summaryrefslogtreecommitdiff
path: root/java/awt/geom/Line2D.java
blob: 3b64f45572708b1b3953c7d859c51fe00003d5d0 (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
1159
1160
1161
1162
1163
1164
1165
1166
1167
1168
1169
1170
1171
1172
1173
1174
1175
1176
1177
1178
1179
1180
1181
1182
/* Line2D.java -- represents a line in 2-D space, plus operations on a line
   Copyright (C) 2000, 2001, 2002 Free Software Foundation

This file is part of GNU Classpath.

GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation; either version 2, or (at your option)
any later version.

GNU Classpath is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with GNU Classpath; see the file COPYING.  If not, write to the
Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA
02111-1307 USA.

Linking this library statically or dynamically with other modules is
making a combined work based on this library.  Thus, the terms and
conditions of the GNU General Public License cover the whole
combination.

As a special exception, the copyright holders of this library give you
permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
modules, and to copy and distribute the resulting executable under
terms of your choice, provided that you also meet, for each linked
independent module, the terms and conditions of the license of that
module.  An independent module is a module which is not derived from
or based on this library.  If you modify this library, you may extend
this exception to your version of the library, but you are not
obligated to do so.  If you do not wish to do so, delete this
exception statement from your version. */

package java.awt.geom;

import java.awt.Rectangle;
import java.awt.Shape;
import java.util.NoSuchElementException;

/**
 * Represents a directed line bewteen two points in (x,y) Cartesian space.
 * Remember, on-screen graphics have increasing x from left-to-right, and
 * increasing y from top-to-bottom. The storage is left to subclasses.
 *
 * @author Tom Tromey (tromey@cygnus.com)
 * @author Eric Blake (ebb9@email.byu.edu)
 * @author David Gilbert
 * @since 1.2
 * @status updated to 1.4
 */
public abstract class Line2D implements Shape, Cloneable
{
  /**
   * The default constructor.
   */
  protected Line2D()
  {
  }

  /**
   * Return the x coordinate of the first point.
   *
   * @return the starting x coordinate
   */
  public abstract double getX1();

  /**
   * Return the y coordinate of the first point.
   *
   * @return the starting y coordinate
   */
  public abstract double getY1();

  /**
   * Return the first point.
   *
   * @return the starting point
   */
  public abstract Point2D getP1();

  /**
   * Return the x coordinate of the second point.
   *
   * @return the ending x coordinate
   */
  public abstract double getX2();

  /**
   * Return the y coordinate of the second point.
   *
   * @return the ending y coordinate
   */
  public abstract double getY2();

  /**
   * Return the second point.
   *
   * @return the ending point
   */
  public abstract Point2D getP2();

  /**
   * Set the coordinates of the line to the given coordinates. Loss of
   * precision may occur due to rounding issues.
   *
   * @param x1 the first x coordinate
   * @param y1 the first y coordinate
   * @param x2 the second x coordinate
   * @param y2 the second y coordinate
   */
  public abstract void setLine(double x1, double y1, double x2, double y2);

  /**
   * Set the coordinates to the given points.
   *
   * @param p1 the first point
   * @param p2 the second point
   * @throws NullPointerException if either point is null
   */
  public void setLine(Point2D p1, Point2D p2)
  {
    setLine(p1.getX(), p1.getY(), p2.getX(), p2.getY());
  }

  /**
   * Set the coordinates to those of the given line.
   *
   * @param l the line to copy
   * @throws NullPointerException if l is null
   */
  public void setLine(Line2D l)
  {
    setLine(l.getX1(), l.getY1(), l.getX2(), l.getY2());
  }

  /**
   * Computes the relative rotation direction needed to pivot the line about
   * the first point in order to have the second point colinear with point p.
   * Because of floating point rounding, don't expect this to be a perfect
   * measure of colinearity. The answer is 1 if the line has a shorter rotation
   * in the direction of the positive X axis to the negative Y axis
   * (counter-clockwise in the default Java coordinate system), or -1 if the
   * shortest rotation is in the opposite direction (clockwise). If p
   * is already colinear, the return value is -1 if it lies beyond the first
   * point, 0 if it lies in the segment, or 1 if it lies beyond the second
   * point. If the first and second point are coincident, this returns 0.
   *
   * @param x1 the first x coordinate
   * @param y1 the first y coordinate
   * @param x2 the second x coordinate
   * @param y2 the second y coordinate
   * @param px the reference x coordinate
   * @param py the reference y coordinate
   * @return the relative rotation direction
   */
  public static int relativeCCW(double x1, double y1, double x2, double y2,
                                double px, double py)
  {
    if ((x1 == x2 && y1 == y2)
        || (x1 == px && y1 == py))
      return 0; // Coincident points.
    // Translate to the origin.
    x2 -= x1;
    y2 -= y1;
    px -= x1;
    py -= y1;
    double slope2 = y2 / x2;
    double slopep = py / px;
    if (slope2 == slopep || (x2 == 0 && px == 0))
      return y2 > 0 // Colinear.
        ? (py < 0 ? -1 : py > y2 ? 1 : 0)
        : (py > 0 ? -1 : py < y2 ? 1 : 0);
    if (x2 >= 0 && slope2 >= 0)
      return px >= 0 // Quadrant 1.
        ? (slope2 > slopep ? 1 : -1)
        : (slope2 < slopep ? 1 : -1);
    if (y2 > 0)
      return px < 0 // Quadrant 2.
        ? (slope2 > slopep ? 1 : -1)
        : (slope2 < slopep ? 1 : -1);
    if (slope2 >= 0.0)
      return px >= 0 // Quadrant 3.
        ? (slope2 < slopep ? 1 : -1)
        : (slope2 > slopep ? 1 : -1);
    return px < 0 // Quadrant 4.
      ? (slope2 < slopep ? 1 : -1)
      : (slope2 > slopep ? 1 : -1);
  }

  /**
   * Computes the relative rotation direction needed to pivot this line about
   * the first point in order to have the second point colinear with point p.
   * Because of floating point rounding, don't expect this to be a perfect
   * measure of colinearity. The answer is 1 if the line has a shorter rotation
   * in the direction of the positive X axis to the negative Y axis
   * (counter-clockwise in the default Java coordinate system), or -1 if the
   * shortest rotation is in the opposite direction (clockwise). If p
   * is already colinear, the return value is -1 if it lies beyond the first
   * point, 0 if it lies in the segment, or 1 if it lies beyond the second
   * point. If the first and second point are coincident, this returns 0.
   *
   * @param px the reference x coordinate
   * @param py the reference y coordinate
   * @return the relative rotation direction
   * @see #relativeCCW(double, double, double, double, double, double)
   */
  public int relativeCCW(double px, double py)
  {
    return relativeCCW(getX1(), getY1(), getX2(), getY2(), px, py);
  }

  /**
   * Computes the relative rotation direction needed to pivot this line about
   * the first point in order to have the second point colinear with point p.
   * Because of floating point rounding, don't expect this to be a perfect
   * measure of colinearity. The answer is 1 if the line has a shorter rotation
   * in the direction of the positive X axis to the negative Y axis
   * (counter-clockwise in the default Java coordinate system), or -1 if the
   * shortest rotation is in the opposite direction (clockwise). If p
   * is already colinear, the return value is -1 if it lies beyond the first
   * point, 0 if it lies in the segment, or 1 if it lies beyond the second
   * point. If the first and second point are coincident, this returns 0.
   *
   * @param p the reference point
   * @return the relative rotation direction
   * @throws NullPointerException if p is null
   * @see #relativeCCW(double, double, double, double, double, double)
   */
  public int relativeCCW(Point2D p)
  {
    return relativeCCW(getX1(), getY1(), getX2(), getY2(), p.getX(), p.getY());
  }

  /**
   * Computes twice the (signed) area of the triangle defined by the three
   * points.  This method is used for intersection testing.
   * 
   * @param x1  the x-coordinate of the first point.
   * @param y1  the y-coordinate of the first point.
   * @param x2  the x-coordinate of the second point.
   * @param y2  the y-coordinate of the second point.
   * @param x3  the x-coordinate of the third point.
   * @param y3  the y-coordinate of the third point.
   * 
   * @return Twice the area.
   */
  private static double area2(double x1, double y1,
                             double x2, double y2,
                             double x3, double y3) 
  {
    return (x2 - x1) * (y3 - y1) - (x3 - x1) * (y2 - y1);    
  }

  /**
   * Returns <code>true</code> if (x3, y3) lies between (x1, y1) and (x2, y2),
   * and false otherwise,  This test assumes that the three points are 
   * collinear, and is used for intersection testing.
   * 
   * @param x1  the x-coordinate of the first point.
   * @param y1  the y-coordinate of the first point.
   * @param x2  the x-coordinate of the second point.
   * @param y2  the y-coordinate of the second point.
   * @param x3  the x-coordinate of the third point.
   * @param y3  the y-coordinate of the third point.
   * 
   * @return A boolean.
   */
  private static boolean between(double x1, double y1, 
                                double x2, double y2, 
                                double x3, double y3) 
  {
    if (x1 != x2) {
      return (x1 <= x3 && x3 <= x2) || (x1 >= x3 && x3 >= x2);   
    }
    else {
      return (y1 <= y3 && y3 <= y2) || (y1 >= y3 && y3 >= y2);   
    }
  }

  /**
   * Test if the line segment (x1,y1)-&gt;(x2,y2) intersects the line segment 
   * (x3,y3)-&gt;(x4,y4).
   *
   * @param x1 the first x coordinate of the first segment
   * @param y1 the first y coordinate of the first segment 
   * @param x2 the second x coordinate of the first segment
   * @param y2 the second y coordinate of the first segment
   * @param x3 the first x coordinate of the second segment
   * @param y3 the first y coordinate of the second segment
   * @param x4 the second x coordinate of the second segment
   * @param y4 the second y coordinate of the second segment
   * @return true if the segments intersect
   */
  public static boolean linesIntersect(double x1, double y1,
                                      double x2, double y2,
                                      double x3, double y3,
                                      double x4, double y4)
  {
    double a1, a2, a3, a4;
  
    // deal with special cases
    if ((a1 = area2(x1, y1, x2, y2, x3, y3)) == 0.0) 
    {
      // check if p3 is between p1 and p2 OR
      // p4 is collinear also AND either between p1 and p2 OR at opposite ends
      if (between(x1, y1, x2, y2, x3, y3)) 
      {
        return true;
      }
      else 
      {
        if (area2(x1, y1, x2, y2, x4, y4) == 0.0) 
        {
          return between(x3, y3, x4, y4, x1, y1) 
                 || between (x3, y3, x4, y4, x2, y2);
        }
        else {
          return false;
        }
      }
    }
    else if ((a2 = area2(x1, y1, x2, y2, x4, y4)) == 0.0) 
    {
      // check if p4 is between p1 and p2 (we already know p3 is not
      // collinear)
      return between(x1, y1, x2, y2, x4, y4);
    }
  
    if ((a3 = area2(x3, y3, x4, y4, x1, y1)) == 0.0) {
      // check if p1 is between p3 and p4 OR
      // p2 is collinear also AND either between p1 and p2 OR at opposite ends
      if (between(x3, y3, x4, y4, x1, y1)) {
        return true;
      }
      else {
        if (area2(x3, y3, x4, y4, x2, y2) == 0.0) {
          return between(x1, y1, x2, y2, x3, y3) 
                 || between (x1, y1, x2, y2, x4, y4);
        }
        else {
          return false;
        }
      }
    }
    else if ((a4 = area2(x3, y3, x4, y4, x2, y2)) == 0.0) {
      // check if p2 is between p3 and p4 (we already know p1 is not
      // collinear)
      return between(x3, y3, x4, y4, x2, y2);
    }
    else {  // test for regular intersection
      return ((a1 > 0.0) ^ (a2 > 0.0)) && ((a3 > 0.0) ^ (a4 > 0.0));
    } 
  }

  /**
   * Test if this line intersects the line given by (x1,y1)-&gt;(x2,y2).
   *
   * @param x1 the first x coordinate of the other segment
   * @param y1 the first y coordinate of the other segment
   * @param x2 the second x coordinate of the other segment
   * @param y2 the second y coordinate of the other segment
   * @return true if the segments intersect
   * @see #linesIntersect(double, double, double, double,
   *                      double, double, double, double)
   */
  public boolean intersectsLine(double x1, double y1, double x2, double y2)
  {
    return linesIntersect(getX1(), getY1(), getX2(), getY2(),
                          x1, y1, x2, y2);
  }

  /**
   * Test if this line intersects the given line.
   *
   * @param l the other segment
   * @return true if the segments intersect
   * @throws NullPointerException if l is null
   * @see #linesIntersect(double, double, double, double,
   *                      double, double, double, double)
   */
  public boolean intersectsLine(Line2D l)
  {
    return linesIntersect(getX1(), getY1(), getX2(), getY2(),
                          l.getX1(), l.getY1(), l.getX2(), l.getY2());
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on the line segment. If the point is on the segment, the
   * result will be 0.
   *
   * @param x1 the first x coordinate of the segment
   * @param y1 the first y coordinate of the segment
   * @param x2 the second x coordinate of the segment
   * @param y2 the second y coordinate of the segment
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the square of the distance from the point to the segment
   * @see #ptSegDist(double, double, double, double, double, double)
   * @see #ptLineDistSq(double, double, double, double, double, double)
   */
  public static double ptSegDistSq(double x1, double y1, double x2, double y2,
                                   double px, double py)
  {
    double pd2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);

    double x, y;
    if (pd2 == 0)
      {
        // Points are coincident.
        x = x1;
        y = y2;
      }
    else
      {
        double u = ((px - x1) * (x2 - x1) + (py - y1) * (y2 - y1)) / pd2;

        if (u < 0)
          {
            // "Off the end"
            x = x1;
            y = y1;
          }
        else if (u > 1.0)
          {
            x = x2;
            y = y2;
          }
        else
          {
            x = x1 + u * (x2 - x1);
            y = y1 + u * (y2 - y1);
          }
      }

    return (x - px) * (x - px) + (y - py) * (y - py);
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * the line segment. If the point is on the segment, the result will be 0.
   *
   * @param x1 the first x coordinate of the segment
   * @param y1 the first y coordinate of the segment
   * @param x2 the second x coordinate of the segment
   * @param y2 the second y coordinate of the segment
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the distance from the point to the segment
   * @see #ptSegDistSq(double, double, double, double, double, double)
   * @see #ptLineDist(double, double, double, double, double, double)
   */
  public static double ptSegDist(double x1, double y1, double x2, double y2,
                                 double px, double py)
  {
    return Math.sqrt(ptSegDistSq(x1, y1, x2, y2, px, py));
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on this line segment. If the point is on the segment, the
   * result will be 0.
   *
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the square of the distance from the point to the segment
   * @see #ptSegDistSq(double, double, double, double, double, double)
   */
  public double ptSegDistSq(double px, double py)
  {
    return ptSegDistSq(getX1(), getY1(), getX2(), getY2(), px, py);
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on this line segment. If the point is on the segment, the
   * result will be 0.
   *
   * @param p the point
   * @return the square of the distance from the point to the segment
   * @throws NullPointerException if p is null
   * @see #ptSegDistSq(double, double, double, double, double, double)
   */
  public double ptSegDistSq(Point2D p)
  {
    return ptSegDistSq(getX1(), getY1(), getX2(), getY2(), p.getX(), p.getY());
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * this line segment. If the point is on the segment, the result will be 0.
   *
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the distance from the point to the segment
   * @see #ptSegDist(double, double, double, double, double, double)
   */
  public double ptSegDist(double px, double py)
  {
    return ptSegDist(getX1(), getY1(), getX2(), getY2(), px, py);
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * this line segment. If the point is on the segment, the result will be 0.
   *
   * @param p the point
   * @return the distance from the point to the segment
   * @throws NullPointerException if p is null
   * @see #ptSegDist(double, double, double, double, double, double)
   */
  public double ptSegDist(Point2D p)
  {
    return ptSegDist(getX1(), getY1(), getX2(), getY2(), p.getX(), p.getY());
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on the infinite line extended from the segment. If the point
   * is on the segment, the result will be 0. If the segment is length 0,
   * the distance is to the common endpoint.
   *
   * @param x1 the first x coordinate of the segment
   * @param y1 the first y coordinate of the segment
   * @param x2 the second x coordinate of the segment
   * @param y2 the second y coordinate of the segment
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the square of the distance from the point to the extended line
   * @see #ptLineDist(double, double, double, double, double, double)
   * @see #ptSegDistSq(double, double, double, double, double, double)
   */
  public static double ptLineDistSq(double x1, double y1, double x2, double y2,
                                    double px, double py)
  {
    double pd2 = (x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2);

    double x, y;
    if (pd2 == 0)
      {
        // Points are coincident.
        x = x1;
        y = y2;
      }
    else
      {
        double u = ((px - x1) * (x2 - x1) + (py - y1) * (y2 - y1)) / pd2;
        x = x1 + u * (x2 - x1);
        y = y1 + u * (y2 - y1);
      }

    return (x - px) * (x - px) + (y - py) * (y - py);
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * the infinite line extended from the segment. If the point is on the
   * segment, the result will be 0. If the segment is length 0, the distance
   * is to the common endpoint.
   *
   * @param x1 the first x coordinate of the segment
   * @param y1 the first y coordinate of the segment
   * @param x2 the second x coordinate of the segment
   * @param y2 the second y coordinate of the segment
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the distance from the point to the extended line
   * @see #ptLineDistSq(double, double, double, double, double, double)
   * @see #ptSegDist(double, double, double, double, double, double)
   */
  public static double ptLineDist(double x1, double y1,
                                   double x2, double y2,
                                   double px, double py)
  {
    return Math.sqrt(ptLineDistSq(x1, y1, x2, y2, px, py));
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on the infinite line extended from this segment. If the point
   * is on the segment, the result will be 0. If the segment is length 0,
   * the distance is to the common endpoint.
   *
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the square of the distance from the point to the extended line
   * @see #ptLineDistSq(double, double, double, double, double, double)
   */
  public double ptLineDistSq(double px, double py)
  {
    return ptLineDistSq(getX1(), getY1(), getX2(), getY2(), px, py);
  }

  /**
   * Measures the square of the shortest distance from the reference point
   * to a point on the infinite line extended from this segment. If the point
   * is on the segment, the result will be 0. If the segment is length 0,
   * the distance is to the common endpoint.
   *
   * @param p the point
   * @return the square of the distance from the point to the extended line
   * @throws NullPointerException if p is null
   * @see #ptLineDistSq(double, double, double, double, double, double)
   */
  public double ptLineDistSq(Point2D p)
  {
    return ptLineDistSq(getX1(), getY1(), getX2(), getY2(),
                        p.getX(), p.getY());
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * the infinite line extended from this segment. If the point is on the
   * segment, the result will be 0. If the segment is length 0, the distance
   * is to the common endpoint.
   *
   * @param px the x coordinate of the point
   * @param py the y coordinate of the point
   * @return the distance from the point to the extended line
   * @see #ptLineDist(double, double, double, double, double, double)
   */
  public double ptLineDist(double px, double py)
  {
    return ptLineDist(getX1(), getY1(), getX2(), getY2(), px, py);
  }

  /**
   * Measures the shortest distance from the reference point to a point on
   * the infinite line extended from this segment. If the point is on the
   * segment, the result will be 0. If the segment is length 0, the distance
   * is to the common endpoint.
   *
   * @param p the point
   * @return the distance from the point to the extended line
   * @throws NullPointerException if p is null
   * @see #ptLineDist(double, double, double, double, double, double)
   */
  public double ptLineDist(Point2D p)
  {
    return ptLineDist(getX1(), getY1(), getX2(), getY2(), p.getX(), p.getY());
  }

  /**
   * Test if a point is contained inside the line. Since a line has no area,
   * this returns false.
   *
   * @param x the x coordinate
   * @param y the y coordinate
   * @return false; the line does not contain points
   */
  public boolean contains(double x, double y)
  {
    return false;
  }

  /**
   * Test if a point is contained inside the line. Since a line has no area,
   * this returns false.
   *
   * @param p the point
   * @return false; the line does not contain points
   */
  public boolean contains(Point2D p)
  {
    return false;
  }

  /**
   * Tests if this line intersects the interior of the specified rectangle.
   *
   * @param x the x coordinate of the rectangle
   * @param y the y coordinate of the rectangle
   * @param w the width of the rectangle
   * @param h the height of the rectangle
   * @return true if the line intersects the rectangle
   */
  public boolean intersects(double x, double y, double w, double h)
  {
    if (w <= 0 || h <= 0)
      return false;
    double x1 = getX1();
    double y1 = getY1();
    double x2 = getX2();
    double y2 = getY2();

    if (x1 >= x && x1 <= x + w && y1 >= y && y1 <= y + h)
      return true;
    if (x2 >= x && x2 <= x + w && y2 >= y && y2 <= y + h)
      return true;

    double x3 = x + w;
    double y3 = y + h;

    return (linesIntersect(x1, y1, x2, y2, x, y, x, y3)
            || linesIntersect(x1, y1, x2, y2, x, y3, x3, y3)
            || linesIntersect(x1, y1, x2, y2, x3, y3, x3, y)
            || linesIntersect(x1, y1, x2, y2, x3, y, x, y));
  }

  /**
   * Tests if this line intersects the interior of the specified rectangle.
   *
   * @param r the rectangle
   * @return true if the line intersects the rectangle
   * @throws NullPointerException if r is null
   */
  public boolean intersects(Rectangle2D r)
  {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * Tests if the line contains a rectangle. Since lines have no area, this
   * always returns false.
   *
   * @param x the x coordinate of the rectangle
   * @param y the y coordinate of the rectangle
   * @param w the width of the rectangle
   * @param h the height of the rectangle
   * @return false; the line does not contain points
   */
  public boolean contains(double x, double y, double w, double h)
  {
    return false;
  }

  /**
   * Tests if the line contains a rectangle. Since lines have no area, this
   * always returns false.
   *
   * @param r the rectangle
   * @return false; the line does not contain points
   */
  public boolean contains(Rectangle2D r)
  {
    return false;
  }

  /**
   * Gets a bounding box (not necessarily minimal) for this line.
   *
   * @return the integer bounding box
   * @see #getBounds2D()
   */
  public Rectangle getBounds()
  {
    return getBounds2D().getBounds();
  }

  /**
   * Return a path iterator, possibly applying a transform on the result. This
   * iterator is not threadsafe.
   *
   * @param at the transform, or null
   * @return a new path iterator
   */
  public PathIterator getPathIterator(final AffineTransform at)
  {
    return new PathIterator()
    {
      /** Current coordinate. */
      private int current = 0;

      public int getWindingRule()
      {
        return WIND_NON_ZERO;
      }

      public boolean isDone()
      {
        return current >= 2;
      }

      public void next()
      {
        current++;
      }

      public int currentSegment(float[] coords)
      {
        int result;
        switch (current)
          {
          case 0:
            coords[0] = (float) getX1();
            coords[1] = (float) getY1();
            result = SEG_MOVETO;
            break;
          case 1:
            coords[0] = (float) getX2();
            coords[1] = (float) getY2();
            result = SEG_LINETO;
            break;
          default:
            throw new NoSuchElementException("line iterator out of bounds");
          }
        if (at != null)
          at.transform(coords, 0, coords, 0, 1);
        return result;
      }

      public int currentSegment(double[] coords)
      {
        int result;
        switch (current)
          {
          case 0:
            coords[0] = getX1();
            coords[1] = getY1();
            result = SEG_MOVETO;
            break;
          case 1:
            coords[0] = getX2();
            coords[1] = getY2();
            result = SEG_LINETO;
            break;
          default:
            throw new NoSuchElementException("line iterator out of bounds");
          }
        if (at != null)
          at.transform(coords, 0, coords, 0, 1);
        return result;
      }
    };
  }

  /**
   * Return a flat path iterator, possibly applying a transform on the result.
   * This iterator is not threadsafe.
   *
   * @param at the transform, or null
   * @param flatness ignored, since lines are already flat
   * @return a new path iterator
   * @see #getPathIterator(AffineTransform)
   */
  public PathIterator getPathIterator(AffineTransform at, double flatness)
  {
    return getPathIterator(at);
  }

  /**
   * Create a new line of the same run-time type with the same contents as
   * this one.
   *
   * @return the clone
   *
   * @exception OutOfMemoryError If there is not enough memory available.
   *
   * @since 1.2
   */
  public Object clone()
  {
    try
      {
        return super.clone();
      }
    catch (CloneNotSupportedException e)
      {
        throw (Error) new InternalError().initCause(e); // Impossible
      }
  }

  /**
   * This class defines a point in <code>double</code> precision.
   *
   * @author Eric Blake (ebb9@email.byu.edu)
   * @since 1.2
   * @status updated to 1.4
   */
  public static class Double extends Line2D
  {
    /** The x coordinate of the first point. */
    public double x1;

    /** The y coordinate of the first point. */
    public double y1;

    /** The x coordinate of the second point. */
    public double x2;

    /** The y coordinate of the second point. */
    public double y2;

    /**
     * Construct the line segment (0,0)-&gt;(0,0).
     */
    public Double()
    {
    }

    /**
     * Construct the line segment with the specified points.
     *
     * @param x1 the x coordinate of the first point
     * @param y1 the y coordinate of the first point
     * @param x2 the x coordinate of the second point
     * @param y2 the y coordinate of the second point
     */
    public Double(double x1, double y1, double x2, double y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Construct the line segment with the specified points.
     *
     * @param p1 the first point
     * @param p2 the second point
     * @throws NullPointerException if either point is null
     */
    public Double(Point2D p1, Point2D p2)
    {
      x1 = p1.getX();
      y1 = p1.getY();
      x2 = p2.getX();
      y2 = p2.getY();
    }

    /**
     * Return the x coordinate of the first point.
     *
     * @return the value of x1
     */
    public double getX1()
    {
      return x1;
    }

    /**
     * Return the y coordinate of the first point.
     *
     * @return the value of y1
     */
    public double getY1()
    {
      return y1;
    }

    /**
     * Return the first point.
     *
     * @return the point (x1,y1)
     */
    public Point2D getP1()
    {
      return new Point2D.Double(x1, y1);
    }

    /**
     * Return the x coordinate of the second point.
     *
     * @return the value of x2
     */
    public double getX2()
    {
      return x2;
    }

    /**
     * Return the y coordinate of the second point.
     *
     * @return the value of y2
     */
    public double getY2()
    {
      return y2;
    }

    /**
     * Return the second point.
     *
     * @return the point (x2,y2)
     */
    public Point2D getP2()
    {
      return new Point2D.Double(x2, y2);
    }

    /**
     * Set this line to the given points.
     *
     * @param x1 the new x coordinate of the first point
     * @param y1 the new y coordinate of the first point
     * @param x2 the new x coordinate of the second point
     * @param y2 the new y coordinate of the second point
     */
    public void setLine(double x1, double y1, double x2, double y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Return the exact bounds of this line segment.
     *
     * @return the bounding box
     */
    public Rectangle2D getBounds2D()
    {
      double x = Math.min(x1, x2);
      double y = Math.min(y1, y2);
      double w = Math.abs(x1 - x2);
      double h = Math.abs(y1 - y2);
      return new Rectangle2D.Double(x, y, w, h);
    }
  } // class Double

  /**
   * This class defines a point in <code>float</code> precision.
   *
   * @author Eric Blake (ebb9@email.byu.edu)
   * @since 1.2
   * @status updated to 1.4
   */
  public static class Float extends Line2D
  {
    /** The x coordinate of the first point. */
    public float x1;

    /** The y coordinate of the first point. */
    public float y1;

    /** The x coordinate of the second point. */
    public float x2;

    /** The y coordinate of the second point. */
    public float y2;

    /**
     * Construct the line segment (0,0)-&gt;(0,0).
     */
    public Float()
    {
    }

    /**
     * Construct the line segment with the specified points.
     *
     * @param x1 the x coordinate of the first point
     * @param y1 the y coordinate of the first point
     * @param x2 the x coordinate of the second point
     * @param y2 the y coordinate of the second point
     */
    public Float(float x1, float y1, float x2, float y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Construct the line segment with the specified points.
     *
     * @param p1 the first point
     * @param p2 the second point
     * @throws NullPointerException if either point is null
     */
    public Float(Point2D p1, Point2D p2)
    {
      x1 = (float) p1.getX();
      y1 = (float) p1.getY();
      x2 = (float) p2.getX();
      y2 = (float) p2.getY();
    }

    /**
     * Return the x coordinate of the first point.
     *
     * @return the value of x1
     */
    public double getX1()
    {
      return x1;
    }

    /**
     * Return the y coordinate of the first point.
     *
     * @return the value of y1
     */
    public double getY1()
    {
      return y1;
    }

    /**
     * Return the first point.
     *
     * @return the point (x1,y1)
     */
    public Point2D getP1()
    {
      return new Point2D.Float(x1, y1);
    }

    /**
     * Return the x coordinate of the second point.
     *
     * @return the value of x2
     */
    public double getX2()
    {
      return x2;
    }

    /**
     * Return the y coordinate of the second point.
     *
     * @return the value of y2
     */
    public double getY2()
    {
      return y2;
    }

    /**
     * Return the second point.
     *
     * @return the point (x2,y2)
     */
    public Point2D getP2()
    {
      return new Point2D.Float(x2, y2);
    }

    /**
     * Set this line to the given points.
     *
     * @param x1 the new x coordinate of the first point
     * @param y1 the new y coordinate of the first point
     * @param x2 the new x coordinate of the second point
     * @param y2 the new y coordinate of the second point
     */
    public void setLine(double x1, double y1, double x2, double y2)
    {
      this.x1 = (float) x1;
      this.y1 = (float) y1;
      this.x2 = (float) x2;
      this.y2 = (float) y2;
    }

    /**
     * Set this line to the given points.
     *
     * @param x1 the new x coordinate of the first point
     * @param y1 the new y coordinate of the first point
     * @param x2 the new x coordinate of the second point
     * @param y2 the new y coordinate of the second point
     */
    public void setLine(float x1, float y1, float x2, float y2)
    {
      this.x1 = x1;
      this.y1 = y1;
      this.x2 = x2;
      this.y2 = y2;
    }

    /**
     * Return the exact bounds of this line segment.
     *
     * @return the bounding box
     */
    public Rectangle2D getBounds2D()
    {
      float x = Math.min(x1, x2);
      float y = Math.min(y1, y2);
      float w = Math.abs(x1 - x2);
      float h = Math.abs(y1 - y2);
      return new Rectangle2D.Float(x, y, w, h);
    }
  } // class Float
} // class Line2D