File size: 68,269 Bytes
10f2621
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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
1708
1709
1710
1711
1712
1713
1714
1715
1716
1717
1718
1719
1720
1721
1722
1723
1724
1725
1726
1727
1728
1729
1730
1731
1732
1733
1734
1735
1736
1737
1738
1739
1740
1741
1742
1743
1744
1745
1746
1747
1748
1749
1750
1751
1752
1753
1754
1755
1756
1757
1758
1759
1760
1761
1762
1763
1764
1765
1766
1767
1768
1769
1770
1771
1772
1773
1774
1775
1776
1777
1778
1779
1780
1781
1782
1783
1784
1785
1786
1787
1788
1789
1790
1791
1792
1793
1794
1795
1796
1797
1798
1799
1800
1801
1802
1803
1804
1805
1806
1807
1808
1809
1810
1811
1812
1813
1814
1815
1816
1817
1818
1819
1820
1821
1822
1823
1824
1825
1826
1827
1828
1829
1830
1831
1832
1833
1834
1835
1836
1837
1838
1839
1840
1841
1842
1843
1844
1845
1846
1847
1848
1849
1850
1851
1852
1853
1854
1855
1856
1857
1858
1859
1860
1861
1862
1863
1864
1865
1866
1867
1868
1869
1870
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
2011
2012
2013
2014
2015
2016
2017
2018
2019
2020
2021
2022
2023
2024
2025
2026
2027
2028
2029
2030
2031
2032
2033
2034
2035
2036
2037
2038
2039
2040
2041
2042
2043
2044
2045
2046
2047
2048
2049
2050
2051
2052
2053
2054
2055
2056
2057
2058
2059
/**
 * @defgroup VV VV class
 * @brief    VV class
 */

/**
 * @defgroup EE EE class
 * @brief    EE class
 */

/**
 * @defgroup FF FF class
 * @brief    FF class
 */

/**
 * @defgroup SS SS class
 * @brief    SS class
 */

/**
 *  @file       ves.h
 *  @ingroup    VV EE FF SS global_mc
 *  @brief      Class V,E,S: the fundamental simplex geometry objects.
 *  @author     Michael Holst
 *  @note       This is an implementation of the RIVER datastructure.
 *              RIVER = RInged-VERtex data Structure
 *  @version    $Id: ves.h,v 1.24 2010/08/12 05:19:07 fetk Exp $ 
 *
 *  @attention
 *  @verbatim
 *
 * MC = < Manifold Code >
 * Copyright (C) 1994-- Michael Holst
 *
 * This library is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public
 * License as published by the Free Software Foundation; either
 * version 2.1 of the License, or (at your option) any later version.
 *
 * This library 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
 * Lesser General Public License for more details.
 *
 * You should have received a copy of the GNU Lesser General Public
 * License along with this library; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
 *
 *  @endverbatim
 */

#ifndef _VES_H_
#define _VES_H_

#include <mc/mc_base.h>

#include <mc/vel.h>

/*
 * ***************************************************************************
 * Class VV,VE,VS: Parameters and datatypes
 * ***************************************************************************
 */

/**
 * @ingroup VV
 * @brief   Class VV: Definition (8+32=40 bytes) 
 * @author  Michael Holst
 */
struct sVV {
  /** @brief --------> Geometric information package           */
    Gip      g;
  /** @brief --------> Vertex information package              */  
    Vip      d;
};

/**
 * @ingroup VV
 * @brief   Declaration of the VV class as the VV structure
 * @author  Michael Holst
 */
typedef struct sVV VV;

/**
 * @ingroup EE
 * @brief   Class EE: Definition (8+20=28 bytes) 
 * @author  Michael Holst
 */
struct sEE {
  /** @brief --------> Geometric information package           */
    Gip      g;
  /** @brief --------> Edge information package                */   
    Eip      d;
};

/**
 * @ingroup EE
 * @brief   Declaration of the EE class as the EE structure
 * @author  Michael Holst
 */
typedef struct sEE EE;

/**
 * @ingroup FF
 * @brief   Class FF: Definition (8+20=28 bytes) 
 * @author  Michael Holst
 */
struct sFF {
  /** @brief --------> Geometric information package           */
    Gip      g;
  /** @brief --------> Face information package                */  
    Fip      d;
};

/**
 * @ingroup FF
 * @brief   Declaration of the FF class as the FF structure
 * @author  Michael Holst
 */
typedef struct sFF FF; 

/**
 * @ingroup SS
 * @brief   Class SS: Definition (8+40=48 bytes OR 8+80=88 bytes) 
 * @author  Michael Holst
 */
struct sSS {
  /** @brief --------> Geometric information package           */
    Gip      g;   
  /** @brief --------> Simplex information package             */  
    Sip      d;   
};

/**
 * @ingroup SS
 * @brief   Declaration of the SS class as the SS structure
 * @author  Michael Holst
 */
typedef struct sSS SS; 


/**
 * @ingroup global_mc
 * @brief   Class T: Definition 
 * @author  Michael Holst
 */
typedef struct TT {

  /** @brief common chart for vertex coordinates        */
    int gchart;  
  /** @brief charts for vertex coordinates              */
    int chart[4]; 

  /** @brief jacobian determinant of the transformation */
    double D;  
  /** @brief jacobian determinant of cooked trans       */
    double Dcook;
  /** @brief face jacobian determinants                 */
    double faceD[4]; 

  /** @brief affine trans from master to arbitrary el   */
    double ff[3][3];
  /** @brief affine trans from master to arbitrary el   */
    double bb[3];
  /** @brief affine trans from arbitrary el to master   */ 
    double gg[3][3];
  /** @brief affine trans from arbitrary el to master   */ 
    double  cc[3];

  /** @brief local ordering of vertices for each face   */
    int loc[4][3];
  /** @brief vertex coordinate labels                   */
    double vx[4][3]; 
  /** @brief normal vectors to the faces                */
    double nvec[4][3];
  /** @brief edge vectors                               */ 
    double evec[6][3];
  /** @brief edge vector lengths                        */
    double elen[6];
  /** @brief baricenter                                 */   
    double bc[4];  

  /** @brief number of vertices in the d-simplex        */
    int dimV;
  /** @brief number of edges in the d-simplex           */
    int dimE;   
  /** @brief number of faces in the d-simplex           */ 
    int dimF; 
  /** @brief number of simplices in the d-simplex (=1)  */  
    int dimS; 

  /** @brief global simplex ID                          */
    int sid;
  /** @brief global vertex IDs                          */
    int vid[4];
  /** @brief global face IDs                            */
    int fid[4]; 
  /** @brief global edge IDs                            */ 
    int eid[6]; 

  /** @brief global simplex type                        */
    int stype;  
  /** @brief global vertex types                        */
    int vtype[4];  
  /** @brief global face types                          */
    int ftype[4];  
  /** @brief LOCAL edge types                           */ 
    int etype[6];  

  /** @brief pointer to the simplex                     */
    SS *s;  
  /** @brief pointers to vertices of the simplex        */
    VV *v[4];

  /** @brief local basis function of the current simplex */
    double phi[4], phix[4][3];

  /** @brief face and/or basis functions that are current focus */
    int focusFace, focusIV, focusIW;
} TT;

/*
 * ***************************************************************************
 * Class V: Inlineable methods (ves.c)
 * ***************************************************************************
 */

#if !defined(VINLINE_GEM)
    /**
     * @ingroup VV
     * @brief   Intialize a vertex.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   dim  the dimension of the mesh
     * @param   id   the ID bits
     */
    VEXTERNC void VV_init(VV *thee, int dim, int id);

    /**
     * @ingroup VV
     * @brief   Re-intialize a vertex.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     */
    VEXTERNC void VV_reinit(VV *thee);

    /**
     * @ingroup VV
     * @brief   Set the reality
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   type the reality bits
     */
    VEXTERNC void VV_setReality(VV *thee, int type);

    /**
     * @ingroup VV
     * @brief   Set the dimension
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   dim  the dimension bits
     */
    VEXTERNC void VV_setDim(VV *thee, int dim);

    /**
     * @ingroup VV
     * @brief   Set the class.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   type the class bits
     */
    VEXTERNC void VV_setClass(VV *thee, int type);

    /**
     * @ingroup VV
     * @brief   Set the type
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   type the type bits
     */
    VEXTERNC void VV_setType(VV *thee, int type);

    /**
     * @ingroup VV
     * @brief   Set the chart.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee  Pointer to a vertex
     * @param   chart the chart bits
     */
    VEXTERNC void VV_setChart(VV *thee, int chart);

    /**
     * @ingroup VV
     * @brief   Set the ID
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   id   the ID bits
     */
    VEXTERNC void VV_setId(VV *thee, int id);

    /**
     * @ingroup VV
     * @brief   Return the reality
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the reality
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_reality(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the dimension
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the dimension
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_dim(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the number of vertices in a simplex. 
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the number of vertices in a simplex. 
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_dimVV(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the number of edges in a simplex.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the number of edges in a simplex.
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_dimEE(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the number of faces in a simplex.          
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the number of faces in a simplex.          
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_dimFF(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the class
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the class
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_class(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the type
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the type
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_type(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the chart
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the chart
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_chart(VV *thee);

    /**
     * @ingroup VV
     * @brief   Return the ID
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the ID
     * @param   thee Pointer to a vertex
     */
    VEXTERNC unsigned int VV_id(VV *thee);

    /**
     * @ingroup VV
     * @brief   Set the coordinate
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   i    index of the coordinate 
     * @param   val  the value of the coordinate
     */
    VEXTERNC void VV_setCoord(VV *thee, int i, double val);

    /**
     * @ingroup VV
     * @brief   Set the first edge in an edge ring.          
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   eg   Pointer to an edge
     */
    VEXTERNC void VV_setFirstEE(VV *thee, EE *eg);

    /**
     * @ingroup VV
     * @brief   Set the first simplex in a simplex ring.     
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   sm   Pointer to a simplex
     */
    VEXTERNC void VV_setFirstSS(VV *thee, SS *sm);

    /**
     * @ingroup VV
     * @brief   Set the parent edge pointer. 
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   eg   Pointer to an edge
     */
    VEXTERNC void VV_setParentEE(VV *thee, EE *eg);

    /**
     * @ingroup VV
     * @brief   Return the coordinate
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  the coordinate
     * @param   thee Pointer to a vertex
     * @param   i    Index for a vertex in one simplex
     */
    VEXTERNC double VV_coord(VV *thee, int i);

    /**
     * @ingroup VV
     * @brief   Set the first edge in an edge ring. 
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  Pointer to the first edge in an edge ring.
     * @param   thee Pointer to a vertex
     */
    VEXTERNC EE* VV_firstEE(VV *thee);

    /**
     * @ingroup VV
     * @brief   Set the first simplex in a simplex ring.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  Pointer to the first simplex in a simplex ring.
     * @param   thee Pointer to a vertex
     */
    VEXTERNC SS* VV_firstSS(VV *thee);

    /**
     * @ingroup VV
     * @brief   the parent edge pointer.
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  Pointer to the parent edge
     * @param   thee Pointer to a vertex
     */
    VEXTERNC EE* VV_parentEE(VV *thee);

    /**
     * @ingroup VV
     * @brief   Add an edge to an edge ring. 
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   eg   Pointer to an edge
     */
    VEXTERNC void VV_addEdgeToRing(VV *thee, EE *eg);

    /**
     * @ingroup VV
     * @brief   Add a simplex to a simplex ring.   
     * @author  Michael Holst
     * @note    Class V: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a vertex
     * @param   sm   Pointer to a simplex
     */
    VEXTERNC void VV_addSimplexToRing(VV *thee, SS *sm);
#else /* if defined(VINLINE_GEM) */
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_init(thee,dim,id) ( \
        (thee)->d.ePtr   = VNULL, \
        (thee)->d.sPtr   = VNULL, \
        (thee)->d.x[0]   = 0.0, \
        (thee)->d.x[1]   = 0.0, \
        (thee)->d.x[2]   = 0.0, \
        Vel_init((Vel*)(thee), dim, id) \
    )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_reinit(thee) ( \
        (thee)->d.ePtr   = VNULL, \
        (thee)->d.sPtr   = VNULL, \
        (thee)->d.x[0]   = 0.0, \
        (thee)->d.x[1]   = 0.0, \
        (thee)->d.x[2]   = 0.0, \
        Vel_reinit((Vel*)(thee)) \
    )

/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setReality(thee,reel) Vel_setReality( (Vel*)(thee), (reel)  )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setDim(thee,dim)      Vel_setDim(     (Vel*)(thee), (dim)   )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setClass(thee,clas)   Vel_setClass(   (Vel*)(thee), (clas)  )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setType(thee,type)    Vel_setType(    (Vel*)(thee), (type)  )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setChart(thee,chart)  Vel_setChart(   (Vel*)(thee), (chart) )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setId(thee,id)        Vel_setId(      (Vel*)(thee), (id)    )

/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_reality(thee)         Vel_reality(    (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_dim(thee)             Vel_dim(        (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_dimVV(thee)           Vel_dimVV(      (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_dimEE(thee)           Vel_dimEE(      (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_dimFF(thee)           Vel_dimFF(      (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_class(thee)           Vel_class(      (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_type(thee)            Vel_type(       (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_chart(thee)           Vel_chart(      (Vel*)(thee)          )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_id(thee)              Vel_id(         (Vel*)(thee)          )

/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setCoord(thee,i,val)  ((thee)->d.x[(i)] = (val))
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setFirstEE(thee,eg)   ((thee)->d.ePtr = (eg))
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setFirstSS(thee,eg)   ((thee)->d.sPtr = (eg))
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_setParentEE(thee,eg)  ((thee)->d.eParent = (eg))

/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_coord(thee,i)  ((thee)->d.x[(i)])
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_firstEE(thee)  (EE*)((thee)->d.ePtr)
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_firstSS(thee)  (SS*)((thee)->d.sPtr)
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_parentEE(thee) (EE*)((thee)->d.eParent)

/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_addEdgeToRing(thee,eg) ( \
        EE_setLink( (eg), (thee), VV_firstEE(thee) ), \
        VV_setFirstEE( (thee), (eg) ) \
    )
/** @brief Class V: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define VV_addSimplexToRing(thee,sm) ( \
        SS_setLink( (sm), (thee), VV_firstSS(thee) ), \
        VV_setFirstSS( (thee), (sm) ) \
    )
#endif /* if !defined(VINLINE_GEM) */

/*
 * ***************************************************************************
 * Class V: Non-inlineable methods (ves.c)
 * ***************************************************************************
 */

/**
 * @ingroup VV
 * @brief   The vertex constructor.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  Pointer to a new allocated vertex
 * @param   dim  the dimension bits
 * @param   myid the ID bits
 */
VEXTERNC VV* VV_ctor(int dim, int myid);

/**
 * @ingroup VV
 * @brief   The vertex destructor.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to a vertex
 */
VEXTERNC void VV_dtor(VV **thee);

/**
 * @ingroup VV
 * @brief   Remove an edge from an edge ring.   
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to a vertex
 * @param   eg   Pointer to an edge
 */
VEXTERNC void VV_removeEdgeFromRing(VV *thee, EE *eg);

/**
 * @ingroup VV
 * @brief   Remove a simplex from a simplex ring.  
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to a vertex
 * @param   sm   Pointer to a simplex
 */
VEXTERNC void VV_removeSimplexFromRing(VV *thee, SS *sm);

/**
 * @ingroup VV
 * @brief   Is an edge in the edge ring.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  Success enumeration
 * @param   thee Pointer to a vertex
 * @param   eg   Pointer to an edge
 */
VEXTERNC int VV_edgeInRing(VV *thee, EE *eg);

/**
 * @ingroup VV
 * @brief   Is a simplex in a simplex ring.    
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  Success enumeration
 * @param   thee Pointer to a vertex
 * @param   sm   Pointer to a simplex
 */
VEXTERNC int VV_simplexInRing(VV *thee, SS *sm);

/**
 * @ingroup VV
 * @brief   Return the common edge between two vertices.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  the common edge between two vertices.
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 */
VEXTERNC EE* VV_commonEdge(VV *thee, VV *v0);

/**
 * @ingroup VV
 * @brief   Return parent edge having one of two vertices as midpoint. 
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  parent edge having one of two vertices as midpoint. 
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 */
VEXTERNC EE* VV_parentEdge(VV *thee, VV *v0);

/**
 * @ingroup VV
 * @brief   Return a 2-simplex that is shared by 2 vertices, 
 *          and which is different from the input simplex sm.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  2-simplex that is shared by 2 vertices, 
 *          and which is different from the input simplex sm.
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 * @param   sm   Pointer to a simplex
 */
VEXTERNC SS* VV_commonSimplex2(VV *thee, VV *v0, SS *sm);

/**
 * @ingroup VV
 * @brief   Return a 3-simplex that is shared by 3 vertices, 
 *          and which is different from the input simplex sm.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  3-simplex that is shared by 3 vertices, 
 *          and which is different from the input simplex sm.
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 * @param   v1   Pointer to a vertex
 * @param   sm   Pointer to a smplex
 */
VEXTERNC SS* VV_commonSimplex3(VV *thee, VV *v0, VV *v1, SS *sm);

/**
 * @ingroup VV
 * @brief   Return a 3-simplex that is shared by 4 vertices, 
 *          and which is different from the input simplex sm.
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  3-simplex that is shared by 4 vertices, 
 *          and which is different from the input simplex sm.
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 * @param   v1   Pointer to a vertex
 * @param   v2   Pointer to a vertex
 * @param   sm   Pointer to a simplex
 */
VEXTERNC SS* VV_commonSimplex4(VV *thee, VV *v0, VV *v1, VV *v2, SS *sm);

/**
 * @ingroup VV
 * @brief   the common vertex pointer
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  Pointer to the common vertex
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 * @param   v1   Pointer to a vertex
 */
VEXTERNC VV* VV_commonVertex3(VV *thee, VV *v0, VV *v1);

/**
 * @ingroup VV
 * @brief   the common vertex pointer
 * @author  Michael Holst
 * @note    Class V: Inlineable methods (ves.c) 
 * @return  Pointer to the common vertex
 * @param   thee Pointer to a vertex
 * @param   v0   Pointer to a vertex
 * @param   v1   Pointer to a vertex
 * @param   v2   Pointer to a vertex
 */
VEXTERNC VV* VV_commonVertex4(VV *thee, VV *v0, VV *v1, VV *v2);


#if !defined(VINLINE_GEM)
    /**
     * @ingroup EE
     * @brief   Initialize an edge. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   dim  the dimension bits
     * @param   id   the ID bits 
     */
    VEXTERNC void EE_init(EE *thee, int dim, int id);

    /**
     * @ingroup EE
     * @brief   Re-initialize an edge. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     */
    VEXTERNC void EE_reinit(EE *thee);

    /**
     * @ingroup EE
     * @brief   Set the reality.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   type the reality bits
     */
    VEXTERNC void EE_setReality(EE *thee, int type);

    /**
     * @ingroup EE
     * @brief   Set the dimension. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   dim  the dimension bits
     */
    VEXTERNC void EE_setDim(EE *thee, int dim);

    /**
     * @ingroup EE
     * @brief   Set the class.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   type the class bits
     */
    VEXTERNC void EE_setClass(EE *thee, int type);

    /**
     * @ingroup EE
     * @brief   Set the type.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   type the type bits
     */
    VEXTERNC void EE_setType(EE *thee, int type);

    /**
     * @ingroup EE
     * @brief   Set the chart.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee  Pointer to a vertex
     * @param   chart the chart bits
     */
    VEXTERNC void EE_setChart(EE *thee, int chart);

    /**
     * @ingroup EE
     * @brief   Set the ID.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   id   the ID bits
     */
    VEXTERNC void EE_setId(EE *thee, int id);

    /**
     * @ingroup EE
     * @brief   Return the dimension.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the dimension.
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_dim(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the number of vertices in a simplex. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the number of vertices in a simplex. 
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_dimVV(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the number of edges in a simplex.     
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the number of edges in a simplex.     
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_dimEE(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the number of faces in a simplex. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the number of faces in a simplex.     
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_dimFF(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the reality
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the reality
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_reality(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the class
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the class
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_class(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the type
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the type
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_type(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the chart
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the chart
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_chart(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the ID
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the ID
     * @param   thee Pointer to an edge
     */
    VEXTERNC unsigned int EE_id(EE *thee);

    /**
     * @ingroup EE
     * @brief   Set one of the two vertices.   
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   i    index for a vertex
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC void EE_setVertex(EE *thee, int i, VV *vx);

    /**
     * @ingroup EE
     * @brief   Set the midpoint of the edge. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC void EE_setMidPoint(EE *thee, VV *vx);

    /**
     * @ingroup EE
     * @brief   Set the parent edge pointer.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   eg   Pointer to an edge
     */
    VEXTERNC void EE_setParent(EE *thee, EE *eg);

    /**
     * @ingroup EE
     * @brief   Set the vertex order.  
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee  Pointer to an edge
     * @param   vxTmp Pointer to a vertex
     */
    VEXTERNC void EE_setVertexOrder(EE *thee, VV* vxTmp);

    /**
     * @ingroup EE
     * @brief   Set the next edge pointer associated with one of the vertices. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to an edge
     * @param   vx   Pointer to a vertex
     * @param   eg   Pointer to an edge
     */
    VEXTERNC void EE_setLink(EE *thee, VV *vx, EE *eg);

    /**
     * @ingroup EE
     * @brief   Return one of the vertices.
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  one of the vertcies.
     * @param   thee Pointer to an edge
     * @param   i    index for a vertex
     */
    VEXTERNC VV* EE_vertex(EE *thee, int i);

    /**
     * @ingroup EE
     * @brief   Return the midpoint of the edge.    
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the midpoint of the edge.
     * @param   thee Pointer to an edge
     */
    VEXTERNC VV* EE_midPoint(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the parent edge pointer.  
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the parent edge pointer.
     * @param   thee Pointer to an edge
     */
    VEXTERNC EE* EE_parent(EE *thee);

    /**
     * @ingroup EE
     * @brief   Return the vertex not matching the input vertex. 
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the vertex not matching the input vertex. 
     * @param   thee Pointer to an edge
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC VV* EE_otherVertex(EE *thee, VV *vx);

    /**
     * @ingroup EE
     * @brief   Return the next edge in the ring around a given vertex.    
     * @author  Michael Holst
     * @note    Class E: Inlineable methods (ves.c) 
     * @return  the next edge in the ring around a given vertex.    
     * @param   thee Pointer to an edge
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC EE* EE_link(EE *thee, VV *vx);
#else /* if defined(VINLINE_GEM) */
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_init(thee,dim,id) ( \
        (thee)->d.vPtr[0] = VNULL, \
        (thee)->d.vPtr[1] = VNULL, \
        (thee)->d.ePtr[0] = VNULL, \
        (thee)->d.ePtr[1] = VNULL, \
        (thee)->d.midPtr  = VNULL, \
        Vel_init((Vel*)(thee), dim, id) \
    )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_reinit(thee) ( \
        (thee)->d.vPtr[0] = VNULL, \
        (thee)->d.vPtr[1] = VNULL, \
        (thee)->d.ePtr[0] = VNULL, \
        (thee)->d.ePtr[1] = VNULL, \
        (thee)->d.midPtr  = VNULL, \
        Vel_reinit((Vel*)(thee)) \
    )

/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setReality(thee,reel) Vel_setReality( (Vel*)(thee), (reel)  )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setDim(thee,dim)      Vel_setDim(     (Vel*)(thee), (dim)   )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setClass(thee,clas)   Vel_setClass(   (Vel*)(thee), (clas)  )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setType(thee,type)    Vel_setType(    (Vel*)(thee), (type)  )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setChart(thee,chart)  Vel_setChart(   (Vel*)(thee), (chart) )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setId(thee,id)        Vel_setId(      (Vel*)(thee), (id)    )

/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_reality(thee)         Vel_reality(    (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_dim(thee)             Vel_dim(        (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_dimVV(thee)           Vel_dimVV(      (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_dimEE(thee)           Vel_dimEE(      (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_dimFF(thee)           Vel_dimFF(      (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_class(thee)           Vel_class(      (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_type(thee)            Vel_type(       (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_chart(thee)           Vel_chart(      (Vel*)(thee)          )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_id(thee)              Vel_id(         (Vel*)(thee)          )

/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setVertex(thee,i,vx) ((thee)->d.vPtr[(i)]=(vx))
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setMidPoint(thee,vx) ((thee)->d.midPtr=(vx))
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setParent(thee,eg)  ((thee)->d.eParent = (eg))
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setVertexOrder(thee,vxTmp) ( \
        (VV_id((thee)->d.vPtr[0]) > VV_id((thee)->d.vPtr[1])) \
            ? ( (vxTmp) = (thee)->d.vPtr[1], \
                (thee)->d.vPtr[1] = (thee)->d.vPtr[0], \
                (thee)->d.vPtr[0] = (vxTmp) ) \
            : VNULL \
    )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_setLink(thee,vx,eg) ( \
           ((vx) == (VV*)(thee)->d.vPtr[0]) ? (thee)->d.ePtr[0] = eg \
        : (((vx) == (VV*)(thee)->d.vPtr[1]) ? (thee)->d.ePtr[1] = eg : VNULL) \
    )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_vertex(thee,i) (VV*)((thee)->d.vPtr[(i)])
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_midPoint(thee) (VV*)((thee)->d.midPtr)
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_parent(thee)   (EE*)((thee)->d.eParent)
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_otherVertex(thee,vx) (VV*)( \
           ((vx) == (VV*)(thee)->d.vPtr[0]) ? (thee)->d.vPtr[1] \
        : (((vx) == (VV*)(thee)->d.vPtr[1]) ? (thee)->d.vPtr[0] : VNULL) \
    )
/** @brief Class E: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#   define EE_link(thee,vx) (EE*)( \
           ((vx) == (VV*)(thee)->d.vPtr[0]) ? (thee)->d.ePtr[0] \
        : (((vx) == (VV*)(thee)->d.vPtr[1]) ? (thee)->d.ePtr[1] : VNULL) \
    )
#endif /* if !defined(VINLINE_GEM) */

/*
 * ***************************************************************************
 * Class E: Non-inlineable methods (ves.c)
 * ***************************************************************************
 */

/**
 * @ingroup EE
 * @brief   The edge constructor
 * @author  Michael Holst
 * @note    Class E: Inlineable methods (ves.c) 
 * @return  Pointer to a new allocated edge
 * @param   dim  the dimension bits
 * @param   myid the ID bits
 */
VEXTERNC EE* EE_ctor(int dim, int myid);

/**
 * @ingroup EE
 * @brief   The edge destructor.     
 * @author  Michael Holst
 * @note    Class E: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to an edge
 */
VEXTERNC void EE_dtor(EE **thee);

/**
 * @ingroup EE
 * @brief   Initialize the edge rings.
 * @author  Michael Holst
 * @note    Class E: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to an edge
 */
VEXTERNC void EE_initRing(EE *thee);

/**
 * @ingroup EE
 * @brief   Destroy the edge rings.   
 * @author  Michael Holst
 * @note    Class E: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to an edge
 */
VEXTERNC void EE_meltRing(EE *thee);

/**
 * @ingroup EE
 * @brief   Build the edge rings.      
 * @author  Michael Holst
 * @note    Class E: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to an edge
 */
VEXTERNC void EE_buildRing(EE *thee);


#if !defined(VINLINE_GEM)
    /**
     * @ingroup SS
     * @brief   Initialize a simplex.   
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   dim  the dimension bits
     * @param   id   the ID bits
     */
    VEXTERNC void SS_init(SS *thee, int dim, int id);

    /**
     * @ingroup SS
     * @brief   Re-Initialize a simplex.   
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     */
    VEXTERNC void SS_reinit(SS *thee);

    /**
     * @ingroup SS
     * @brief   Set the reality
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   type the reality ID
     */
    VEXTERNC void SS_setReality(SS *thee, int type);

    /**
     * @ingroup SS
     * @brief   Set the dimension
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   dim  the dimension bits
     */
    VEXTERNC void SS_setDim(SS *thee, int dim);

    /**
     * @ingroup SS
     * @brief   Set the class
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   type the class bits
     */
    VEXTERNC void SS_setClass(SS *thee, int type);

    /**
     * @ingroup SS
     * @brief   Set the type
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   type the type value of a simplex
     */
    VEXTERNC void SS_setType(SS *thee, int type);

    /**
     * @ingroup SS
     * @brief   Set the chart
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee  Pointer to a vertex
     * @param   chart index for a chart in a simplex
     */
    VEXTERNC void SS_setChart(SS *thee, int chart);

    /**
     * @ingroup SS
     * @brief   Set the ID
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   id   index for the simplex ID
     */
    VEXTERNC void SS_setId(SS *thee, int id);

    /**
     * @ingroup SS
     * @brief   Return the reality
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the reality
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_reality(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the dimension
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the dimension
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_dim(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the number of vertices in a simplex.  
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the number of vertices in a simplex.  
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_dimVV(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the number of edges in a simplex.  
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the number of edges in a simplex.  
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_dimEE(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the number of faces in a simplex.  
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the number of faces in a simplex.  
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_dimFF(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the class
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the class
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_class(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the type
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the type
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_type(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the chart
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the chart
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_chart(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the ID
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the ID
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_id(SS *thee);

    /**
     * @ingroup SS
     * @brief   Set the face type
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   f    index for a face
     * @param   type number of the face type
     */
    VEXTERNC void SS_setFaceType(SS *thee, int f, int type);

    /**
     * @ingroup SS
     * @brief   Set the refinement edge.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    the refinement edge
     */
    VEXTERNC void SS_setRefinementEdge(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Set the first marked edge.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    the first marked edge
     */
    VEXTERNC void SS_setMarkedEdge1(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Set the second marked edge.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    the second marked edge
     */
    VEXTERNC void SS_setMarkedEdge2(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Set the third marked edge.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    the third marked edge.
     */
    VEXTERNC void SS_setMarkedEdge3(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Set degenerate marking flag.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    degenerate marking flag
     */
    VEXTERNC void SS_setDegen(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Set refinement count.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    index for refinement count
     */
    VEXTERNC void SS_setRefinementCount(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Set refinement key.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee  Pointer to a simplex
     * @param   which index for the refinement
     * @param   key   the value for the refinement
     */
    VEXTERNC void SS_setRefineKey(SS *thee, int which, int key);
#   if defined(VG_ELEMENT)
        /**
	 * @ingroup SS
	 * @brief   the ID numer of a face
	 * @author  Michael Holst
	 * @note    Class S: Inlineable methods (ves.c) 
	 * @return  None
	 * @param   thee  Pointer to a simplex
	 * @param   i     index of a face
	 * @param   fn    the ID numer of a face
	 */
        VEXTERNC void SS_setFaceNumber(SS *thee, int i, int fn);

        /**
	 * @ingroup SS
	 * @brief   the ID numer of an edge
	 * @author  Michael Holst
	 * @note    Class S: Inlineable methods (ves.c) 
	 * @return  None
	 * @param   thee  Pointer to a simplex
	 * @param   i     index for an edge
	 * @param   fn    the ID numer of an edge
	 */
        VEXTERNC void SS_setEdgeNumber(SS *thee, int i, int en);
#   endif
    /**
     * @ingroup SS
     * @brief   Set a given vertex.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   i    index of a vertex
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC void SS_setVertex(SS *thee, int i, VV *vx);

    /**
     * @ingroup SS
     * @brief   Set the next simplex pointer for a given simplex ring.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   vx   Pointer to a vertex
     * @param   sm   Pointer to a simplex
     */
    VEXTERNC void SS_setLink(SS *thee, VV *vx, SS *sm);

    /**
     * @ingroup SS
     * @brief   Set the type of a given face.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  None
     * @param   thee Pointer to a simplex
     * @param   f    index of a face
     */
    VEXTERNC unsigned int SS_faceType(SS *thee, int f);

    /**
     * @ingroup SS
     * @brief   Return the refinement edge. 
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the refinement edge.
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_refinementEdge(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the first marked edge.    
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the first marked edge.
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_markedEdge1(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the second marked edge.   
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the second marked edge.
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_markedEdge2(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the third marked edge.   
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the third marked edge.
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_markedEdge3(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the degenerate edge marker.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the degenerate edge marker.
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_degen(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the refinement count.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the refinement count.
     * @param   thee Pointer to a simplex
     */
    VEXTERNC unsigned int SS_refinementCount(SS *thee);

    /**
     * @ingroup SS
     * @brief   Return the refinement key.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the refinement key.
     * @param   thee  Pointer to a simplex
     * @param   which index for refinement nor not
     */
    VEXTERNC unsigned int SS_refineKey(SS *thee, int which);

#   if defined(VG_ELEMENT)
       /**
        * @ingroup SS
        * @brief   the ID number of a face
        * @author  Michael Holst
        * @note    Class S: Inlineable methods (ves.c) 
        * @return  the ID number of a face
        * @param   thee  Pointer to a simplex
        * @param   i     index for a face
        */
        VEXTERNC int SS_faceNumber(SS *thee, int i);

       /**
        * @ingroup SS
        * @brief   the ID number of an edge
        * @author  Michael Holst
        * @note    Class S: Inlineable methods (ves.c) 
        * @return  the ID number of an edge
        * @param   thee  Pointer to a simplex
        * @param   i     index for an edge
        */
        VEXTERNC int SS_edgeNumber(SS *thee, int i);
#   endif

    /**
     * @ingroup SS
     * @brief   Return a given vertex.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  a given vertex.
     * @param   thee Pointer to a simplex
     * @param   i    index for a vertex in a simplex
     */
    VEXTERNC VV* SS_vertex(SS *thee, int i);

    /**
     * @ingroup SS
     * @brief   Return the next simplex in a given simplex ring. 
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the next simplex in a given simplex ring. 
     * @param   thee Pointer to a simplex
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC SS* SS_link(SS *thee, VV *vx);

    /**
     * @ingroup SS
     * @brief   Return local vertex number i for face f.  
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  local vertex number i for face f.  
     * @param   thee Pointer to a simplex
     * @param   f    index of the face
     * @param   i    local vertex number
     */
    VEXTERNC int SS_faceVertexNumber(SS *thee, int f, int i);

    /**
     * @ingroup SS
     * @brief   Return the local vertex number associated with a given vertex.
     * @author  Michael Holst
     * @note    Class S: Inlineable methods (ves.c) 
     * @return  the local vertex number associated with a given vertex.
     * @param   thee Pointer to a simplex
     * @param   vx   Pointer to a vertex
     */
    VEXTERNC int SS_vptr2localVnum(SS *thee, VV *vx);
#else /* if defined(VINLINE_GEM) */
#   if defined(VG_ELEMENT)
/** @brief Class S: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#       define SS_init(thee,dim,id) ( \
            (thee)->d.vPtr[0] = VNULL, \
            (thee)->d.vPtr[1] = VNULL, \
            (thee)->d.vPtr[2] = VNULL, \
            (thee)->d.vPtr[3] = VNULL, \
            (thee)->d.sPtr[0] = VNULL, \
            (thee)->d.sPtr[1] = VNULL, \
            (thee)->d.sPtr[2] = VNULL, \
            (thee)->d.sPtr[3] = VNULL, \
            (thee)->d.fNum[0] = -1, \
            (thee)->d.fNum[1] = -1, \
            (thee)->d.fNum[2] = -1, \
            (thee)->d.fNum[3] = -1, \
            (thee)->d.eNum[0] = -1, \
            (thee)->d.eNum[1] = -1, \
            (thee)->d.eNum[2] = -1, \
            (thee)->d.eNum[3] = -1, \
            (thee)->d.eNum[4] = -1, \
            (thee)->d.eNum[5] = -1, \
            (thee)->d.tags    = MASK_00000000000000000000000000000000, \
            Vel_init((Vel*)(thee), dim, id) \
        )
/** @brief Class S: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#       define SS_reinit(thee) ( \
            (thee)->d.vPtr[0] = VNULL, \
            (thee)->d.vPtr[1] = VNULL, \
            (thee)->d.vPtr[2] = VNULL, \
            (thee)->d.vPtr[3] = VNULL, \
            (thee)->d.sPtr[0] = VNULL, \
            (thee)->d.sPtr[1] = VNULL, \
            (thee)->d.sPtr[2] = VNULL, \
            (thee)->d.sPtr[3] = VNULL, \
            (thee)->d.fNum[0] = -1, \
            (thee)->d.fNum[1] = -1, \
            (thee)->d.fNum[2] = -1, \
            (thee)->d.fNum[3] = -1, \
            (thee)->d.eNum[0] = -1, \
            (thee)->d.eNum[1] = -1, \
            (thee)->d.eNum[2] = -1, \
            (thee)->d.eNum[3] = -1, \
            (thee)->d.eNum[4] = -1, \
            (thee)->d.eNum[5] = -1, \
            (thee)->d.tags    = MASK_00000000000000000000000000000000, \
            Vel_reinit((Vel*)(thee)) \
        )
#   else
/** @brief Class S: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#       define SS_init(thee,dim,id) ( \
            (thee)->d.vPtr[0] = VNULL, \
            (thee)->d.vPtr[1] = VNULL, \
            (thee)->d.vPtr[2] = VNULL, \
            (thee)->d.vPtr[3] = VNULL, \
            (thee)->d.sPtr[0] = VNULL, \
            (thee)->d.sPtr[1] = VNULL, \
            (thee)->d.sPtr[2] = VNULL, \
            (thee)->d.sPtr[3] = VNULL, \
            (thee)->d.tags    = MASK_00000000000000000000000000000000, \
            Vel_init((Vel*)(thee), dim, id) \
        )
/** @brief Class S: Inlineable methods (ves.c) if defined(VINLINE_GEM) */
#       define SS_reinit(thee) ( \
            (thee)->d.vPtr[0] = VNULL, \
            (thee)->d.vPtr[1] = VNULL, \
            (thee)->d.vPtr[2] = VNULL, \
            (thee)->d.vPtr[3] = VNULL, \
            (thee)->d.sPtr[0] = VNULL, \
            (thee)->d.sPtr[1] = VNULL, \
            (thee)->d.sPtr[2] = VNULL, \
            (thee)->d.sPtr[3] = VNULL, \
            (thee)->d.tags    = MASK_00000000000000000000000000000000, \
            Vel_reinit((Vel*)(thee)) \
        )
#   endif

/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setReality(thee,reel) Vel_setReality( (Vel*)(thee), (reel)  )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setDim(thee,dim)      Vel_setDim(     (Vel*)(thee), (dim)   )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setClass(thee,clas)   Vel_setClass(   (Vel*)(thee), (clas)  )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setType(thee,type)    Vel_setType(    (Vel*)(thee), (type)  )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setChart(thee,chart)  Vel_setChart(   (Vel*)(thee), (chart) )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setId(thee,id)        Vel_setId(      (Vel*)(thee), (id)    )

/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_reality(thee)         Vel_reality(    (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_dim(thee)             Vel_dim(        (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_dimVV(thee)           Vel_dimVV(      (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_dimEE(thee)           Vel_dimEE(      (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_dimFF(thee)           Vel_dimFF(      (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_class(thee)           Vel_class(      (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_type(thee)            Vel_type(       (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_chart(thee)           Vel_chart(      (Vel*)(thee)          )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_id(thee)              Vel_id(         (Vel*)(thee)          )

/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setFaceType(thee,f,type) (void)( \
           ((f) == 0) ? \
              ( (thee)->d.faces &= MASK_11111111111111111111111100000000, \
                (thee)->d.faces |= (type) ) \
        : (((f) == 1) ? \
              ( (thee)->d.faces &= MASK_11111111111111110000000011111111, \
                (thee)->d.faces |= ((type) << 8) ) \
        : (((f) == 2) ? \
              ( (thee)->d.faces &= MASK_11111111000000001111111111111111, \
                (thee)->d.faces |= ((type) << 16) ) \
        : (((f) == 3) ? \
              ( (thee)->d.faces &= MASK_00000000111111111111111111111111, \
                (thee)->d.faces |= ((type) << 24) ) \
        : 0))) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setRefinementEdge(thee,i) ( \
        (thee)->d.tags &= MASK_11111111111111111111111111111000, \
        (thee)->d.tags |=  (i) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setMarkedEdge1(thee,i) ( \
        (thee)->d.tags &= MASK_11111111111111111111111111000111, \
        (thee)->d.tags |= ((i) << 3) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setMarkedEdge2(thee,i) ( \
        (thee)->d.tags &= MASK_11111111111111111111111000111111, \
        (thee)->d.tags |= ((i) << 6) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setMarkedEdge3(thee,i) ( \
        (thee)->d.tags &= MASK_11111111111111111111000111111111, \
        (thee)->d.tags |= ((i) << 9) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setDegen(thee,i) ( \
        (thee)->d.tags &= MASK_11111111111111111000111111111111, \
        (thee)->d.tags |= ((i) << 12) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setRefinementCount(thee,i) ( \
        (thee)->d.tags &= MASK_11111111111111000111111111111111, \
        (thee)->d.tags |= ((i) << 15) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setRefineKey(thee,which,key) (void)( \
        ((which) == 0) \
            ? ( (thee)->d.tags &= MASK_11111111111110111111111111111111, \
                (thee)->d.tags |= ((key) << 18) ) \
            : ( (thee)->d.tags &= MASK_11111111111101111111111111111111, \
                (thee)->d.tags |= ((key) << 19) ) \
    )
#   if defined(VG_ELEMENT)
/** @brief Class S: Inlineable methods (ves.c) */
#       define SS_setFaceNumber(thee,i,fn) ((thee)->d.fNum[(i)] = (fn))
/** @brief Class S: Inlineable methods (ves.c) */
#       define SS_setEdgeNumber(thee,i,en) ((thee)->d.eNum[(i)] = (en))
#   endif
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setVertex(thee,i,vx) ((thee)->d.vPtr[(i)] = (vx))
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_setLink(thee,vx,sm) ( \
           ((vx) == (VV*)(thee)->d.vPtr[0]) ? (thee)->d.sPtr[0] = sm \
        : (((vx) == (VV*)(thee)->d.vPtr[1]) ? (thee)->d.sPtr[1] = sm \
        : (((vx) == (VV*)(thee)->d.vPtr[2]) ? (thee)->d.sPtr[2] = sm \
        : (((vx) == (VV*)(thee)->d.vPtr[3]) ? (thee)->d.sPtr[3] = sm \
        : VNULL))) \
    )

/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_faceType(thee,f) ( \
           ((f) == 0) ? \
               ((thee)->d.faces & MASK_00000000000000000000000011111111) \
        : (((f) == 1) ? \
               ((thee)->d.faces & MASK_00000000000000001111111100000000) >> 8 \
        : (((f) == 2) ? \
               ((thee)->d.faces & MASK_00000000111111110000000000000000) >> 16 \
        : (((f) == 3) ? \
               ((thee)->d.faces & MASK_11111111000000000000000000000000) >> 24 \
        : 0))) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_refinementEdge(thee) ( \
         ((thee)->d.tags & MASK_00000000000000000000000000000111) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_markedEdge1(thee) ( \
        (((thee)->d.tags & MASK_00000000000000000000000000111000) >> 3) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_markedEdge2(thee) ( \
        (((thee)->d.tags & MASK_00000000000000000000000111000000) >> 6) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_markedEdge3(thee) ( \
        (((thee)->d.tags & MASK_00000000000000000000111000000000) >> 9) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_degen(thee) ( \
        (((thee)->d.tags & MASK_00000000000000000111000000000000) >> 12) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_refinementCount(thee) ( \
        (((thee)->d.tags & MASK_00000000000000111000000000000000) >> 15) \
    )
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_refineKey(thee,which) ( \
        (which == 0) \
          ? (((thee)->d.tags & MASK_00000000000001000000000000000000) >> 18) \
          : (((thee)->d.tags & MASK_00000000000010000000000000000000) >> 19) \
    )
#   if defined(VG_ELEMENT)
/** @brief Class S: Inlineable methods (ves.c) */
#       define SS_faceNumber(thee,i) ((thee)->d.fNum[(i)])
/** @brief Class S: Inlineable methods (ves.c) */
#       define SS_edgeNumber(thee,i) ((thee)->d.eNum[(i)])
#   endif
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_vertex(thee,i) (VV*)((thee)->d.vPtr[(i)])
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_link(thee,vx) (SS*)( \
           ((vx) == (VV*)((thee)->d.vPtr[0])) \
                  ?      ((thee)->d.sPtr[0]) \
        : (((vx) == (VV*)((thee)->d.vPtr[1])) \
                  ?      ((thee)->d.sPtr[1]) \
        : (((vx) == (VV*)((thee)->d.vPtr[2])) \
                  ?      ((thee)->d.sPtr[2]) \
        : (((vx) == (VV*)((thee)->d.vPtr[3])) \
                  ?      ((thee)->d.sPtr[3]) : VNULL))) \
    )

/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_faceVertexNumber(thee,f,i) (vmapF[(f)][(i)])
/** @brief Class S: Inlineable methods (ves.c) */
#   define SS_vptr2localVnum(thee,vx) ( \
           ((vx) == (VV*)(thee)->d.vPtr[0]) ? 0 \
        : (((vx) == (VV*)(thee)->d.vPtr[1]) ? 1 \
        : (((vx) == (VV*)(thee)->d.vPtr[2]) ? 2 \
        : (((vx) == (VV*)(thee)->d.vPtr[3]) ? 3 \
        : 0))) \
    )
#endif /* if !defined(VINLINE_GEM) */

/*
 * ***************************************************************************
 * Class S: Non-inlineable methods (ves.c)
 * ***************************************************************************
 */

/**
 * @ingroup SS
 * @brief   The simplex constructor.
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  Pointer to a new allocated simplex object
 * @param   dim  the dimension bits
 * @param   myid the ID bits
 */
VEXTERNC SS* SS_ctor(int dim, int myid);

/**
 * @ingroup SS
 * @brief   The simplex destructor.
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to a simplex
 */
VEXTERNC void SS_dtor(SS **thee);

/**
 * @ingroup SS
 * @brief   Initialize the simplex rings.
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c)
 * @return  None
 * @param   thee Pointer to a simplex
 */
VEXTERNC void SS_initRing(SS *thee);

/**
 * @ingroup SS
 * @brief   Destroy the simplex rings.  
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to a simplex
 */
VEXTERNC void SS_meltRing(SS *thee);

/**
 * @ingroup SS
 * @brief   Build the simplex rings.     
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  None
 * @param   thee Pointer to a simplex
 */
VEXTERNC void SS_buildRing(SS *thee);

/**
 * @ingroup SS
 * @brief   Return the simplex sharing face i (opposite vertex i).   
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  the simplex sharing face i (opposite vertex i).   
 * @param   thee Pointer to a simplex
 * @param   i    index for the face
 */
VEXTERNC SS* SS_nabor(SS *thee, int i);

/**
 * @ingroup SS
 * @brief   Return the edge connecting vertices i and j.      
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  the edge connecting vertices i and j.      
 * @param   thee Pointer to a simplex
 * @param   i    index for a vertex
 * @param   j    index for a vertex
 */
VEXTERNC EE* SS_edge(SS *thee, int i, int j);

/**
 * @ingroup SS
 * @brief   Return local face number of face shared between two simplices. 
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c) 
 * @return  local face number of face shared between two simplices. 
 * @param   thee Pointer to a simplex
 * @param   sm   Pointer to a simplex
 */
VEXTERNC int SS_sharedFaceLocNum(SS *thee, SS *sm);

/**
 * @ingroup SS
 * @brief   Return the proper edge type (interior/boundary) of an edge
 *          connecting the two given vertices. 
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c)\n
 *          ASSUME that the edge DOES NOT exist or does not have a correct
 *          and consistent type, and calculate its type from the face types.
 *          \n
 *          The type we calculate is based only on local info; in 3D it may
 *          NOT be the correct edge type for the edge as far as the global
 *          mesh is concerned.  However, the local information about all
 *          simplices using the edge can be combined to determine the 
 *          correct global type.
 *          \n
 *          We must not be tempted to look for an existing edge and then 
 *          grab its type; the edge may have just been created (with 
 *          interior type by default), and in fact WE are being called as 
 *          part of an attempt to calculate its global type...          
 * @return  the proper edge type (interior/boundary) of an edge connecting the two
 *          given vertices
 * @param   thee Pointer to a simplex
 * @param   v0   Pointer to a vertex
 * @param   v1   Pointer to a vertex
 */
VEXTERNC int SS_localEdgeType(SS *thee, VV *v0, VV *v1);

/**
 * @ingroup SS
 * @brief   Reverse the orientation of a simplex by swapping vertices.    
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c)
 * @return  None
 * @param   thee Pointer to a vertex
 */
VEXTERNC void SS_reverse(SS *thee);

/**
 * @ingroup FF
 * @brief   The FF constructor.
 * @author  Michael Holst
 * @note    Class S: Inlineable methods (ves.c)
 * @return  Pointer to a new allocated FF class
 * @param   grandParentFace ID number for gip sub-structure
 * @param   sPtr            Pointer to a simplex 
 * @param   color           index for a face
 */
VPUBLIC FF* FF_ctor(int grandParentFace, SS *sPtr, int color);

#endif /* _VES_H_ */