This file is indexed.

/usr/share/pythoncad/PythonCAD/Generic/circle.py is in pythoncad 0.1.37.0-3.

This file is owned by root:root, with mode 0o644.

The actual contents of the file can be viewed below.

   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
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
1226
1227
1228
1229
1230
1231
1232
1233
1234
1235
1236
1237
1238
1239
1240
1241
1242
1243
1244
1245
1246
1247
1248
1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
1271
1272
1273
1274
1275
1276
1277
1278
1279
1280
1281
1282
1283
1284
1285
1286
1287
1288
1289
1290
1291
1292
1293
1294
1295
1296
1297
1298
1299
1300
1301
1302
1303
1304
1305
1306
1307
1308
1309
1310
1311
1312
1313
1314
1315
1316
1317
1318
1319
1320
1321
1322
1323
1324
1325
1326
1327
1328
1329
1330
1331
1332
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
1387
1388
1389
1390
1391
1392
1393
1394
1395
1396
1397
1398
1399
1400
1401
1402
1403
1404
1405
1406
1407
1408
1409
1410
1411
1412
1413
1414
1415
1416
1417
1418
1419
1420
1421
1422
1423
1424
1425
1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
1437
1438
1439
1440
1441
1442
1443
1444
1445
1446
1447
1448
1449
1450
1451
1452
1453
1454
1455
1456
1457
1458
1459
1460
1461
1462
1463
1464
1465
1466
1467
1468
1469
1470
1471
1472
1473
1474
1475
1476
1477
1478
1479
1480
1481
1482
1483
1484
1485
1486
1487
1488
1489
1490
1491
1492
1493
1494
1495
1496
1497
1498
1499
1500
1501
1502
1503
1504
1505
1506
1507
1508
1509
1510
1511
1512
1513
1514
1515
1516
1517
1518
1519
1520
1521
1522
1523
1524
1525
1526
1527
1528
1529
1530
1531
1532
1533
1534
1535
1536
1537
1538
1539
1540
1541
1542
1543
1544
1545
1546
1547
1548
1549
1550
1551
1552
1553
1554
1555
1556
1557
1558
1559
1560
1561
1562
1563
1564
1565
1566
1567
1568
1569
1570
1571
1572
1573
1574
1575
1576
1577
1578
1579
1580
1581
1582
1583
1584
1585
1586
1587
1588
1589
1590
1591
1592
1593
1594
1595
1596
1597
1598
1599
1600
1601
1602
1603
1604
1605
1606
1607
1608
1609
1610
1611
1612
1613
1614
1615
1616
1617
1618
1619
1620
1621
1622
1623
1624
1625
1626
1627
1628
1629
1630
1631
1632
1633
1634
1635
1636
1637
1638
1639
1640
1641
1642
1643
1644
1645
1646
1647
1648
1649
1650
1651
1652
1653
1654
1655
1656
1657
1658
1659
1660
1661
1662
1663
1664
1665
1666
1667
1668
1669
1670
1671
1672
1673
1674
1675
1676
1677
1678
1679
1680
1681
1682
1683
1684
1685
1686
1687
1688
1689
1690
1691
1692
1693
1694
1695
1696
1697
1698
1699
1700
1701
1702
1703
1704
1705
1706
1707
#
# Copyright (c) 2002, 2003, 2004, 2005, 2006 Art Haas
#
# This file is part of PythonCAD.
#
# PythonCAD 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 of the License, or
# (at your option) any later version.
#
# PythonCAD 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 PythonCAD; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
#
#
# class stuff for circles
#


from __future__ import generators

import math

from PythonCAD.Generic import tolerance
from PythonCAD.Generic import point
from PythonCAD.Generic import graphicobject
from PythonCAD.Generic import style
from PythonCAD.Generic import linetype
from PythonCAD.Generic import color
from PythonCAD.Generic import quadtree
from PythonCAD.Generic import util
from PythonCAD.Generic import tangent
from PythonCAD.Generic.pyGeoLib import Vector

class Circle(graphicobject.GraphicObject):
    """A base-class for Circles and Arcs

A Circle has two attributes:

center: A Point object
radius: The Circle's radius

A Circle has the following methods:

{get/set}Center(): Get/Set the center Point of a Circle.
{get/set}Radius(): Get/Set the radius of a Circle.
move(): Move the Circle.
circumference(): Get the Circle's circumference.
area(): Get the Circle's area.
mapCoords(): Find the nearest Point on the Circle to a coordinate pair.
inRegion(): Returns whether or not a Circle can be seen in a bounded area.
clone(): Return an indentical copy of a Circle.
    """

    __defstyle = None

    __messages = {
        'moved' : True,
        'center_changed' : True,
        'radius_changed' : True,
        }

    def __init__(self, center, radius, st=None, lt=None, col=None, th=None, **kw):
        """Initialize a Circle.

Circle(center, radius[, st, lt, col, th])

The center should be a Point, or a two-entry tuple of floats,
and the radius should be a float greater than 0.
        """
        _cp = center
        if not isinstance(_cp, point.Point):
            _cp = point.Point(center)
        _r = util.get_float(radius)
        if not _r > 0.0:
            raise ValueError, "Invalid radius: %g" % _r
        _st = st
        if _st is None:
            _st = self.getDefaultStyle()
        super(Circle, self).__init__(_st, lt, col, th, **kw)
        self.__radius = _r
        self.__center = _cp
        _cp.connect('moved', self.__movePoint)
        _cp.connect('change_pending', self.__pointChangePending)
        _cp.connect('change_complete', self.__pointChangeComplete)
        _cp.storeUser(self)

    def __eq__(self, obj):
        """Compare a Circle to another for equality.
        """
        if not isinstance(obj, Circle):
            return False
        if obj is self:
            return True
        return (self.__center == obj.getCenter() and
                abs(self.__radius - obj.getRadius()) < 1e-10)

    def __ne__(self, obj):
        """Compare a Circle to another for inequality.
        """
        if not isinstance(obj, Circle):
            return True
        if obj is self:
            return False
        return (self.__center != obj.getCenter() or
                abs(self.__radius - obj.getRadius()) > 1e-10)

    def getDefaultStyle(cls):
        if cls.__defstyle is None:
            _s = style.Style(u'Default Circle Style',
                             linetype.Linetype(u'Solid', None),
                             color.Color(0xffffff),
                             1.0)
            cls.__defstyle = _s
        return cls.__defstyle

    getDefaultStyle = classmethod(getDefaultStyle)

    def setDefaultStyle(cls, s):
        if not isinstance(s, style.Style):
            raise TypeError, "Invalid style: " + `type(s)`
        cls.__defstyle = s

    setDefaultStyle = classmethod(setDefaultStyle)

    def finish(self):
        self.__center.disconnect(self)
        self.__center.freeUser(self)
        self.__center = self.__radius = None
        super(Circle, self).finish()

    def setStyle(self, s):
        """Set the Style of the Circle.

setStyle(s)

This method extends GraphicObject::setStyle().
        """
        _s = s
        if _s is None:
            _s = self.getDefaultStyle()
        super(Circle, self).setStyle(_s)

    def getValues(self):
        """Return values comprising the Circle.

getValues()

This method extends the GraphicObject::getValues() method.
        """
        _data = super(Circle, self).getValues()
        _data.setValue('type', 'circle')
        _data.setValue('center', self.__center.getID())
        _data.setValue('radius', self.__radius)
        return _data

    def getCenter(self):
        """Return the center Point of the Circle.

getCenter()
        """
        return self.__center

    def setCenter(self, c):
        """Set the center Point of the Circle.

setCenter(c)

The argument must be a Point or a tuple containing
two float values.
        """
        if self.isLocked():
            raise RuntimeError, "Setting center not allowed - object locked."
        _cp = self.__center
        if not isinstance(c, point.Point):
            raise TypeError, "Invalid center point: " + `type(c)`
        if _cp is not c:
            _cp.disconnect(self)
            _cp.freeUser(self)
            self.startChange('center_changed')
            self.__center = c
            self.endChange('center_changed')
            self.sendMessage('center_changed', _cp)
            c.connect('moved', self.__movePoint)
            c.connect('change_pending', self.__pointChangePending)
            c.connect('change_complete', self.__pointChangeComplete)
            c.storeUser(self)
            if abs(_cp.x - c.x) > 1e-10 or abs(_cp.y - c.y) > 1e-10:
                self.sendMessage('moved', _cp.x, _cp.y, self.__radius)
            self.modified()

    center = property(getCenter, setCenter, None, "Circle center")

    def getRadius(self):
        """Return the radius of the the Circle.

getRadius()
        """
        return self.__radius

    def setRadius(self, radius):
        """Set the radius of the Circle.

setRadius(radius)

The argument must be float value greater than 0.
        """
        if self.isLocked():
            raise RuntimeError, "Setting radius not allowed - object locked."
        _r = util.get_float(radius)
        if not _r > 0.0:
            raise ValueError, "Invalid radius: %g" % _r
        _cr = self.__radius
        if abs(_cr - _r) > 1e-10:
            self.startChange('radius_changed')
            self.__radius = _r
            self.endChange('radius_changed')
            self.sendMessage('radius_changed', _cr)
            _cx, _cy = self.__center.getCoords()
            self.sendMessage('moved', _cx, _cy, _cr)
            self.modified()

    radius = property(getRadius, setRadius, None, "Circle radius")

    def move(self, dx, dy):
        """Move a Circle.

move(dx, dy)

The first argument gives the x-coordinate displacement,
and the second gives the y-coordinate displacement. Both
values should be floats.
        """
        if self.isLocked():
            raise RuntimeError, "Setting radius not allowed - object locked."
        _dx = util.get_float(dx)
        _dy = util.get_float(dy)
        if abs(_dx) > 1e-10 or abs(_dy) > 1e-10:
            _x, _y = self.__center.getCoords()
            self.ignore('moved')
            try:
                self.__center.move(_dx, _dy)
            finally:
                self.receive('moved')
            self.sendMessage('moved', _x, _y, self.__radius)

    def circumference(self):
        """Return the circumference of the Circle.

circumference()
        """
        return 2.0 * math.pi * self.__radius

    def area(self):
        """Return the area enclosed by the Circle.

area()
        """
        return math.pi * pow(self.__radius, 2)
    def GetTangentPoint(self,x,y,outx,outy):
        """
            Get the tangent from an axternal point
            args:
                x,y is a point near the circle
                xout,yout is a point far from the circle
            return:
                a tuple(x,y,x1,xy) that define the tangent line
        """
        firstPoint=point.Point(x,y)
        fromPoint=point.Point(outx,outy)
        twoPointDistance=self.__center.Dist(fromPoint)
        if(twoPointDistance<self.__radius):
            return None,None
        originPoint=point.Point(0.0,0.0)        
        tanMod=math.sqrt(pow(twoPointDistance,2)-pow(self.__radius,2))
        tgAngle=math.asin(self.__radius/twoPointDistance)
        #Compute the x versor
        xPoint=point.Point(1.0,0.0)
        xVector=Vector(originPoint,xPoint)
        twoPointVector=Vector(fromPoint,self.__center)
        rightAngle=twoPointVector.Ang(xVector)                
        cx,cy=self.__center.getCoords()        
        if(outy>cy): #stupid situation 
            rightAngle=-rightAngle
        posAngle=rightAngle+tgAngle
        negAngle=rightAngle-tgAngle
        #Compute the Positive Tangent
        xCord=math.cos(posAngle)
        yCord=math.sin(posAngle)
        dirPoint=point.Point(xCord,yCord)#Versor that point at the tangentPoint
        ver=Vector(originPoint,dirPoint)
        ver.Mult(tanMod)
        tangVectorPoint=ver.Point()
        posPoint=point.Point(tangVectorPoint+(outx,outy))
        #Compute the Negative Tangent
        xCord=math.cos(negAngle)
        yCord=math.sin(negAngle)
        dirPoint=point.Point(xCord,yCord)#Versor that point at the tangentPoint
        ver=Vector(originPoint,dirPoint)
        ver.Mult(tanMod)
        tangVectorPoint=ver.Point()
        negPoint=point.Point(tangVectorPoint+(outx,outy))
        if(firstPoint.Dist(posPoint)<firstPoint.Dist(negPoint)):
            return posPoint.getCoords()     
        else:
            return negPoint.getCoords()        
    def GetRadiusPointFromExt(self,x,y):
        """
            get The intersecrion point from the line(x,y,cx,cy) and the circle
        """
        _cx, _cy = self.__center.getCoords()
        _r = self.__radius
        centerPoint=point.Point(_cx,_cy)
        outPoint=point.Point(x,y)
        vector=Vector(outPoint,centerPoint)
        vNorm=vector.Norm()
        newNorm=abs(vNorm-_r)
        magVector=vector.Mag()
        magVector.Mult(newNorm)
        newPoint=magVector.Point()
        intPoint=point.Point(outPoint+newPoint)
        return intPoint.getCoords()        
    def mapCoords(self, x, y, tol=tolerance.TOL):
        """Return the nearest Point on the Circle to a coordinate pair.

mapCoords(x, y[, tol])

The function has two required arguments:

x: A Float value giving the x-coordinate
y: A Float value giving the y-coordinate

There is a single optional argument:

tol: A float value equal or greater than 0.0

This function is used to map a possibly near-by coordinate pair to
an actual Point on the Circle. If the distance between the actual
Point and the coordinates used as an argument is less than the tolerance,
the actual Point is returned. Otherwise, this function returns None.
        """
        _x = util.get_float(x)
        _y = util.get_float(y)
        _t = tolerance.toltest(tol)
        _cx, _cy = self.__center.getCoords()
        _r = self.__radius
        _dist = math.hypot((_x - _cx), (_y - _cy))
        if abs(_dist - _r) < _t:
            _angle = math.atan2((_y - _cy),(_x - _cx))
            _xoff = _r * math.cos(_angle)
            _yoff = _r * math.sin(_angle)
            return (_cx + _xoff), (_cy + _yoff)
        return None

    def inRegion(self, xmin, ymin, xmax, ymax, fully=False):
        """Return whether or not an Circle exists within a region.

inRegion(xmin, ymin, xmax, ymax[, fully])

The first four arguments define the boundary. The optional
fifth argument 'fully' indicates whether or not the Circle
must be completely contained within the region or just pass
through it.
        """
        _xmin = util.get_float(xmin)
        _ymin = util.get_float(ymin)
        _xmax = util.get_float(xmax)
        if _xmax < _xmin:
            raise ValueError, "Illegal values: xmax < xmin"
        _ymax = util.get_float(ymax)
        if _ymax < _ymin:
            raise ValueError, "Illegal values: ymax < ymin"
        util.test_boolean(fully)
        _xc, _yc = self.__center.getCoords()
        _r = self.__radius
        #
        # cheap test to see if circle cannot be in region
        #
        if (((_xc - _r) > _xmax) or
            ((_yc - _r) > _ymax) or
            ((_xc + _r) < _xmin) or
            ((_yc + _r) < _ymin)):
            return False
        _val = False
        _bits = 0
        #
        # calculate distances from center to region boundary
        #
        if abs(_xc - _xmin) < _r: _bits = _bits | 1 # left edge
        if abs(_xc - _xmax) < _r: _bits = _bits | 2 # right edge
        if abs(_yc - _ymin) < _r: _bits = _bits | 4 # bottom edge
        if abs(_yc - _ymax) < _r: _bits = _bits | 8 # top edge
        if _bits == 0:
            #
            # circle must be visible - the center is in
            # the region and is more than the radius from
            # each edge
            #
            _val = True
        else:
            #
            # calculate distance to corners of region
            #
            if math.hypot((_xc - _xmin), (_yc - _ymax)) < _r:
                _bits = _bits | 0x10 # upper left
            if math.hypot((_xc - _xmax), (_yc - _ymin)) < _r:
                _bits = _bits | 0x20 # lower right
            if math.hypot((_xc - _xmin), (_yc - _ymin)) < _r:
                _bits = _bits | 0x40 # lower left
            if math.hypot((_xc - _xmax), (_yc - _ymax)) < _r:
                _bits = _bits | 0x80 # upper right
            #
            # if all bits are set then distance from circle center
            # to region endpoints is less than radius - circle
            # entirely outside the region
            #
            _val = not ((_bits == 0xff) or fully)
        return _val

    def __pointChangePending(self, p, *args):
        _alen = len(args)
        if _alen < 1:
            raise ValueError, "Invalid argument count: %d" % _alen
        if args[0] == 'moved':
            self.startChange('moved')

    def __pointChangeComplete(self, p, *args):
        _alen = len(args)
        if _alen < 1:
            raise ValueError, "Invalid argument count: %d" % _alen
        if args[0] == 'moved':
            self.endChange('moved')

    def __movePoint(self, p, *args):
        _alen = len(args)
        if _alen < 2:
            raise ValueError, "Invalid argument count: %d" % _alen
        _x = util.get_float(args[0])
        _y = util.get_float(args[1])
        _cp = self.__center
        if p is not _cp:
            raise ValueError, "Point is not circle center: " + `p`
        _x, _y = _cp.getCoords()
        self.sendMessage('moved', _x, _y, self.__radius)

    def clone(self):
        """Create an identical copy of a Circle

clone()
        """
        _cp = self.__center.clone()
        _st = self.getStyle()
        _lt = self.getLinetype()
        _col = self.getColor()
        _th = self.getThickness()
        return Circle(_cp, self.__radius, _st, _lt, _col, _th)

    def sendsMessage(self, m):
        if m in Circle.__messages:
            return True
        return super(Circle, self).sendsMessage(m)

    def clipToRegion(self, xmin, ymin, xmax, ymax):
        """Return the portions of a circle visible in a region.

clipToRegion(xmin, ymin, xmax, ymax)

This method returns a list of tuples. Each tuple contains two
float values representing arcs which are seen in the region. Each
tuple has the start angle and end angle.
        """
        _xmin = util.get_float(xmin)
        _ymin = util.get_float(ymin)
        _xmax = util.get_float(xmax)
        if _xmax < _xmin:
            raise ValueError, "Illegal values: xmax < xmin"
        _ymax = util.get_float(ymax)
        if _ymax < _ymin:
            raise ValueError, "Illegal values: ymax < ymin"
        _xc, _yc = self.__center.getCoords()
        _r = self.__radius
        _bits = 0
        _arcs = []
        #
        # calculate distances from center to region boundaries
        #
        if abs(_xc - _xmin) < _r: _bits = _bits | 1 # left edge
        if abs(_xc - _xmax) < _r: _bits = _bits | 2 # right edge
        if abs(_yc - _ymin) < _r: _bits = _bits | 4 # bottom edge
        if abs(_yc - _ymax) < _r: _bits = _bits | 8 # top edge
        #
        # test if the circle is entirely contained or entirely
        # outside the region
        #
        # print "bits: %#02x" % _bits
        if _bits == 0:
            #
            # if the circle center is in region then the entire
            # circle is visible since the distance from the center
            # to any edge is greater than the radius. If the center
            # is not in the region then the circle is not visible in
            # the region because the distance to any edge is greater
            # than the radius, and so one of the bits should have been
            # set
            #
            if ((_xmin < _xc <_xmax) and (_ymin < _yc < _ymax)):
                print "circle completely inside region"
                _arcs.append((0.0, 360.0)) # fully in region
        else:
            #
            # calculate distance to corners of region
            #
            if math.hypot((_xc - _xmin), (_yc - _ymax)) < _r:
                _bits = _bits | 0x10 # upper left, NW corner
            if math.hypot((_xc - _xmax), (_yc - _ymin)) < _r:
                _bits = _bits | 0x20 # lower right, SE corner
            if math.hypot((_xc - _xmin), (_yc - _ymin)) < _r:
                _bits = _bits | 0x40 # lower left, SW corner
            if math.hypot((_xc - _xmax), (_yc - _ymax)) < _r:
                _bits = _bits | 0x80 # upper right, NE corner
            #
            # based on the bit pattern the various possible intersections
            # can be determined
            #
            # there is much room for optimization in here - many
            # of the distances from the center point to the region
            # edges and corners are calculated numerous times, the
            # square of these values are also repeatedly calculated ...
            #
            _rsqr = _r * _r
            # _rtd = 180.0/math.pi
            print "bits: %#02x" % _bits
            if _bits == 0x01: # circle crosses left edge twice
                print "circle crosses left edge twice"
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _yt = _yc + _yd
                _yb = _yc - _yd
                print "yt: %g; yb: %g" % (_yt, _yb)
                assert _yt < _ymax, "ytop > ymax"
                assert _yb > _ymin, "ybot < ymin"
                if (_ymin < _yc < _ymax): # must be true
                    _at = _calc_angle((_yt - _yc), (_xmin - _xc))
                    _ab = _calc_angle((_yb - _yc), (_xmin - _xc))
                    _arcs.append((_ab, ((360.0 - _ab) + _at)))
                    if _xc > _xmin: # circle inside region
                        print "circle center inside region"
                    else:
                        print "circle center outside"
                else:
                    if _yc < _ymin:
                        print "yc < ymin (%g < %g)" % (_yc, _ymin)
                    elif _yc > _ymax:
                        print "yc > ymax (%g > %g)" % (_yc, _ymax)
                    else:
                        print "unexpected y: (%g, %g, %g)" % (_ymin, _yc, _ymax)
            elif _bits == 0x02: # circle crosses right edge twice
                print "circle crosses right edge twice"
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yt = _yc + _yd
                _yb = _yc - _yd
                print "yt: %g; yb: %g" % (_yt, _yb)
                assert _yt < _ymax, "ytop > ymax"
                assert _yb > _ymin, "ybot < ymin"
                if (_ymin < _yc < _ymax): # must be true
                    _at = _calc_angle((_yt - _yc), (_xmin - _xc))
                    _ab = _calc_angle((_yb - _yc), (_xmin - _xc))
                    _arcs.append((_at, (_ab - _at)))
                    if _xc < _xmax: # circle inside region
                        print "circle inside"
                    else:
                        print "circle outside"
                else:
                    if _yc < _ymin:
                        print "yc < ymin (%g < %g)" % (_yc, _ymin)
                    elif _yc > _ymax:
                        print "yc > ymax (%g > %g)" % (_yc, _ymax)
                    else:
                        print "unexpected y: (%g, %g, %g)" % (_ymin, _yc, _ymax)
            elif _bits == 0x04: # circle crosses bottom twice
                print "circle crosses bottom twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xr = _xc + _xd
                _xl = _xc - _xd
                print "xl: %g; xr: %g" % (_xl, _xr)
                assert _xr < _xmax, "xright > xmax"
                assert _xl > _xmin, "xeft < xmin"
                if (_xmin < _xc < _xmax): # must be true
                    _al = _calc_angle((_ymin - _yc), (_xl - _xc))
                    _ar = _calc_angle((_ymin - _yc), (_xr - _xc))
                    _arcs.append((_ar, (360.0 - _ar + _al)))
                    if _yc > _ymin: # circle inside region
                        print "circle inside"
                    else:
                        print "circle outside"
                else:
                    if _xc < _xmin:
                        print "xc < xmin (%g < %g)" % (_xc, _xmin)
                    elif _yc > _ymax:
                        print "xc > xmax (%g > %g)" % (_xc, _xmax)
                    else:
                        print "unexpected x: (%g, %g, %g)" % (_xmin, _xc, _xmax)
            elif _bits == 0x08: # circle crosses top twice
                print "circle crosses top twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xr = _xc + _xd
                _xl = _xc - _xd
                print "xl: %g; xr: %g" % (_xl, _xr)
                assert _xr < _xmax, "xright > xmax"
                assert _xl > _xmin, "xeft < xmin"
                if (_xmin < _xc < _xmax): # must be true
                    _al = _calc_angle((_ymax - _yc), (_xl - _xc))
                    _ar = _calc_angle((_ymax - _yc), (_xr - _xc))
                    _arcs.append((_al, (360.0 - _al + _ar)))
                    if _yc < _ymax: # circle inside region
                        print "circle inside"
                    else:
                        print "circle outside"
                else:
                    if _xc < _xmin:
                        print "xc < xmin (%g < %g)" % (_xc, _xmin)
                    elif _yc > _ymax:
                        print "xc > xmax (%g > %g)" % (_xc, _xmax)
                    else:
                        print "unexpected x: (%g, %g, %g)" % (_xmin, _xc, _xmax)
            elif _bits == 0x09: # circle crosses left and top twice
                print "circle crosses left and top twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xr = _xc + _xd
                _xl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _yt = _yc + _yd
                _yb = _yc - _yd
                # top -> left
                _a1 = _calc_angle((_ymax - _yc), (_xl - _xc))
                _a2 = _calc_angle((_yt - _yc), (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> top
                _a1 = _calc_angle((_yb - _yc), (_xmin - _xc))
                _a2 = _calc_angle((_ymax - _yc), (_xr - _xc))
                _arcs.append((_a1, (360.0 - _a1 + _a2)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside"
                else:
                    print "unexpected center for region: (%g, %g)" % (_xc, _yc)
            elif _bits == 0x0a: # circle crosses top and right twice
                print "circle crosses top and right twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xr = _xc + _xd
                _xl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yt = _yc + _yd
                _yb = _yc - _yd
                # top -> right
                _a1 = _calc_angle((_ymax - _yc), (_xl - _xc))
                _a2 = _calc_angle((_yb - _yc), (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> top
                _a1 = _calc_angle((_yt - _yc), (_xmax - _xc))
                _a2 = _calc_angle((_ymax - _yc), (_xr - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside"
                else:
                    print "unexpected center for region: (%g, %g)" % (_xc, _yc)
            elif _bits == 0x06: # circle crosses right and bottom twice
                print "circle crosses right and bottom twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xr = _xc + _xd
                _xl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yt = _yc + _yd
                _yb = _yc - _yd
                # right -> bottom
                _a1 = _calc_angle((_yt - _yc), (_xmax - _xc))
                _a2 = _calc_angle((_ymin - _yc), (_xl - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right
                _a1 = _calc_angle((_ymin - _yc), (_xr - _xc))
                _a2 = _calc_angle((_yb - _yc), (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside"
                else:
                    print "unexpected center for region: (%g, %g)" % (_xc, _yc)
            elif _bits == 0x05: # circle crosses bottom and left twice
                print "circle crosses bottom and left twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xr = _xc + _xd
                _xl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _yt = _yc + _yd
                _yb = _yc - _yd
                # left -> bottom
                _a1 = _calc_angle((_yb - _yc), (_xmin - _xc))
                _a2 = _calc_angle((_ymin - _yc), (_xl - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> left
                _a1 = _calc_angle((_ymin - _yc), (_xr - _xc))
                _a2 = _calc_angle((_yt - _xc), (_xmin - _xc))
                _arcs.append((_a1, (360.0 - _a1 + _a2)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside"
                else:
                    print "unexpected center for region: (%g, %g)" % (_xc, _yc)
            elif _bits == 0x0c: # circle crosses top and bottom twice
                print "circle crosses top and bottom twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xtr = _xc + _xd
                _xtl = _xc - _xd
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xbr = _xc + _xd
                _xbl = _xc - _xd
                # top -> bottom
                _a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
                _a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> top
                _a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
                _a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
                _arcs.append((_a1, (360.0 - _a1 + _a2)))
                if (_ymin < _yc < _ymax): # needed?
                    print "circle inside region"
                elif _yc < _ymin:
                    print "circle below region"
                else:
                    print "circle above region"
            elif _bits == 0x03: # circle crosses left and right twice
                print "circle crosses left and right twice"
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _ylt = _yc + _yd
                _ylb = _yc - _yd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yrt = _yc + _yd
                _yrb = _yc - _yd
                # left -> right
                _a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
                _a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> left
                _a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
                _a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if (_xmin < _xc < _xmax):
                    print "circle inside region"
                elif _xc < _xmin:
                    print "circle left of region"
                else:
                    print "circle right of region"
            elif _bits == 0x0b: # circle through left, top, right twice
                print "circle through left & top & right twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xtr = _xc + _xd
                _xtl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _ylt = _yc + _yd
                _ylb = _yc - _yd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yrt = _yc + _yd
                _yrb = _yc - _yd
                # top -> left
                _a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
                _a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> right
                _a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
                _a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right > top
                _a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
                _a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if (_xmin < _xc < _xmax):
                    print "circle inside region"
                elif _xc < _xmin:
                    print "xc < xmin (%g, %g)" % (_xc, _xmin)
                else:
                    print "xc > xmax (%g, %g)" % (_xc, _xmax)
                if _yc < _ymin:
                    print "yc < ymin (%g, %g)" % (_yc, _ymin)
                else:
                    if _yc > _ymax:
                        print "yc > ymax (%g, %g)" % (_yc, _ymax)
            elif _bits == 0x0e: # circle through top, right, bottom twice
                print "circle through top & right & bottom twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xtr = _xc + _xd
                _xtl = _xc - _xd
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xbr = _xc + _xd
                _xbl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yrt = _yc + _yd
                _yrb = _yc - _yd
                # top -> bottom
                _a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
                _a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right
                _a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
                _a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> top
                _a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
                _a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if (_ymin < _yc < _ymax):
                    print "circle inside region"
                elif _yc < _ymin:
                    print "yc < ymin (%g, %g)" % (_yc, _ymin)
                else:
                    print "yc > ymax (%g, %g)" % (_yc, _ymax)
                if _xc < _xmin:
                    print "xc < xmin (%g, %g)" % (_xc, _xmin)
                else:
                    if _xc > _xmax:
                        print "xc > xmax (%g, %g)" % (_xc, _xmax)
            elif _bits == 0x07: # circle though right, bottom, left twice
                print "circle through right & bottom & left twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xbr = _xc + _xd
                _xbl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _yrt = _yc + _yd
                _yrb = _yc - _yd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _ylt = _yc + _yd
                _ylb = _yc - _yd
                # right -> left
                _a1 = _calc_angle((_yrt - _yc), (_xmax - _xc))
                _a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom
                _a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
                _a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right
                _a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
                _a2 = _calc_angle((_yrb - _yc), (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if (_xmin < _xc < _xmax):
                    print "circle inside region"
                elif _xc < _xmin:
                    print "xc < xmin (%g, %g)" % (_xc, _xmin)
                else:
                    print "xc > xmax (%g, %g)" % (_xc, _xmax)
                if _yc < _ymin:
                    print "yc < ymin (%g, %g)" % (_yc, _ymin)
                else:
                    if _yc > _ymax:
                        print "yc > ymax (%g, %g)" % (_yc, _ymax)
            elif _bits == 0x0d: # circle through bottom, left, top twice
                print "circle through bottom & left & top twice"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _xbr = _xc + _xd
                _xbl = _xc - _xd
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xtr = _xc + _xd
                _xtl = _xc - _xd
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _ylt = _yc + _yd
                _ylb = _yc - _yd
                # bottom -> top
                _a1 = _calc_angle((_ymin - _yc), (_xbr - _xc))
                _a2 = _calc_angle((_ymax - _yc), (_xtr - _xc))
                _arcs.append((_a1, (360.0 - _a1 + _a2)))
                # top -> left
                _a1 = _calc_angle((_ymax - _yc), (_xtl - _xc))
                _a2 = _calc_angle((_ylt - _yc), (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom
                _a1 = _calc_angle((_ylb - _yc), (_xmin - _xc))
                _a2 = _calc_angle((_ymin - _yc), (_xbl - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if (_ymin < _yc < _ymax):
                    print "circle inside region"
                elif _yc < _ymin:
                    print "yc < ymin (%g, %g)" % (_yc, _ymin)
                else:
                    print "yc > ymax (%g, %g)" % (_yc, _ymax)
                if _xc < _xmin:
                    print "xc < xmin (%g, %g)" % (_xc, _xmin)
                else:
                    if _xc > _xmax:
                        print "xc > xmax (%g, %g)" % (_xc, _xmax)
            elif _bits == 0x19: # circle through left, top, and NW corner
                print "circle through left and top with NW corner"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                if _xc > _xmax:
                    _arcs.append((_a1, (_a2 - _a1)))
                else:
                    _arcs.append((_a1, (360.0 - _a1 + _a2)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside region"
                else:
                    print "circle outside region"
            elif _bits == 0x8a: # circle through right, top, and NE corner
                print "circle through right and top with NE corner"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside region"
                else:
                    print "circle outside region"
            elif _bits == 0x26: # circle through right, bottom, and SE corner
                print "circle through right and bottom with SE corner"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside region"
                else:
                    print "circle outside region"
            elif _bits == 0x45: # circle through left, bottom, and SW corner
                print "circle through left and bottom with SW corner"
                _xd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                if _xc < _xmin:
                    _arcs.append((_a1, (_a2 - _a1)))
                else:
                    _arcs.append((_a1, (360.0 - _a1 + _a2)))
                if ((_xmin < _xc < _xmax) and
                    (_ymin < _yc < _ymax)):
                    print "circle inside region"
                else:
                    print "circle outside region"
            elif _bits == 0x9b: # circle through left, right, NE and NW corner
                print "circle through left and right with NE, NW corners"
                _yd = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _yd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc < _xmin:
                    print "x < xmin (%g < %g)" % (_xc, _xmin)
                elif _xc > _xmax:
                    print "x > xmax (%g > %g)" % (_xc, _xmax)
                else:
                    if _yc < _ymax:
                        print "circle center in region"
                    else:
                        print "circle center outside region"
            elif _bits == 0xae: # circle through top, botton, NE and SE corner
                print "circle through top and bottom with NE, SE corners"
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc < _ymin:
                    print "y < ymin (%g < %g)" % (_yc, _ymin)
                elif _yc > _ymax:
                    print "y > ymax (%g > %g)" % (_yc, _ymax)
                else:
                    if _xc < _xmax:
                        print "circle center in region"
                    else:
                        print "circle center outside region"
            elif _bits == 0x67: # circle through left, right, SE and SW corner
                print "circle through left and right with SE, SW corners"
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc < _xmin:
                    print "x < xmin (%g < %g)" % (_xc, _xmin)
                elif _xc > _xmax:
                    print "x > xmax (%g > %g)" % (_xc, _xmax)
                else:
                    if _yc > _ymin:
                        print "circle center inside region"
                    else:
                        print "circle center outside region"
            elif _bits == 0x5d: # circle through top, bottom, SW and NW corner
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                if _xc > _xmin:
                    _arcs.append((_a1, (_a2 - _a1)))
                else:
                    _arcs.append((_a1, (360.0 - _a1 + _a2)))
                print "circle through top and bottom with SW, NW corners"
                if _yc < _ymin:
                    print "y < ymin (%g < %g)" % (_yc, _ymin)
                elif _yc > _ymax:
                    print "y > ymax (%g > %g)" % (_yc, _ymax)
                else:
                    if _xc > _xmin:
                        print "circle center inside region"
                    else:
                        print "circle center outside region"
            elif _bits == 0xbf: # circle center NE, crosses left and bottom
                print "circle center NE of region, crosses left and bottom"
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
            elif _bits == 0xef: # circle center SE, crosses left and top
                print "circle center SE of region, crosses left and top"
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
            elif _bits == 0x7f: # circle center SW, crosses top and right
                print "circle center SW of region, crosses top and right"
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
            elif _bits == 0xdf: # circle center NW, crosses right and bottom
                print "circle center NW of region, crosses right and bottom"
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
            elif _bits == 0x9f: # circle center N, crosses left, right, bottom
                print "circle center N, crosses left, right, and twice bottom"
                # left -> bottom
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a1 = _calc_angle(-_yd, (xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right; _xd now positive
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc < _ymax:
                    print "yc < ymax (%g < %g)" % (_yc, _ymax)
                if ((_xc <  _xmin) or (_xc > _xmax)):
                    print "xc: %g; xmin: %g; xmax: %g" % (_xc, _xmin, _xmax)
            elif _bits == 0xaf: # circle center W, crosses bottom, left, top
                print "circle center W, crosses bottom, top, and twice left"
                # top -> left
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom; _yd now negative
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc < _xmax:
                    print "xc < xmax (%g < %g)" % (_xc, _xmax)
                if ((_yc < _ymin) or (_yc > _ymax)):
                    print "yc: %g; ymin: %g; ymax: %g" % (_yc, _ymin, _ymax)
            elif _bits == 0x6f: # circle center S, crosses left, top, right
                print "circle center S, crosses left, right, and twice top"
                # right -> top
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # top -> left; _xd now negative
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc > _ymin:
                    print "yc > ymin (%g > %g)" % (_yc, _ymin)
                if ((_xc <  _xmin) or (_xc > _xmax)):
                    print "xc: %g; xmin: %g; xmax: %g" % (_xc, _xmin, _xmax)
            elif _bits == 0x5f: # circle center E, crosses top, right, bottom
                print "circle center E, crosses top, bottom, and twice right"
                # bottom -> right
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> top, _yd now positive
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc > _xmin:
                    print "xc > xmin (%g > %g)" % (_xc, _xmin)
                if ((_yc < _ymin) or (_yc > _ymax)):
                    print "yc: %g; ymin: %g; ymax: %g" % (_yc, _ymin, _ymax)
            elif _bits == 0x1d:
                print "circle center N near NW, crosses T&L once, B twice"
                # left -> bottom
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # top -> bottom; _xd now positive
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                if _yc > _ymax:
                    _arcs.append((_a1, (_a2 - _a1)))
                else:
                    _arcs.append((_a1, (360.0 - _a1 + _a2)))
                if _xc < _xmin:
                    print "x < xmin (%g < %g)" % (_xc, _xmin)
                if _yc < _ymax:
                    print "y < ymax (%g < %g)" % (_yc, _ymax)
            elif _bits == 0x4d:
                print "circle center S near SW, crosses B&L once, T twice"
                # bottom -> top
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # top -> left, _xd now negative
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc < _xmin:
                    print "x < xmin (%g < %g)" % (_xc, _xmin)
                if _yc > _ymin:
                    print "y > ymin (%g > %g)" % (_yc, _ymin)
            elif _bits == 0x2e:
                print "circle center S near SE, crosses B&R once, T twice"
                # right -> top
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # top -> bottom; _xd now negative
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc > _xmax:
                    print "x > xmax (%g > %g)" % (_xc, _xmax)
                if _yc > _ymin:
                    print "y > ymin (%g > %g)" % (_yc, _ymin)
            elif _bits == 0x8e:
                print "circle center N near NE, crosses T&R once, B twice"
                # top -> bottom
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right, _xd now positive
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _xc > _xmax:
                    print "x > xmax (%g > %g)" % (_xc, _xmax)
                if _yc < _ymax:
                    print "y < ymax (%g < %g)" % (_yc, _ymax)
            elif _bits == 0x1b:
                print "circle center E near NW, crosses T&L once, R twice"
                # left -> right
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> top; _yd now positive
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc > _ymax:
                    print "y > ymax (%g > %g)" % (_yc, _ymax)
                if _xc > _xmin:
                    print "x > xmin (%g > %g)" % (_xc, _xmin)
            elif _bits == 0x8b:
                print "circle center W near NE, crosses T&R once, L twice"
                # top -> left
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> right; _yd now negative
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc > _ymax:
                    print "y > ymax (%g > %g)" % (_yc, _ymax)
                if _xc < _xmax:
                    print "x < xmax (%g < %g)" % (_xc, _xmax)
            elif _bits == 0x27:
                print "circle center W near SE, crosses B&R once, L twice"
                # right -> left
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                print "a1: %g; a2: %g" % (_a1, _a2)
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom; now _yd is negative
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                print "a1: %g; a2: %g" % (_a1, _a2)
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc < _ymin:
                    print "y < ymin (%g < %g)" % (_yc, _ymin)
                if _xc < _xmax:
                    print "x < xmax (%g < %g)" % (_xc, _xmax)
            elif _bits == 0x47:
                print "circle center E near SW, crosses B&L once, R twice"
                # bottom -> right
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> left; now _yd is positive
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if _yc < ymin:
                    print "y < ymin (%g < %g)" % (_yc, _ymin)
                if _xc > _xmin:
                    print "x > xmin (%g > %g)" % (_xc, _xmin)
            elif _bits == 0x1f:
                print "circle center NW, crosses L&T once, R&B twice"
                # right -> top
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right; _xd now positive
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
                    print "circle center in region"
                else:
                    print "circle center out of region"
            elif _bits == 0x8f:
                print "circle center NE, crosses T&R once, B&L twice"
                # top -> left
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom; _yd now negative
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right; _xd now positive
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
                    print "circle center in region"
                else:
                    print "circle center out of region"
            elif _bits == 0x2f:
                print "circle center SE, crosses L&T twice, R&B once"
                # top -> left
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom; _yd now negative
                _a1 = _calc_angle(-_yd, (_xmin - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a2 = _calc_angle((_ymin - _yc), -_xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> top
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
                    print "circle center in region"
                else:
                    print "circle center out of region"
            elif _bits == 0x4f:
                print "circle center SW, crosses T&R twice, B&L once"
                # bottom -> right
                _xd = math.sqrt(_rsqr - pow((_ymin - _yc), 2))
                _a1 = _calc_angle((_ymin - _yc), _xd)
                _yd = math.sqrt(_rsqr - pow((_xmax - _xc), 2))
                _a2 = _calc_angle(-_yd, (_xmax - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # right -> top; _yd now positive
                _a1 = _calc_angle(_yd, (_xmax - _xc))
                _xd = math.sqrt(_rsqr - pow((_ymax - _yc), 2))
                _a2 = _calc_angle((_ymax - _yc), _xd)
                _arcs.append((_a1, (_a2 - _a1)))
                # top -> left; _xd now negative
                _a1 = _calc_angle((_ymax - _yc), -_xd)
                _yd = math.sqrt(_rsqr - pow((_xmin - _xc), 2))
                _a2 = _calc_angle(_yd, (_xmin - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                if ((_xmin < _xc < _xmax) and (_ymin < _yc < _ymax)):
                    print "circle center in region"
                else:
                    print "circle center out of region"
            elif _bits == 0x0f:
                print "circle crosses all edges twice"
                _yld = math.sqrt(_rsqr - pow((_xc - _xmin), 2))
                _yrd = math.sqrt(_rsqr - pow((_xc - _xmax), 2))
                _xtd = math.sqrt(_rsqr - pow((_yc - _ymax), 2))
                _xbd = math.sqrt(_rsqr - pow((_yc - _ymin), 2))
                # right -> top
                _x1 = _xmax
                _y1 = _yc + _yrd
                _x2 = _xc + _xtd
                _y2 = _ymax
                _a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
                _a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # top -> left
                _x1 = _xc - _xtd
                _y1 = _ymax
                _x2 = _xmin
                _y2 = _yc + _yld
                _a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
                _a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # left -> bottom
                _x1 = _xmin
                _y1 = _yc - _yld
                _x2 = _xc - _xbd
                _y2 = _ymin
                _a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
                _a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
                # bottom -> right
                _x1 = _xc + _xbd
                _y1 = _ymin
                _x2 = _xmax
                _y2 = _yc - _yrd
                _a1 = _calc_angle((_y1 - _yc), (_x1 - _xc))
                _a2 = _calc_angle((_y2 - _yc), (_x2 - _xc))
                _arcs.append((_a1, (_a2 - _a1)))
            elif _bits == 0xff:
                print "circle outside region"
            else:
                print "Unexpected bit pattern: %#02x" % _bits
        return _arcs

def _calc_angle(dy, dx):
    _angle = math.atan2(dy, dx) * (180.0/math.pi)
    if _angle < 0.0:
        _angle = _angle + 360.0
    return _angle

#
# Quadtree Circle storage
#

class CircleQuadtree(quadtree.Quadtree):
    def __init__(self):
        super(CircleQuadtree, self).__init__()

    def getNodes(self, *args):
        _alen = len(args)
        if _alen != 3:
            raise ValueError, "Expected 3 arguments, got %d" % _alen
        _x = util.get_float(args[0])
        _y = util.get_float(args[1])
        _r = util.get_float(args[2])
        _cxmin = _x - _r
        _cxmax = _x + _r
        _cymin = _y - _r
        _cymax = _y + _r
        _nodes = [self.getTreeRoot()]
        while len(_nodes):
            _node = _nodes.pop()
            _xmin, _ymin, _xmax, _ymax = _node.getBoundary()
            if ((_cxmin > _xmax) or
                (_cxmax < _xmin) or
                (_cymin > _ymax) or
                (_cymax < _ymin)):
                continue
            if _node.hasSubnodes():
                _xmid = (_xmin + _xmax)/2.0
                _ymid = (_ymin + _ymax)/2.0
                _ne = _nw = _sw = _se = True
                if _cxmax < _xmid: # circle on left side
                    _ne = _se = False
                if _cxmin > _xmid: # circle on right side
                    _nw = _sw = False
                if _cymax < _ymid: # circle below
                    _nw = _ne = False
                if _cymin > _ymid: # circle above
                    _sw = _se = False
                if _ne:
                    _nodes.append(_node.getSubnode(quadtree.QTreeNode.NENODE))
                if _nw:
                    _nodes.append(_node.getSubnode(quadtree.QTreeNode.NWNODE))
                if _sw:
                    _nodes.append(_node.getSubnode(quadtree.QTreeNode.SWNODE))
                if _se:
                    _nodes.append(_node.getSubnode(quadtree.QTreeNode.SENODE))
            else:
                yield _node

    def addObject(self, obj):
        if not isinstance(obj, Circle):
            raise TypeError, "Invalid Circle object: " + `type(obj)`
        if obj in self:
            return
        _x, _y = obj.getCenter().getCoords()
        _r = obj.getRadius()
        _bounds = self.getTreeRoot().getBoundary()
        _xmin = _ymin = _xmax = _ymax = None
        _cxmin = _x - _r
        _cxmax = _x + _r
        _cymin = _y - _r
        _cymax = _y + _r
        _resize = False
        if _bounds is None: # first node in tree
            _resize = True
            _xmin = _cxmin - 1.0
            _ymin = _cymin - 1.0
            _xmax = _cxmax + 1.0
            _ymax = _cymax + 1.0
        else:
            _xmin, _ymin, _xmax, _ymax = _bounds
            if _cxmin < _xmin:
                _xmin = _cxmin - 1.0
                _resize = True
            if _cxmax > _xmax:
                _xmax = _cxmax + 1.0
                _resize = True
            if _cymin < _ymin:
                _ymin = _cymin - 1.0
                _resize = True
            if _cymax > _ymax:
                _ymax = _cymax + 1.0
                _resize = True
        if _resize:
            self.resize(_xmin, _ymin, _xmax, _ymax)
        for _node in self.getNodes(_x, _y, _r):
            _xmin, _ymin, _xmax, _ymax = _node.getBoundary()            
            if obj.inRegion(_xmin, _ymin, _xmax, _ymax):
                _node.addObject(obj)
        super(CircleQuadtree, self).addObject(obj)
        obj.connect('moved', self._moveCircle)

    def delObject(self, obj):
        if obj not in self:
            return
        _x, _y = obj.getCenter().getCoords()
        _r = obj.getRadius()
        _pdict = {}
        for _node in self.getNodes(_x, _y, _r):
            _node.delObject(obj) # circle may not be in the node ...
            _parent = _node.getParent()
            if _parent is not None:
                _pid = id(_parent)
                if _pid not in _pdict:
                    _pdict[_pid] = _parent
        super(CircleQuadtree, self).delObject(obj)
        obj.disconnect(self)
        for _parent in _pdict.values():
            self.purgeSubnodes(_parent)

    def find(self, *args):
        _alen = len(args)
        if _alen < 3:
            raise ValueError, "Invalid argument count: %d" % _alen
        _x = util.get_float(args[0])
        _y = util.get_float(args[1])
        _r = util.get_float(args[2])
        _t = tolerance.TOL
        if _alen > 3:
            _t = tolerance.toltest(args[4])
        _xmin = _x - _r - _t
        _xmax = _x + _r + _t
        _ymin = _y - _r - _t
        _ymax = _y + _r + _t
        _circs = []
        for _circ in self.getInRegion(_xmin, _ymin, _xmax, _ymax):
            _cx, _cy = _circ.getCenter().getCoords()
            if ((abs(_cx - _x) < _t) and
                (abs(_cy - _y) < _t) and
                (abs(_circ.getRadius() - _r) < _t)):
                _circs.append(_circ)
        return _circs

    def _moveCircle(self, obj, *args):
        if obj not in self:
            raise ValueError, "Circle not stored in Quadtree: " + `obj`
        _alen = len(args)
        if _alen < 3:
            raise ValueError, "Invalid argument count: %d" % _alen
        _x = util.get_float(args[0])
        _y = util.get_float(args[1])
        _r = util.get_float(args[2])
        for _node in self.getNodes(_x, _y, _r):
            _node.delObject(obj) # circle may not be in node ...
        super(CircleQuadtree, self).delObject(obj)
        obj.disconnect(self)
        self.addObject(obj)

    def getClosest(self, x, y, tol=tolerance.TOL):
        _x = util.get_float(x)
        _y = util.get_float(y)
        _t = tolerance.toltest(tol)
        _circ = _tsep = None
        _bailout = False
        _cdict = {}
        _nodes = [self.getTreeRoot()]
        while len(_nodes):
            _node = _nodes.pop()
            _xmin, _ymin, _xmax, _ymax = _node.getBoundary()
            if ((_x < (_xmin - _t)) or
                (_x > (_xmax + _t)) or
                (_y < (_ymin - _t)) or
                (_y > (_ymax + _t))):
                continue
            if _node.hasSubnodes():
                _nodes.extend(_node.getSubnodes())
            else:
                for _c in _node.getObjects():
                    _cid = id(_c)
                    if _cid not in _cdict:
                        _cp = _c.mapCoords(_x, _y, _t)
                        if _cp is not None:
                            _cx, _cy = _cp
                            _sep = math.hypot((_cx - _x), (_cy - _y))
                            if _tsep is None:
                                _tsep = _sep
                                _circ = _c
                            else:
                                if _sep < _tsep:
                                    _tsep = _sep
                                    _circ = _c
                            if _sep < 1e-10 and _circ is not None:
                                _bailout = True
                                break
            if _bailout:
                break
        return _circ

    def getInRegion(self, xmin, ymin, xmax, ymax):
        _xmin = util.get_float(xmin)
        _ymin = util.get_float(ymin)
        _xmax = util.get_float(xmax)
        if _xmax < _xmin:
            raise ValueError, "Illegal values: xmax < xmin"
        _ymax = util.get_float(ymax)
        if _ymax < _ymin:
            raise ValueError, "Illegal values: ymax < ymin"
        _circs = []
        if not len(self):
            return _circs
        _nodes = [self.getTreeRoot()]
        _cdict = {}
        while len(_nodes):
            _node = _nodes.pop()
            if _node.hasSubnodes():
                for _subnode in _node.getSubnodes():
                    _sxmin, _symin, _sxmax, _symax = _subnode.getBoundary()
                    if ((_sxmin > _xmax) or
                        (_symin > _ymax) or
                        (_sxmax < _xmin) or
                        (_symax < _ymin)):
                        continue
                    _nodes.append(_subnode)
            else:
                for _circ in _node.getObjects():
                    _cid = id(_circ)
                    if _cid not in _cdict:
                        if _circ.inRegion(_xmin, _ymin, _xmax, _ymax):
                            _circs.append(_circ)
                        _cdict[_cid] = True
        return _circs

#
# Circle history class
#

class CircleLog(graphicobject.GraphicObjectLog):
    def __init__(self, c):
        if not isinstance(c, Circle):
            raise TypeError, "Invalid circle: " + `type(c)`
        super(CircleLog, self).__init__(c)
        c.connect('center_changed', self.__centerChanged)
        c.connect('radius_changed', self.__radiusChanged)

    def __radiusChanged(self, c, *args):
        _alen = len(args)
        if _alen < 1:
            raise ValueError, "Invalid argument count: %d" % _alen
        _r = args[0]
        if not isinstance(_r, float):
            raise TypeError, "Unxpected type for radius: " + `type(_r)`
        self.saveUndoData('radius_changed', _r)

    def __centerChanged(self, c, *args):
        _alen = len(args)
        if _alen < 1:
            raise ValueError, "Invalid argument count: %d" % _alen
        _old = args[0]
        if not isinstance(_old, point.Point):
            raise TypeError, "Invalid old center point: " + `type(_old)`
        self.saveUndoData('center_changed', _old.getID())

    def execute(self, undo, *args):
        util.test_boolean(undo)
        _alen = len(args)
        if _alen == 0:
            raise ValueError, "No arguments to execute()"
        _c = self.getObject()
        _cp = _c.getCenter()        
        _op = args[0]
        if _op == 'radius_changed':
            if len(args) < 2:
                raise ValueError, "Invalid argument count: %d" % _alen
            _r = args[1]
            if not isinstance(_r, float):
                raise TypeError, "Unexpected type for radius: " + `type(_r)`
            _sdata = _c.getRadius()
            self.ignore(_op)
            try:
                if undo:
                    _c.startUndo()
                    try:
                        _c.setRadius(_r)
                    finally:
                        _c.endUndo()
                else:
                    _c.startRedo()
                    try:
                        _c.setRadius(_r)
                    finally:
                        _c.endRedo()
            finally:
                self.receive(_op)
            self.saveData(undo, _op, _sdata)
        elif _op == 'center_changed':
            if _alen < 2:
                raise ValueError, "Invalid argument count: %d" % _alen
            _oid = args[1]
            _parent = _c.getParent()
            if _parent is None:
                raise ValueError, "Circle has no parent - cannot undo"
            _pt = _parent.getObject(_oid)
            if _pt is None or not isinstance(_pt, point.Point):
                raise ValueError, "Center point missing: id=%d" % _oid
            _sdata = _cp.getID()            
            self.ignore(_op)
            try:
                if undo:
                    _c.startUndo()
                    try:
                        _c.setCenter(_pt)
                    finally:
                        _c.endUndo()
                else:
                    _c.startRedo()
                    try:
                        _c.setCenter(_pt)
                    finally:
                        _c.endRedo()
            finally:
                self.receive(_op)
            self.saveData(undo, _op, _sdata)
        else:
            super(CircleLog, self).execute(undo, *args)