removeCrossings];
    [graph removeCrossings];
    
    return result;
}

- (void) markCrossingsAsEntryOrExitWithBezierGraphForUnion:(FBBezierGraph *)otherGraph
{
    for (FBBezierContour *contour in self.contours) {
        NSArray *intersectingContours = contour.intersectingContours;
        for (FBBezierContour *otherContour in intersectingContours) {
            if ( otherContour.inside == FBContourInsideHole )
                [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:YES];
            else
                [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:NO];
        }
    }
}

- (FBBezierGraph *) intersectWithBezierGraph:(FBBezierGraph *)graph
{
    [self insertCrossingsWithBezierGraph:graph];
    
    [self markCrossingsAsEntryOrExitWithBezierGraphForIntersect:graph];
    [graph markCrossingsAsEntryOrExitWithBezierGraphForIntersect:self];
    
    FBBezierGraph *result = [self bezierGraphFromIntersections];
    [result round];
    
    NSArray *ourNonintersectingContours = [self nonintersectingContours];
    NSArray *theirNonintersectinContours = [graph nonintersectingContours];
    NSMutableArray *finalNonintersectingContours = [NSMutableArray arrayWithCapacity:[ourNonintersectingContours count] + [theirNonintersectinContours count]];
    // There are no crossings, which means one contains the other, or they're completely disjoint 
    for (FBBezierContour *ourContour in ourNonintersectingContours) {
        BOOL clipContainsSubject = [graph containsContour:ourContour];
        if ( clipContainsSubject )
            [finalNonintersectingContours addObject:ourContour];
    }
    for (FBBezierContour *theirContour in theirNonintersectinContours) {
        BOOL subjectContainsClip = [self containsContour:theirContour];
        if ( subjectContainsClip )
            [finalNonintersectingContours addObject:theirContour];
    }
    
    // Append the final nonintersecting contours
    for (FBBezierContour *contour in finalNonintersectingContours)
        [result addContour:contour];
    
    // Clean up crossings so the graphs can be reused
    [self removeCrossings];
    [graph removeCrossings];
    
    return result;
}

- (void) markCrossingsAsEntryOrExitWithBezierGraphForIntersect:(FBBezierGraph *)otherGraph
{
    for (FBBezierContour *contour in self.contours) {
        NSArray *intersectingContours = contour.intersectingContours;
        for (FBBezierContour *otherContour in intersectingContours) {
            if ( otherContour.inside == FBContourInsideHole )
                [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:NO];
            else
                [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:YES];
        }
    }
}

- (FBBezierGraph *) differenceWithBezierGraph:(FBBezierGraph *)graph
{
#if 1
    [self insertCrossingsWithBezierGraph:graph];
    
    [self markCrossingsAsEntryOrExitWithBezierGraphForDifference:graph markInside:NO];
    [graph markCrossingsAsEntryOrExitWithBezierGraphForDifference:self markInside:YES];
    
    FBBezierGraph *result = [self bezierGraphFromIntersections];
    [result round];
    
    NSArray *ourNonintersectingContours = [self nonintersectingContours];
    NSArray *theirNonintersectinContours = [graph nonintersectingContours];
    NSMutableArray *finalNonintersectingContours = [NSMutableArray arrayWithCapacity:[ourNonintersectingContours count] + [theirNonintersectinContours count]];
    // There are no crossings, which means one contains the other, or they're completely disjoint 
    for (FBBezierContour *ourContour in ourNonintersectingContours) {
        BOOL clipContainsSubject = [graph containsContour:ourContour];
        if ( !clipContainsSubject )
            [finalNonintersectingContours addObject:ourContour];
    }
    for (FBBezierContour *theirContour in theirNonintersectinContours) {
        BOOL subjectContainsClip = [self containsContour:theirContour];
        if ( subjectContainsClip )
            [finalNonintersectingContours addObject:theirContour]; // add it as a hole
    }
    
    // Append the final nonintersecting contours
    for (FBBezierContour *contour in finalNonintersectingContours)
        [result addContour:contour];
    
    // Clean up crossings so the graphs can be reused
    [self removeCrossings];
    [graph removeCrossings];
    
    return result;  
#else
    BOOL hasCrossings = [self insertCrossingsWithBezierGraph:graph];
    if ( !hasCrossings ) {
        // There are no crossings, which means one contains the other, or they're completely disjoint 
        BOOL subjectContainsClip = [self containsPoint:graph.testPoint];
        BOOL clipContainsSubject = [graph containsPoint:self.testPoint];
        
        // Clean up crossings so the graphs can be reused
        [self removeCrossings];
        [graph removeCrossings];
        
        if ( subjectContainsClip ) {
            // Clip punches a clean (non-intersecting) hole in subject
            FBBezierGraph *result = [FBBezierGraph bezierGraph];
            [result addBezierGraph:self];
            [result addBezierGraph:graph];
            return result;
        }
        
        if ( clipContainsSubject )
            // We're subtracting out everything
            return [FBBezierGraph bezierGraph];
        
        // No crossings, so nothing to subtract from subject
        return self;
    }
    
    [self markCrossingsAsEntryOrExitWithBezierGraph:graph markInside:NO];
    [graph markCrossingsAsEntryOrExitWithBezierGraph:self markInside:YES];
    
    FBBezierGraph *result = [self bezierGraphFromIntersections];
    [result round];
    
    // Clean up crossings so the graphs can be reused
    [self removeCrossings];
    [graph removeCrossings];
    
    return result;
#endif
}

- (void) markCrossingsAsEntryOrExitWithBezierGraphForDifference:(FBBezierGraph *)otherGraph markInside:(BOOL)markInside
{
    for (FBBezierContour *contour in self.contours) {
        NSArray *intersectingContours = contour.intersectingContours;
        for (FBBezierContour *otherContour in intersectingContours) {
            if ( otherContour.inside == FBContourInsideHole )
                [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:!markInside];
            else
                [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:markInside];
        }
    }
}


- (FBBezierGraph *) xorWithBezierGraph:(FBBezierGraph *)graph
{
    FBBezierGraph *allParts = [self unionWithBezierGraph:graph];
    FBBezierGraph *intersectingParts = [self intersectWithBezierGraph:graph];
    return [allParts differenceWithBezierGraph:intersectingParts];
}

- (NSBezierPath *) bezierPath
{
    NSBezierPath *path = [NSBezierPath bezierPath];
    [path setWindingRule:NSEvenOddWindingRule];

    for (FBBezierContour *contour in _contours) {
        BOOL firstPoint = YES;        
        for (FBContourEdge *edge in contour.edges) {
            if ( firstPoint ) {
                [path moveToPoint:edge.curve.endPoint1];
                firstPoint = NO;
            }
            
            [path curveToPoint:edge.curve.endPoint2 controlPoint1:edge.curve.controlPoint1 controlPoint2:edge.curve.controlPoint2];
        }
    }
    
    return path;
}

- (void) round
{
    for (FBBezierContour *contour in _contours)
        [contour round];
}

- (BOOL) insertCrossingsWithBezierGraph:(FBBezierGraph *)other
{
    // Find all intersections and, if they cross the other graph, create crossings for them
    for (FBBezierContour *ourContour in self.contours) {
        for (FBContourEdge *ourEdge in ourContour.edges) {
            for (FBBezierContour *theirContour in other.contours) {
                for (FBContourEdge *theirEdge in theirContour.edges) {
                    NSArray *intersections = [ourEdge.curve intersectionsWithBezierCurve:theirEdge.curve];
                    for (FBBezierIntersection *intersection in intersections) {
                        // Mark shared points
                        if ( intersection.isAtStartOfCurve1 ) {
                            ourEdge.startShared = YES;
                            ourEdge.previous.stopShared = YES;
                        } else if ( intersection.isAtStopOfCurve1 ) {
                            ourEdge.stopShared = YES;
                            ourEdge.next.startShared = YES;
                        }
                        if ( intersection.isAtStartOfCurve2 ) {
                            theirEdge.startShared = YES;
                            theirEdge.previous.stopShared = YES;
                        } else if ( intersection.isAtStopOfCurve2 ) {
                            theirEdge.stopShared = YES;
                            theirEdge.next.startShared = YES;
                        }

                        // Don't add a crossing unless one edge actually crosses the other
                        if ( ![self doesEdge:ourEdge crossEdge:theirEdge atIntersection:intersection] )
                            continue;

                        FBEdgeCrossing *ourCrossing = [FBEdgeCrossing crossingWithIntersection:intersection];
                        FBEdgeCrossing *theirCrossing = [FBEdgeCrossing crossingWithIntersection:intersection];

                        ourCrossing.counterpart = theirCrossing;
                        theirCrossing.counterpart = ourCrossing;
                        
                        [ourEdge addCrossing:ourCrossing];
                        [theirEdge addCrossing:theirCrossing];
                    }
                }
            }
            
        }
    }
 
    [self removeDuplicateCrossings];
    [other removeDuplicateCrossings];

    return [self numberOfCrossings];
}

- (void) removeDuplicateCrossings
{
    // Find any duplicate crossings. These will happen at the endpoints of edges
    for (FBBezierContour *ourContour in self.contours) {
        for (FBContourEdge *ourEdge in ourContour.edges) {
            NSArray *crossings = [[ourEdge.crossings copy] autorelease];
            for (FBEdgeCrossing *crossing in crossings) {
                if ( crossing.isAtStart && crossing.edge.previous.lastCrossing.isAtEnd ) {
                    FBEdgeCrossing *counterpart = crossing.counterpart;
                    [crossing removeFromEdge];
                    [counterpart removeFromEdge];
                }
                if ( crossing.isAtEnd && crossing.edge.next.firstCrossing.isAtStart ) {
                    FBEdgeCrossing *counterpart = crossing.edge.next.firstCrossing.counterpart;
                    [crossing.edge.next.firstCrossing removeFromEdge];
                    [counterpart removeFromEdge];
                }
            }
        }
    }
}

- (NSUInteger) numberOfCrossings
{
    NSUInteger count = 0;
    for (FBBezierContour *ourContour in self.contours)
        for (FBContourEdge *ourEdge in ourContour.edges)
            count += [ourEdge.crossings count];
    return count;
}

- (BOOL) doesEdge:(FBContourEdge *)edge1 crossEdge:(FBContourEdge *)edge2 atIntersection:(FBBezierIntersection *)intersection
{
    // Handle the main case first
    if ( !intersection.isAtEndPointOfCurve )
        return YES;
    if ( intersection.isTangent )
        return NO;
    
    // The intersection happens at the end of one of the edges, meaning we'll have to look at the next
    //  edge in sequence to see if it crosses or not
    
    // Calculate the four tangents
    NSPoint edge1Tangents[] = { NSZeroPoint, NSZeroPoint };
    NSPoint edge2Tangents[] = { NSZeroPoint, NSZeroPoint };
    if ( intersection.isAtStartOfCurve1 ) {
        FBContourEdge *otherEdge1 = edge1.previous;
        edge1Tangents[0] = FBSubtractPoint(otherEdge1.curve.controlPoint2, otherEdge1.curve.endPoint2);
        edge1Tangents[1] = FBSubtractPoint(edge1.curve.controlPoint1, edge1.curve.endPoint1);
    } else if ( intersection.isAtStopOfCurve1 ) {
        FBContourEdge *otherEdge1 = edge1.next;
        edge1Tangents[0] = FBSubtractPoint(edge1.curve.controlPoint2, edge1.curve.endPoint2);
        edge1Tangents[1] = FBSubtractPoint(otherEdge1.curve.controlPoint1, otherEdge1.curve.endPoint1);
    } else {
        edge1Tangents[0] = FBSubtractPoint(intersection.curve1LeftBezier.controlPoint2, intersection.curve1LeftBezier.endPoint2);
        edge1Tangents[1] = FBSubtractPoint(intersection.curve1RightBezier.controlPoint1, intersection.curve1RightBezier.endPoint1);
    }
    if ( intersection.isAtStartOfCurve2 ) {
        FBContourEdge *otherEdge2 = edge2.previous;
        edge2Tangents[0] = FBSubtractPoint(otherEdge2.curve.controlPoint2, otherEdge2.curve.endPoint2);
        edge2Tangents[1] = FBSubtractPoint(edge2.curve.controlPoint1, edge2.curve.endPoint1);
    } else if ( intersection.isAtStopOfCurve2 ) {
        FBContourEdge *otherEdge2 = edge2.next;
        edge2Tangents[0] = FBSubtractPoint(edge2.curve.controlPoint2, edge2.curve.endPoint2);
        edge2Tangents[1] = FBSubtractPoint(otherEdge2.curve.controlPoint1, otherEdge2.curve.endPoint1);
    } else {
        edge2Tangents[0] = FBSubtractPoint(intersection.curve2LeftBezier.controlPoint2, intersection.curve2LeftBezier.endPoint2);
        edge2Tangents[1] = FBSubtractPoint(intersection.curve2RightBezier.controlPoint1, intersection.curve2RightBezier.endPoint1);
    }

    // Calculate angles between the tangents
    CGFloat edge1Angles[] = { PolarAngle(edge1Tangents[0]), PolarAngle(edge1Tangents[1]) };
    CGFloat edge2Angles[] = { PolarAngle(edge2Tangents[0]), PolarAngle(edge2Tangents[1]) };
    
    // Count how many times edge2 angles are between edge1 angles
    FBAngleRange range1 = FBAngleRangeMake(edge1Angles[0], edge1Angles[1]);
    NSUInteger rangeCount1 = 0;
    if ( FBAngleRangeContainsAngle(range1, edge2Angles[0]) )
        rangeCount1++;
    if ( FBAngleRangeContainsAngle(range1, edge2Angles[1]) )
        rangeCount1++;
    
    FBAngleRange range2 = FBAngleRangeMake(edge1Angles[1], edge1Angles[0]);
    NSUInteger rangeCount2 = 0;
    if ( FBAngleRangeContainsAngle(range2, edge2Angles[0]) )
        rangeCount2++;
    if ( FBAngleRangeContainsAngle(range2, edge2Angles[1]) )
        rangeCount2++;

    return rangeCount1 == 1 && rangeCount2 == 1;
}

- (NSRect) bounds
{
    if ( !NSEqualRects(_bounds, NSZeroRect) )
        return _bounds;
    if ( [_contours count] == 0 )
        return NSZeroRect;
    
    for (FBBezierContour *contour in _contours)
        _bounds = NSUnionRect(_bounds, contour.bounds);
    
    return _bounds;
}

- (BOOL) containsPoint:(NSPoint)testPoint
{
    // Create a test line from our point to somewhere outside our graph. We'll see how many times the test
    //  line intersects edges of the graph. Based on the winding rule, if it's an odd number, we're inside
    //  the graph, if even, outside.
    NSPoint lineEndPoint = NSMakePoint(testPoint.x > NSMinX(self.bounds) ? NSMinX(self.bounds) - 10 : NSMaxX(self.bounds) + 10, testPoint.y); /* just move us outside the bounds of the graph */
    FBBezierCurve *testCurve = [FBBezierCurve bezierCurveWithLineStartPoint:testPoint endPoint:lineEndPoint];
    
    NSUInteger intersectCount = 0;
    for (FBBezierContour *contour in self.contours) {
        for (FBContourEdge *edge in contour.edges) {
            NSArray *intersections = [testCurve intersectionsWithBezierCurve:edge.curve];
            for (FBBezierIntersection *intersection in intersections) {
                if ( intersection.isTangent )
                    continue;
                intersectCount++;
            }
        }
    }
    
    return (intersectCount % 2) == 1;
}

- (FBContourInside) contourInsides:(FBBezierContour *)testContour
{
    NSPoint testPoint = testContour.firstPoint;
    NSPoint lineEndPoint = NSMakePoint(testPoint.x > NSMinX(self.bounds) ? NSMinX(self.bounds) - 10 : NSMaxX(self.bounds) + 10, testPoint.y); /* just move us outside the bounds of the graph */
    FBBezierCurve *testCurve = [FBBezierCurve bezierCurveWithLineStartPoint:testPoint endPoint:lineEndPoint];

    NSUInteger intersectCount = 0;
    for (FBBezierContour *contour in self.contours) {
        if ( contour == testContour )
            continue; // don't test self intersections
        for (FBContourEdge *edge in contour.edges) {
            NSArray *intersections = [testCurve intersectionsWithBezierCurve:edge.curve];
            for (FBBezierIntersection *intersection in intersections) {
                if ( intersection.isTangent )
                    continue;
                intersectCount++;
            }
        }
    }

    return (intersectCount % 2) == 1 ? FBContourInsideHole : FBContourInsideFilled;
}

- (BOOL) containsContour:(FBBezierContour *)testContour
{
    FBBezierContour *container = [self containerForContour:testContour];
    return container != nil && container.inside == FBContourInsideFilled;
}

- (FBBezierContour *) containerForContour:(FBBezierContour *)testContour
{
    static const CGFloat FBRayOverlap = 10.0;
    
    NSMutableArray *containers = [[_contours mutableCopy] autorelease];
    
    NSUInteger count = MAX(ceilf(NSWidth(testContour.bounds)), ceilf(NSHeight(testContour.bounds)));
    for (NSUInteger fraction = 2; fraction <= count; fraction++) {
        BOOL didEliminate = NO;
        
        CGFloat verticalSpacing = NSHeight(testContour.bounds) / (CGFloat)fraction;
        for (CGFloat y = NSMinY(testContour.bounds) + verticalSpacing; y < NSMaxY(testContour.bounds); y += verticalSpacing) {
            FBBezierCurve *ray = [FBBezierCurve bezierCurveWithLineStartPoint:NSMakePoint(MIN(NSMinX(self.bounds), NSMinX(testContour.bounds)) - FBRayOverlap, y) endPoint:NSMakePoint(MAX(NSMaxX(self.bounds), NSMaxX(testContour.bounds)) + FBRayOverlap, y)];
            BOOL eliminated = [self eliminateContainers:containers thatDontContainContour:testContour usingRay:ray];
            if ( eliminated )
                didEliminate = YES;
        }
        
        CGFloat horizontalSpacing = NSWidth(testContour.bounds) / (CGFloat)fraction;
        for (CGFloat x = NSMinX(testContour.bounds) + horizontalSpacing; x < NSMaxX(testContour.bounds); x += horizontalSpacing) {
            FBBezierCurve *ray = [FBBezierCurve bezierCurveWithLineStartPoint:NSMakePoint(x, MIN(NSMinY(self.bounds), NSMinY(testContour.bounds)) - FBRayOverlap) endPoint:NSMakePoint(x, MAX(NSMaxY(self.bounds), NSMaxY(testContour.bounds)) + FBRayOverlap)];
            BOOL eliminated = [self eliminateContainers:containers thatDontContainContour:testContour usingRay:ray];
            if ( eliminated )
                didEliminate = YES;
        }
        
        if ( [containers count] == 0 )
            return nil;
        if ( didEliminate && [containers count] == 1 )
            return [containers objectAtIndex:0];
    }

    return nil;
}

- (BOOL) findBoundsOfContour:(FBBezierContour *)testContour onRay:(FBBezierCurve *)ray minimum:(NSPoint *)testMinimum maximum:(NSPoint *)testMaximum
{
    BOOL horizontalRay = ray.endPoint1.y == ray.endPoint2.y; // ray has to be a vertical or horizontal line
    
    // First determine the exterior bounds of testContour on the given ray
    NSMutableArray *rayIntersections = [NSMutableArray arrayWithCapacity:9];
    for (FBContourEdge *edge in testContour.edges)
        [rayIntersections addObjectsFromArray:[ray intersectionsWithBezierCurve:edge.curve]];
    if ( [rayIntersections count] == 0 )
        return NO; // shouldn't happen
    FBBezierIntersection *firstRayIntersection = [rayIntersections objectAtIndex:0];
    *testMinimum = firstRayIntersection.location;
    *testMaximum = *testMinimum;    
    for (FBBezierIntersection *intersection in rayIntersections) {
        if ( horizontalRay ) {
            if ( intersection.location.x < testMinimum->x )
                *testMinimum = intersection.location;
            if ( intersection.location.x > testMaximum->x )
                *testMaximum = intersection.location;
        } else {
            if ( intersection.location.y < testMinimum->y )
                *testMinimum = intersection.location;
            if ( intersection.location.y > testMaximum->y )
                *testMaximum = intersection.location;            
        }
    }
    return YES;
}

- (BOOL) findCrossingsOnContainers:(NSArray *)containers onRay:(FBBezierCurve *)ray beforeMinimum:(NSPoint)testMinimum afterMaximum:(NSPoint)testMaximum crossingsBefore:(NSMutableArray *)crossingsBeforeMinimum crossingsAfter:(NSMutableArray *)crossingsAfterMaximum
{
    BOOL horizontalRay = ray.endPoint1.y == ray.endPoint2.y; // ray has to be a vertical or horizontal line

    NSMutableArray *ambiguousCrossings = [NSMutableArray arrayWithCapacity:10];
    for (FBBezierContour *container in containers) {
        for (FBContourEdge *containerEdge in container.edges) {
            NSArray *intersections = [ray intersectionsWithBezierCurve:containerEdge.curve];
            for (FBBezierIntersection *intersection in intersections) {
                if ( intersection.isTangent )
                    continue;
                
                if ( intersection.parameter2 == 0.0 || intersection.parameter2 == 1.0 )
                    return NO;
                
                // only examine those intersections outside of or on testContour
                if ( horizontalRay && intersection.location.x < testMaximum.x && intersection.location.x > testMinimum.x )
                    continue;
                else if ( !horizontalRay && intersection.location.y < testMaximum.y && intersection.location.y > testMinimum.y )
                    continue;
                
                FBEdgeCrossing *crossing = [FBEdgeCrossing crossingWithIntersection:intersection];
                crossing.edge = containerEdge;
                
                // Special case if the bounds are just a point, and this crossing is on that point
                if ( NSEqualPoints(testMaximum, testMinimum) && NSEqualPoints(testMaximum, intersection.location) ) {
                    [ambiguousCrossings addObject:crossing];
                    continue;
                }
                
                if ( horizontalRay && intersection.location.x <= testMinimum.x )
                    [crossingsBeforeMinimum addObject:crossing];
                else if ( !horizontalRay && intersection.location.y <= testMinimum.y )
                    [crossingsBeforeMinimum addObject:crossing];
                if ( horizontalRay && intersection.location.x >= testMaximum.x )
                    [crossingsAfterMaximum addObject:crossing];
                else if ( !horizontalRay && intersection.location.y >= testMaximum.y )
                    [crossingsAfterMaximum addObject:crossing];
            }
        }
    }
    
    for (FBEdgeCrossing *ambiguousCrossing in ambiguousCrossings) {
        NSUInteger numberOfTimesContourAppearsBefore = [self numberOfTimesContour:ambiguousCrossing.edge.contour appearsInCrossings:crossingsBeforeMinimum];
        NSUInteger numberOfTimesContourAppearsAfter = [self numberOfTimesContour:ambiguousCrossing.edge.contour appearsInCrossings:crossingsAfterMaximum];
        if ( numberOfTimesContourAppearsBefore < numberOfTimesContourAppearsAfter )
            [crossingsBeforeMinimum addObject:ambiguousCrossing];
        else
            [crossingsAfterMaximum addObject:ambiguousCrossing];            
    }
    
    return YES;
}

- (NSUInteger) numberOfTimesContour:(FBBezierContour *)contour appearsInCrossings:(NSArray *)crossings
{
    NSUInteger count = 0;
    for (FBEdgeCrossing *crossing in crossings) {
        if ( crossing.edge.contour == contour )
            count++;
    }
    return count;
}

- (NSArray *) minimumCrossings:(NSArray *)crossings onRay:(FBBezierCurve *)ray
{
    if ( [crossings count] == 0 )
        return [NSArray array];
    
    BOOL horizontalRay = ray.endPoint1.y == ray.endPoint2.y; // ray has to be a vertical or horizontal line
    
    NSMutableArray *minimums = [NSMutableArray arrayWithCapacity:[crossings count]];
    FBEdgeCrossing *firstCrossing = [crossings objectAtIndex:0];
    NSPoint minimum = firstCrossing.location;
    for (FBEdgeCrossing *crossing in crossings) {
        if ( horizontalRay ) {
            if ( crossing.location.x < minimum.x ) {
                minimum = crossing.location;
                [minimums removeAllObjects];
                [minimums addObject:crossing];
            } else if ( crossing.location.x == minimum.x ) 
                [minimums addObject:crossing];                
        } else {
            if ( crossing.location.y < minimum.y ) {
                minimum = crossing.location;
                [minimums removeAllObjects];
                [minimums addObject:crossing];
            } else if ( crossing.location.y == minimum.y ) 
                [minimums addObject:crossing];
        }
    }
    
    return minimums;
}

- (NSArray *) maximumCrossings:(NSArray *)crossings onRay:(FBBezierCurve *)ray
{
    if ( [crossings count] == 0 )
        return [NSArray array];
    
    BOOL horizontalRay = ray.endPoint1.y == ray.endPoint2.y; // ray has to be a vertical or horizontal line
    
    NSMutableArray *maximums = [NSMutableArray arrayWithCapacity:[crossings count]];
    FBEdgeCrossing *firstCrossing = [crossings objectAtIndex:0];
    NSPoint maximum = firstCrossing.location;
    for (FBEdgeCrossing *crossing in crossings) {
        if ( horizontalRay ) {
            if ( crossing.location.x > maximum.x ) {
                maximum = crossing.location;
                [maximums removeAllObjects];
                [maximums addObject:crossing];
            } else if ( crossing.location.x == maximum.x ) 
                [maximums addObject:crossing];                
        } else {
            if ( crossing.location.y > maximum.y ) {
                maximum = crossing.location;
                [maximums removeAllObjects];
                [maximums addObject:crossing];
            } else if ( crossing.location.y == maximum.y ) 
                [maximums addObject:crossing];
        }
    }
    
    return maximums;
}

- (BOOL) eliminateContainers:(NSMutableArray *)containers thatDontContainContour:(FBBezierContour *)testContour usingRay:(FBBezierCurve *)ray
{    
    // First determine the exterior bounds of testContour on the given ray
    NSPoint testMinimum = NSZeroPoint;
    NSPoint testMaximum = NSZeroPoint;    
    BOOL foundBounds = [self findBoundsOfContour:testContour onRay:ray minimum:&testMinimum maximum:&testMaximum];
    if ( !foundBounds)
        return NO;
    
    // Find all the containers on either side of the otherContour
    NSMutableArray *crossingsBeforeMinimum = [NSMutableArray arrayWithCapacity:[containers count]];
    NSMutableArray *crossingsAfterMaximum = [NSMutableArray arrayWithCapacity:[containers count]];
    BOOL foundCrossings = [self findCrossingsOnContainers:containers onRay:ray beforeMinimum:testMinimum afterMaximum:testMaximum crossingsBefore:crossingsBeforeMinimum crossingsAfter:crossingsAfterMaximum];
    if ( !foundCrossings )
        return NO;
    
    // Remove containers that appear an even number of times on either side
    [self removeContoursThatDontContain:crossingsBeforeMinimum];
    [self removeContoursThatDontContain:crossingsAfterMaximum];
    
    // Find the container(s) that are the closest
    [crossingsBeforeMinimum setArray:[self maximumCrossings:crossingsBeforeMinimum onRay:ray]];
    [crossingsAfterMaximum setArray:[self minimumCrossings:crossingsAfterMaximum onRay:ray]];
    
    // Remove containers that appear only on one side
    [self removeContourCrossings:crossingsBeforeMinimum thatDontAppearIn:crossingsAfterMaximum];
    [self removeContourCrossings:crossingsAfterMaximum thatDontAppearIn:crossingsBeforeMinimum];
    
    // Although crossingsBeforeMinimum and crossingsAfterMaximum contain different crossings, they should contain the same
    //  contours, so just pick one to pull the contours from
    [containers setArray:[self contoursFromCrossings:crossingsBeforeMinimum]];
    
    return YES;
}

- (NSArray *) contoursFromCrossings:(NSArray *)crossings
{
    NSMutableArray *contours = [NSMutableArray arrayWithCapacity:[crossings count]];
    for (FBEdgeCrossing *crossing in crossings) {
        if ( ![contours containsObject:crossing.edge.contour] )
            [contours addObject:crossing.edge.contour];
    }
    return contours;
}

- (void) removeContourCrossings:(NSMutableArray *)crossings1 thatDontAppearIn:(NSMutableArray *)crossings2
{
    NSMutableArray *containersToRemove = [NSMutableArray arrayWithCapacity:[crossings1 count]];
    for (FBEdgeCrossing *crossingToTest in crossings1) {
        FBBezierContour *containerToTest = crossingToTest.edge.contour;
        BOOL existsInOther = NO;
        for (FBEdgeCrossing *crossing in crossings2) {
            if ( crossing.edge.contour == containerToTest ) {
                existsInOther = YES;
                break;
            }
        }
        if ( !existsInOther )
            [containersToRemove addObject:containerToTest];
    }
    [self removeCrossings:crossings1 forContours:containersToRemove];
}

- (void) removeContoursThatDontContain:(NSMutableArray *)crossings
{
    NSMutableArray *containersToRemove = [NSMutableArray arrayWithCapacity:[crossings count]];
    for (FBEdgeCrossing *crossingToTest in crossings) {
        FBBezierContour *containerToTest = crossingToTest.edge.contour;
        NSUInteger count = 0;
        for (FBEdgeCrossing *crossing in crossings) {
            if ( crossing.edge.contour == containerToTest )
                count++;
        }
        if ( (count % 2) != 1 )
            [containersToRemove addObject:containerToTest];
    }
    [self removeCrossings:crossings forContours:containersToRemove];
}

- (void) removeCrossings:(NSMutableArray *)crossings forContours:(NSArray *)containersToRemove
{
    NSMutableArray *crossingsToRemove = [NSMutableArray arrayWithCapacity:[crossings count]];
    for (FBBezierContour *contour in containersToRemove) {
        for (FBEdgeCrossing *crossing in crossings) {
            if ( crossing.edge.contour == contour )
                [crossingsToRemove addObject:crossing];
        }
    }
    for (FBEdgeCrossing *crossing in crossingsToRemove)
        [crossings removeObject:crossing];
}

- (void) markCrossingsAsEntryOrExitWithBezierGraph:(FBBezierGraph *)otherGraph markInside:(BOOL)markInside
{
    for (FBBezierContour *contour in self.contours) {
        NSArray *intersectingContours = contour.intersectingContours;
        for (FBBezierContour *otherContour in intersectingContours)
            [contour markCrossingsAsEntryOrExitWithContour:otherContour markInside:markInside];
    }
}


- (FBEdgeCrossing *) firstUnprocessedCrossing
{
    for (FBBezierContour *contour in _contours) {
        for (FBContourEdge *edge in contour.edges) {
            for (FBEdgeCrossing *crossing in edge.crossings) {
               if ( !crossing.isProcessed )
                   return crossing;
            }
        }
    }
    return nil;
}

- (FBBezierGraph *) bezierGraphFromIntersections
{
    FBBezierGraph *result = [FBBezierGraph bezierGraph];
    
    FBEdgeCrossing *crossing = [self firstUnprocessedCrossing];
    while ( crossing != nil ) {
        
        // This is the start of a contour
        FBBezierContour *contour = [[[FBBezierContour alloc] init] autorelease];
        [result addContour:contour];
        
        // keep going until run into processed crossing
        while ( !crossing.isProcessed ) {
            crossing.processed = YES;
            
            if ( crossing.isEntry ) {
                // Keep going to next until meet a crossing
                [contour addCurveFrom:crossing to:crossing.next];
                if ( crossing.next == nil ) {
                    // we hit the end of the edge without finding another crossing, so go find the next crossing
                    FBContourEdge *edge = crossing.edge.next;
                    while ( [edge.crossings count] == 0 ) {
                        // output this edge whole
                        [contour addCurve:edge.curve];
                        
                        edge = edge.next;
                    }
                    // We have an edge that has at least one intersection
                    crossing = edge.firstCrossing;
                    [contour addCurveFrom:nil to:crossing];
                } else
                    crossing = crossing.next;
            } else {
                // Keep going to previous until meet a crossing
                [contour addReverseCurveFrom:crossing.previous to:crossing];
                if ( crossing.previous == nil ) {
                    // we hit the end of the edge without finding another crossing, so go find the previous crossing
                    FBContourEdge *edge = crossing.edge.previous;
                    while ( [edge.crossings count] == 0 ) {
                        // output this edge whole
                        [contour addReverseCurve:edge.curve];
                        
                        edge = edge.previous;
                    }
                    // We have an edge that has at least one intersection
                    crossing = edge.lastCrossing;
                    [contour addReverseCurveFrom:crossing to:nil];
                } else
                    crossing = crossing.previous;
            }
            
            // Switch over to counterpart
            crossing.processed = YES;
            crossing = crossing.counterpart;
        }
        
        // See if there's another contour
        crossing = [self firstUnprocessedCrossing];
    }
    
    return result;
}

- (void) removeCrossings
{
    for (FBBezierContour *contour in _contours)
        for (FBContourEdge *edge in contour.edges)
            [edge removeAllCrossings];
}

- (void) addContour:(FBBezierContour *)contour
{
    [_contours addObject:contour];
    _bounds = NSZeroRect;
}

- (void) addBezierGraph:(FBBezierGraph *)graph
{
    for (FBBezierContour *contour in graph.contours)
        [self addContour:[[contour copy] autorelease]];
}

- (NSPoint) testPoint
{
    if ( [_contours count] == 0 )
        return NSZeroPoint;
    FBBezierContour *contour = [_contours objectAtIndex:0];
    return contour.testPoint;
}

- (NSArray *) nonintersectingContours
{
    NSMutableArray *contours = [NSMutableArray arrayWithCapacity:[_contours count]];
    for (FBBezierContour *contour in self.contours) {
        if ( [contour.intersectingContours count] == 0 )
            [contours addObject:contour];
    }
    return contours;
}

- (NSString *) description
{
    return [NSString stringWithFormat:@"<%@: bounds = (%f, %f)(%f, %f) contours = %@>", 
            NSStringFromClass([self class]), 
            NSMinX(self.bounds), NSMinY(self.bounds),
            NSWidth(self.bounds), NSHeight(self.bounds),
            FBArrayDescription(_contours)];
}

@end