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
2060
2061
2062
2063
2064
2065
2066
2067
2068
2069
2070
2071
2072
2073
2074
2075
2076
2077
2078
2079
2080
2081
2082
2083
2084
2085
2086
2087
2088
2089
2090
2091
2092
2093
2094
2095
2096
2097
2098
2099
2100
2101
2102
2103
2104
2105
2106
2107
2108
2109
2110
2111
2112
2113
2114
2115
2116
2117
2118
2119
2120
2121
2122
2123
2124
2125
2126
2127
2128
2129
2130
2131
2132
2133
2134
2135
2136
2137
2138
2139
2140
2141
2142
2143
2144
2145
2146
2147
2148
2149
2150
2151
2152
2153
2154
2155
2156
2157
2158
2159
2160
2161
2162
2163
2164
2165
2166
2167
2168
2169
2170
2171
2172
2173
2174
2175
2176
2177
2178
2179
2180
2181
2182
2183
2184
2185
2186
2187
2188
2189
2190
2191
2192
2193
2194
2195
2196
2197
2198
2199
2200
2201
2202
2203
2204
2205
2206
2207
2208
2209
2210
2211
2212
2213
2214
2215
2216
2217
2218
2219
2220
2221
2222
2223
2224
2225
2226
2227
2228
2229
2230
2231
2232
2233
2234
2235
2236
2237
2238
2239
2240
2241
2242
2243
2244
2245
2246
2247
2248
2249
2250
2251
2252
2253
2254
2255
2256
2257
2258
2259
2260
2261
2262
2263
2264
2265
2266
2267
2268
2269
2270
2271
2272
2273
2274
2275
2276
2277
2278
2279
2280
2281
2282
2283
2284
2285
2286
2287
2288
2289
2290
2291
2292
2293
2294
2295
2296
2297
2298
2299
2300
2301
2302
2303
2304
2305
2306
2307
2308
2309
2310
2311
2312
2313
2314
2315
2316
2317
2318
2319
2320
2321
2322
2323
2324
2325
2326
2327
2328
2329
2330
2331
2332
2333
2334
2335
2336
2337
2338
2339
2340
2341
2342
2343
2344
2345
2346
2347
2348
2349
2350
2351
2352
2353
2354
2355
2356
2357
2358
2359
2360
2361
2362
2363
2364
2365
2366
2367
2368
2369
2370
2371
2372
2373
2374
2375
2376
2377
2378
2379
2380
2381
2382
2383
2384
2385
2386
2387
2388
2389
2390
2391
2392
2393
2394
2395
2396
2397
2398
2399
2400
2401
2402
2403
2404
2405
2406
2407
2408
2409
2410
2411
2412
2413
2414
2415
2416
2417
2418
2419
2420
2421
2422
2423
2424
2425
2426
2427
2428
2429
2430
2431
2432
2433
2434
2435
2436
2437
2438
2439
2440
2441
2442
2443
2444
2445
2446
2447
2448
2449
2450
2451
2452
2453
2454
2455
2456
2457
2458
2459
2460
2461
2462
2463
2464
2465
2466
2467
2468
2469
2470
2471
2472
2473
2474
2475
2476
2477
2478
2479
2480
2481
2482
2483
2484
2485
2486
2487
2488
2489
2490
2491
2492
2493
2494
2495
2496
2497
2498
2499
2500
2501
2502
2503
2504
2505
2506
2507
2508
2509
2510
2511
2512
2513
2514
2515
2516
2517
2518
2519
2520
2521
2522
2523
2524
2525
2526
2527
2528
2529
2530
2531
2532
2533
2534
2535
2536
2537
2538
2539
2540
2541
2542
2543
2544
2545
2546
2547
2548
2549
2550
2551
2552
2553
2554
2555
2556
2557
2558
2559
2560
2561
2562
2563
2564
2565
2566
2567
2568
2569
2570
2571
2572
2573
2574
2575
2576
2577
2578
2579
2580
2581
2582
2583
2584
2585
2586
2587
2588
2589
2590
2591
2592
2593
2594
2595
2596
2597
2598
2599
2600
2601
2602
2603
2604
2605
2606
2607
2608
2609
2610
2611
2612
2613
2614
2615
2616
2617
2618
2619
2620
2621
2622
2623
2624
2625
2626
2627
2628
2629
2630
2631
2632
2633
2634
2635
2636
2637
2638
2639
2640
2641
2642
2643
2644
2645
2646
2647
2648
2649
2650
2651
2652
2653
2654
2655
2656
2657
2658
2659
2660
2661
2662
2663
2664
2665
2666
2667
2668
2669
2670
2671
2672
2673
2674
2675
2676
2677
2678
2679
2680
2681
2682
2683
2684
2685
2686
2687
2688
2689
2690
2691
2692
2693
2694
2695
2696
2697
2698
2699
2700
2701
2702
2703
2704
2705
2706
2707
2708
2709
2710
2711
2712
2713
2714
2715
2716
2717
2718
2719
2720
2721
2722
2723
2724
2725
2726
2727
2728
2729
2730
2731
2732
2733
2734
2735
2736
2737
2738
2739
2740
2741
2742
2743
2744
2745
2746
2747
2748
2749
2750
2751
2752
2753
2754
2755
2756
2757
2758
2759
2760
2761
2762
2763
2764
2765
2766
2767
2768
2769
2770
2771
2772
2773
2774
2775
2776
2777
2778
2779
2780
2781
2782
2783
2784
2785
2786
2787
2788
2789
2790
2791
2792
2793
2794
2795
2796
2797
2798
2799
2800
2801
2802
2803
2804
2805
2806
2807
2808
2809
2810
2811
2812
2813
2814
2815
2816
2817
2818
2819
2820
2821
2822
2823
2824
2825
2826
2827
2828
2829
2830
2831
2832
2833
2834
2835
2836
2837
2838
2839
2840
2841
2842
2843
2844
2845
2846
2847
2848
2849
2850
2851
2852
2853
2854
2855
2856
2857
2858
2859
2860
2861
2862
2863
2864
2865
2866
2867
2868
2869
2870
2871
2872
2873
2874
2875
2876
2877
2878
2879
2880
2881
2882
2883
2884
2885
2886
2887
2888
2889
2890
2891
2892
2893
2894
2895
2896
2897
2898
2899
2900
2901
2902
2903
2904
2905
2906
2907
2908
2909
2910
2911
2912
2913
2914
2915
2916
2917
2918
2919
2920
2921
2922
2923
2924
2925
2926
2927
2928
2929
2930
2931
2932
2933
2934
2935
2936
2937
2938
2939
2940
2941
2942
2943
2944
2945
2946
2947
2948
2949
2950
2951
2952
2953
2954
2955
2956
2957
2958
2959
2960
2961
2962
2963
2964
2965
2966
2967
2968
2969
2970
2971
2972
2973
2974
2975
2976
2977
2978
2979
2980
2981
2982
2983
2984
2985
2986
2987
2988
2989
2990
2991
2992
2993
2994
2995
2996
2997
2998
2999
3000
3001
3002
3003
3004
3005
3006
3007
3008
3009
3010
3011
3012
3013
3014
3015
3016
3017
3018
3019
3020
3021
3022
3023
3024
3025
3026
3027
3028
3029
3030
3031
3032
3033
3034
3035
3036
3037
3038
3039
3040
3041
3042
3043
3044
3045
3046
3047
3048
3049
3050
3051
3052
3053
3054
3055
3056
3057
3058
3059
3060
3061
3062
3063
3064
3065
3066
3067
3068
3069
3070
|
/*<html><pre> -<a href="qh-poly.htm"
>-------------------------------</a><a name="TOP">-</a>
poly2.c
implements polygons and simplices
see qh-poly.htm, poly.h and qhull.h
frequently used code is in poly.c
copyright (c) 1993-2002, The Geometry Center
*/
#include "qhull_a.h"
/*======== functions in alphabetical order ==========*/
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="addhash">-</a>
qh_addhash( newelem, hashtable, hashsize, hash )
add newelem to linear hash table at hash if not already there
*/
void qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash) {
int scan;
void *elem;
for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
scan= (++scan >= hashsize ? 0 : scan)) {
if (elem == newelem)
break;
}
/* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
if (!elem)
SETelem_(hashtable, scan)= newelem;
} /* addhash */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="check_bestdist">-</a>
qh_check_bestdist()
check that all points are within max_outside of the nearest facet
if qh.ONLYgood,
ignores !good facets
see:
qh_check_maxout(), qh_outerinner()
notes:
only called from qh_check_points()
seldom used since qh.MERGING is almost always set
if notverified>0 at end of routine
some points were well inside the hull. If the hull contains
a lens-shaped component, these points were not verified. Use
options 'Qi Tv' to verify all points. (Exhaustive check also verifies)
design:
determine facet for each point (if any)
for each point
start with the assigned facet or with the first facet
find the best facet for the point and check all coplanar facets
error if point is outside of facet
*/
void qh_check_bestdist (void) {
boolT waserror= False, unassigned;
facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
facetT *facetlist;
realT dist, maxoutside, maxdist= -REALmax;
pointT *point;
int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
setT *facets;
trace1((qh ferr, "qh_check_bestdist: check points below nearest facet. Facet_list f%d\n",
qh facet_list->id));
maxoutside= qh_maxouter();
maxoutside += qh DISTround;
/* one more qh.DISTround for check computation */
trace1((qh ferr, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
facets= qh_pointfacet (/*qh facet_list*/);
if (!qh_QUICKhelp && qh PRINTprecision)
fprintf (qh ferr, "\n\
qhull output completed. Verifying that %d points are\n\
below %2.2g of the nearest %sfacet.\n",
qh_setsize(facets), maxoutside, (qh ONLYgood ? "good " : ""));
FOREACHfacet_i_(facets) { /* for each point with facet assignment */
if (facet)
unassigned= False;
else {
unassigned= True;
facet= qh facet_list;
}
point= qh_point(facet_i);
if (point == qh GOODpointp)
continue;
qh_distplane(point, facet, &dist);
numpart++;
bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
/* occurs after statistics reported */
maximize_(maxdist, dist);
if (dist > maxoutside) {
if (qh ONLYgood && !bestfacet->good
&& !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
&& dist > maxoutside))
notgood++;
else {
waserror= True;
fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
facet_i, bestfacet->id, dist, maxoutside);
if (errfacet1 != bestfacet) {
errfacet2= errfacet1;
errfacet1= bestfacet;
}
}
}else if (unassigned && dist < -qh MAXcoplanar)
notverified++;
}
qh_settempfree (&facets);
if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
fprintf(qh ferr, "\n%d points were well inside the hull. If the hull contains\n\
a lens-shaped component, these points were not verified. Use\n\
options 'Qci Tv' to verify all points.\n", notverified);
if (maxdist > qh outside_err) {
fprintf( qh ferr, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull. The maximum value (qh.outside_err) is %6.2g\n",
maxdist, qh outside_err);
qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
}else if (waserror && qh outside_err > REALmax/2)
qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
else if (waserror)
; /* the error was logged to qh.ferr but does not effect the output */
trace0((qh ferr, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
} /* check_bestdist */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="check_maxout">-</a>
qh_check_maxout()
updates qh.max_outside by checking all points against bestfacet
if qh.ONLYgood, ignores !good facets
returns:
updates facet->maxoutside via qh_findbesthorizon()
sets qh.maxoutdone
if printing qh.min_vertex (qh_outerinner),
it is updated to the current vertices
removes inside/coplanar points from coplanarset as needed
notes:
defines coplanar as min_vertex instead of MAXcoplanar
may not need to check near-inside points because of qh.MAXcoplanar
and qh.KEEPnearinside (before it was -DISTround)
see also:
qh_check_bestdist()
design:
if qh.min_vertex is needed
for all neighbors of all vertices
test distance from vertex to neighbor
determine facet for each point (if any)
for each point with an assigned facet
find the best facet for the point and check all coplanar facets
(updates outer planes)
remove near-inside points from coplanar sets
*/
#ifndef qh_NOmerge
void qh_check_maxout (void) {
facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
realT dist, maxoutside, minvertex, old_maxoutside;
pointT *point;
int numpart= 0, facet_i, facet_n, notgood= 0;
setT *facets, *vertices;
vertexT *vertex;
trace1((qh ferr, "qh_check_maxout: check and update maxoutside for each facet.\n"));
maxoutside= minvertex= 0;
if (qh VERTEXneighbors
&& (qh PRINTsummary || qh KEEPinside || qh KEEPcoplanar
|| qh TRACElevel || qh PRINTstatistics
|| qh PRINTout[0] == qh_PRINTsummary || qh PRINTout[0] == qh_PRINTnone)) {
trace1((qh ferr, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
vertices= qh_pointvertex (/*qh facet_list*/);
FORALLvertices {
FOREACHneighbor_(vertex) {
zinc_(Zdistvertex); /* distance also computed by main loop below */
qh_distplane (vertex->point, neighbor, &dist);
minimize_(minvertex, dist);
if (-dist > qh TRACEdist || dist > qh TRACEdist
|| neighbor == qh tracefacet || vertex == qh tracevertex)
fprintf (qh ferr, "qh_check_maxout: p%d (v%d) is %.2g from f%d\n",
qh_pointid (vertex->point), vertex->id, dist, neighbor->id);
}
}
if (qh MERGING) {
wmin_(Wminvertex, qh min_vertex);
}
qh min_vertex= minvertex;
qh_settempfree (&vertices);
}
facets= qh_pointfacet (/*qh facet_list*/);
do {
old_maxoutside= fmax_(qh max_outside, maxoutside);
FOREACHfacet_i_(facets) { /* for each point with facet assignment */
if (facet) {
point= qh_point(facet_i);
if (point == qh GOODpointp)
continue;
zinc_(Ztotcheck);
qh_distplane(point, facet, &dist);
numpart++;
bestfacet= qh_findbesthorizon (qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
if (bestfacet && dist > maxoutside) {
if (qh ONLYgood && !bestfacet->good
&& !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
&& dist > maxoutside))
notgood++;
else
maxoutside= dist;
}
if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
fprintf (qh ferr, "qh_check_maxout: p%d is %.2g above f%d\n",
qh_pointid (point), dist, bestfacet->id);
}
}
}while
(maxoutside > 2*old_maxoutside);
/* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
zzadd_(Zcheckpart, numpart);
qh_settempfree (&facets);
wval_(Wmaxout)= maxoutside - qh max_outside;
wmax_(Wmaxoutside, qh max_outside);
qh max_outside= maxoutside;
qh_nearcoplanar (/*qh.facet_list*/);
qh maxoutdone= True;
trace1((qh ferr, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
maxoutside, qh min_vertex, notgood));
} /* check_maxout */
#else /* qh_NOmerge */
void qh_check_maxout (void) {
}
#endif
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="check_output">-</a>
qh_check_output()
performs the checks at the end of qhull algorithm
Maybe called after voronoi output. Will recompute otherwise centrums are Voronoi centers instead
*/
void qh_check_output (void) {
int i;
if (qh STOPcone)
return;
if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
qh_checkpolygon (qh facet_list);
qh_checkflipped_all (qh facet_list);
qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
}else if (!qh MERGING && qh_newstats (qhstat precision, &i)) {
qh_checkflipped_all (qh facet_list);
qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
}
} /* check_output */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="check_point">-</a>
qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
check that point is less than maxoutside from facet
*/
void qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
realT dist;
/* occurs after statistics reported */
qh_distplane(point, facet, &dist);
if (dist > *maxoutside) {
if (*errfacet1 != facet) {
*errfacet2= *errfacet1;
*errfacet1= facet;
}
fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
qh_pointid(point), facet->id, dist, *maxoutside);
}
maximize_(*maxdist, dist);
} /* qh_check_point */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="check_points">-</a>
qh_check_points()
checks that all points are inside all facets
notes:
if many points and qh_check_maxout not called (i.e., !qh.MERGING),
calls qh_findbesthorizon (seldom done).
ignores flipped facets
maxoutside includes 2 qh.DISTrounds
one qh.DISTround for the computed distances in qh_check_points
qh_printafacet and qh_printsummary needs only one qh.DISTround
the computation for qh.VERIFYdirect does not account for qh.other_points
design:
if many points
use qh_check_bestdist()
else
for all facets
for all points
check that point is inside facet
*/
void qh_check_points (void) {
facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
realT total, maxoutside, maxdist= -REALmax;
pointT *point, **pointp, *pointtemp;
boolT testouter;
maxoutside= qh_maxouter();
maxoutside += qh DISTround;
/* one more qh.DISTround for check computation */
trace1((qh ferr, "qh_check_points: check all points below %2.2g of all facet planes\n",
maxoutside));
if (qh num_good) /* miss counts other_points and !good facets */
total= (float) qh num_good * qh num_points;
else
total= (float) qh num_facets * qh num_points;
if (total >= qh_VERIFYdirect && !qh maxoutdone) {
if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
fprintf (qh ferr, "\n\
qhull input warning: merging without checking outer planes ('Q5' or 'Po').\n\
Verify may report that a point is outside of a facet.\n");
qh_check_bestdist();
}else {
if (qh_MAXoutside && qh maxoutdone)
testouter= True;
else
testouter= False;
if (!qh_QUICKhelp) {
if (qh MERGEexact)
fprintf (qh ferr, "\n\
qhull input warning: exact merge ('Qx'). Verify may report that a point\n\
is outside of a facet. See qh-optq.htm#Qx\n");
else if (qh SKIPcheckmax || qh NOnearinside)
fprintf (qh ferr, "\n\
qhull input warning: no outer plane check ('Q5') or no processing of\n\
near-inside points ('Q8'). Verify may report that a point is outside\n\
of a facet.\n");
}
if (qh PRINTprecision) {
if (testouter)
fprintf (qh ferr, "\n\
Output completed. Verifying that all points are below outer planes of\n\
all %sfacets. Will make %2.0f distance computations.\n",
(qh ONLYgood ? "good " : ""), total);
else
fprintf (qh ferr, "\n\
Output completed. Verifying that all points are below %2.2g of\n\
all %sfacets. Will make %2.0f distance computations.\n",
maxoutside, (qh ONLYgood ? "good " : ""), total);
}
FORALLfacets {
if (!facet->good && qh ONLYgood)
continue;
if (facet->flipped)
continue;
if (!facet->normal) {
fprintf( qh ferr, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
continue;
}
if (testouter) {
#if qh_MAXoutside
maxoutside= facet->maxoutside + 2* qh DISTround;
/* one DISTround to actual point and another to computed point */
#endif
}
FORALLpoints {
if (point != qh GOODpointp)
qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
}
FOREACHpoint_(qh other_points) {
if (point != qh GOODpointp)
qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
}
}
if (maxdist > qh outside_err) {
fprintf( qh ferr, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull. The maximum value (qh.outside_err) is %6.2g\n",
maxdist, qh outside_err );
qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
}else if (errfacet1 && qh outside_err > REALmax/2)
qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
else if (errfacet1)
; /* the error was logged to qh.ferr but does not effect the output */
trace0((qh ferr, "qh_check_points: max distance outside %2.2g\n", maxdist));
}
} /* check_points */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="checkconvex">-</a>
qh_checkconvex( facetlist, fault )
check that each ridge in facetlist is convex
fault = qh_DATAfault if reporting errors
= qh_ALGORITHMfault otherwise
returns:
counts Zconcaveridges and Zcoplanarridges
errors if concaveridge or if merging an coplanar ridge
note:
if not merging,
tests vertices for neighboring simplicial facets
else if ZEROcentrum,
tests vertices for neighboring simplicial facets
else
tests centrums of neighboring facets
design:
for all facets
report flipped facets
if ZEROcentrum and simplicial neighbors
test vertices for neighboring simplicial facets
else
test centrum against all neighbors
*/
void qh_checkconvex(facetT *facetlist, int fault) {
facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
vertexT *vertex;
realT dist;
pointT *centrum;
boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
int neighbor_i;
trace1((qh ferr, "qh_checkconvex: check all ridges are convex\n"));
if (!qh RERUN) {
zzval_(Zconcaveridges)= 0;
zzval_(Zcoplanarridges)= 0;
}
FORALLfacet_(facetlist) {
if (facet->flipped) {
qh_precision ("flipped facet");
fprintf (qh ferr, "qhull precision error: f%d is flipped (interior point is outside)\n",
facet->id);
errfacet1= facet;
waserror= True;
continue;
}
if (qh MERGING && (!qh ZEROcentrum || !facet->simplicial || facet->tricoplanar))
allsimplicial= False;
else {
allsimplicial= True;
neighbor_i= 0;
FOREACHneighbor_(facet) {
vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
if (!neighbor->simplicial || neighbor->tricoplanar) {
allsimplicial= False;
continue;
}
qh_distplane (vertex->point, neighbor, &dist);
if (dist > -qh DISTround) {
if (fault == qh_DATAfault) {
qh_precision ("coplanar or concave ridge");
fprintf (qh ferr, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
qh_errexit(qh_ERRsingular, NULL, NULL);
}
if (dist > qh DISTround) {
zzinc_(Zconcaveridges);
qh_precision ("concave ridge");
fprintf (qh ferr, "qhull precision error: f%d is concave to f%d, since p%d (v%d) is %6.4g above\n",
facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}else if (qh ZEROcentrum) {
if (dist > 0) { /* qh_checkzero checks that dist < - qh DISTround */
zzinc_(Zcoplanarridges);
qh_precision ("coplanar ridge");
fprintf (qh ferr, "qhull precision error: f%d is clearly not convex to f%d, since p%d (v%d) is %6.4g above\n",
facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}
}else {
zzinc_(Zcoplanarridges);
qh_precision ("coplanar ridge");
trace0((qh ferr, "qhull precision error: f%d may be coplanar to f%d, since p%d (v%d) is within %6.4g during p%d\n",
facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist, qh furthest_id));
}
}
}
}
if (!allsimplicial) {
if (qh CENTERtype == qh_AScentrum) {
if (!facet->center)
facet->center= qh_getcentrum (facet);
centrum= facet->center;
}else {
if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
centrum_warning= True;
fprintf (qh ferr, "qhull note: recomputing centrums for convexity test. This may lead to false, precision errors.\n");
}
centrum= qh_getcentrum(facet);
tempcentrum= True;
}
FOREACHneighbor_(facet) {
if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
continue;
if (facet->tricoplanar || neighbor->tricoplanar)
continue;
zzinc_(Zdistconvex);
qh_distplane (centrum, neighbor, &dist);
if (dist > qh DISTround) {
zzinc_(Zconcaveridges);
qh_precision ("concave ridge");
fprintf (qh ferr, "qhull precision error: f%d is concave to f%d. Centrum of f%d is %6.4g above f%d\n",
facet->id, neighbor->id, facet->id, dist, neighbor->id);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}else if (dist >= 0.0) { /* if arithmetic always rounds the same,
can test against centrum radius instead */
zzinc_(Zcoplanarridges);
qh_precision ("coplanar ridge");
fprintf (qh ferr, "qhull precision error: f%d is coplanar or concave to f%d. Centrum of f%d is %6.4g above f%d\n",
facet->id, neighbor->id, facet->id, dist, neighbor->id);
errfacet1= facet;
errfacet2= neighbor;
waserror= True;
}
}
if (tempcentrum)
qh_memfree(centrum, qh normal_size);
}
}
if (waserror && !qh FORCEoutput)
qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
} /* checkconvex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="checkfacet">-</a>
qh_checkfacet( facet, newmerge, waserror )
checks for consistency errors in facet
newmerge set if from merge.c
returns:
sets waserror if any error occurs
checks:
vertex ids are inverse sorted
unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
if non-simplicial, at least as many ridges as neighbors
neighbors are not duplicated
ridges are not duplicated
in 3-d, ridges=verticies
(qh.hull_dim-1) ridge vertices
neighbors are reciprocated
ridge neighbors are facet neighbors and a ridge for every neighbor
simplicial neighbors match facetintersect
vertex intersection matches vertices of common ridges
vertex neighbors and facet vertices agree
all ridges have distinct vertex sets
notes:
uses neighbor->seen
design:
check sets
check vertices
check sizes of neighbors and vertices
check for qh_MERGEridge and qh_DUPLICATEridge flags
check neighbor set
check ridge set
check ridges, neighbors, and vertices
*/
void qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp) {
facetT *neighbor, **neighborp, *errother=NULL;
ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
vertexT *vertex, **vertexp;
unsigned previousid= INT_MAX;
int numneighbors, numvertices, numridges=0, numRvertices=0;
boolT waserror= False;
int skipA, skipB, ridge_i, ridge_n, i;
setT *intersection;
if (facet->visible) {
fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
if (!facet->normal) {
fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have a normal\n",
facet->id);
waserror= True;
}
qh_setcheck (facet->vertices, "vertices for f", facet->id);
qh_setcheck (facet->ridges, "ridges for f", facet->id);
qh_setcheck (facet->outsideset, "outsideset for f", facet->id);
qh_setcheck (facet->coplanarset, "coplanarset for f", facet->id);
qh_setcheck (facet->neighbors, "neighbors for f", facet->id);
FOREACHvertex_(facet->vertices) {
if (vertex->deleted) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
waserror= True;
}
if (vertex->id >= previousid) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
waserror= True;
break;
}
previousid= vertex->id;
}
numneighbors= qh_setsize(facet->neighbors);
numvertices= qh_setsize(facet->vertices);
numridges= qh_setsize(facet->ridges);
if (facet->simplicial) {
if (numvertices+numneighbors != 2*qh hull_dim
&& !facet->degenerate && !facet->redundant) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh hull_dim\n",
facet->id, numvertices, numneighbors);
qh_setprint (qh ferr, "", facet->neighbors);
waserror= True;
}
}else { /* non-simplicial */
if (!newmerge
&&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
&& !facet->degenerate && !facet->redundant) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
facet->id, numvertices, numneighbors);
waserror= True;
}
/* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
if (numridges < numneighbors
||(qh hull_dim == 3 && numvertices > numridges && !qh NEWfacets)
||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
if (!facet->degenerate && !facet->redundant) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or (3-d) > #vertices %d or (2-d) not all 2\n",
facet->id, numridges, numneighbors, numvertices);
waserror= True;
}
}
}
FOREACHneighbor_(facet) {
if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
neighbor->seen= True;
}
FOREACHneighbor_(facet) {
if (!qh_setin(neighbor->neighbors, facet)) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
facet->id, neighbor->id, neighbor->id, facet->id);
errother= neighbor;
waserror= True;
}
if (!neighbor->seen) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
facet->id, neighbor->id);
errother= neighbor;
waserror= True;
}
neighbor->seen= False;
}
FOREACHridge_(facet->ridges) {
qh_setcheck (ridge->vertices, "vertices for r", ridge->id);
ridge->seen= False;
}
FOREACHridge_(facet->ridges) {
if (ridge->seen) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
facet->id, ridge->id);
errridge= ridge;
waserror= True;
}
ridge->seen= True;
numRvertices= qh_setsize(ridge->vertices);
if (numRvertices != qh hull_dim - 1) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
ridge->top->id, ridge->bottom->id, numRvertices);
errridge= ridge;
waserror= True;
}
neighbor= otherfacet_(ridge, facet);
neighbor->seen= True;
if (!qh_setin(facet->neighbors, neighbor)) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
facet->id, neighbor->id, ridge->id);
errridge= ridge;
waserror= True;
}
}
if (!facet->simplicial) {
FOREACHneighbor_(facet) {
if (!neighbor->seen) {
fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
facet->id, neighbor->id);
errother= neighbor;
waserror= True;
}
intersection= qh_vertexintersect_new(facet->vertices, neighbor->vertices);
qh_settemppush (intersection);
FOREACHvertex_(facet->vertices) {
vertex->seen= False;
vertex->seen2= False;
}
FOREACHvertex_(intersection)
vertex->seen= True;
FOREACHridge_(facet->ridges) {
if (neighbor != otherfacet_(ridge, facet))
continue;
FOREACHvertex_(ridge->vertices) {
if (!vertex->seen) {
fprintf (qh ferr, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
vertex->id, ridge->id, facet->id, neighbor->id);
qh_errexit (qh_ERRqhull, facet, ridge);
}
vertex->seen2= True;
}
}
if (!newmerge) {
FOREACHvertex_(intersection) {
if (!vertex->seen2) {
if (qh IStracing >=3 || !qh MERGING) {
fprintf (qh ferr, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
not in a ridge. This is ok under merging. Last point was p%d\n",
vertex->id, facet->id, neighbor->id, qh furthest_id);
if (!qh FORCEoutput && !qh MERGING) {
qh_errprint ("ERRONEOUS", facet, neighbor, NULL, vertex);
if (!qh MERGING)
qh_errexit (qh_ERRqhull, NULL, NULL);
}
}
}
}
}
qh_settempfree (&intersection);
}
}else { /* simplicial */
FOREACHneighbor_(facet) {
if (neighbor->simplicial) {
skipA= SETindex_(facet->neighbors, neighbor);
skipB= qh_setindex (neighbor->neighbors, facet);
if (!qh_setequal_skip (facet->vertices, skipA, neighbor->vertices, skipB)) {
fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
facet->id, skipA, neighbor->id, skipB);
errother= neighbor;
waserror= True;
}
}
}
}
if (qh hull_dim < 5 && (qh IStracing > 2 || qh CHECKfrequently)) {
FOREACHridge_i_(facet->ridges) { /* expensive */
for (i= ridge_i+1; i < ridge_n; i++) {
ridge2= SETelemt_(facet->ridges, i, ridgeT);
if (qh_setequal (ridge->vertices, ridge2->vertices)) {
fprintf (qh ferr, "qh_checkfacet: ridges r%d and r%d have the same vertices\n",
ridge->id, ridge2->id);
errridge= ridge;
waserror= True;
}
}
}
}
if (waserror) {
qh_errprint("ERRONEOUS", facet, errother, errridge, NULL);
*waserrorp= True;
}
} /* checkfacet */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="checkflipped_all">-</a>
qh_checkflipped_all( facetlist )
checks orientation of facets in list against interior point
*/
void qh_checkflipped_all (facetT *facetlist) {
facetT *facet;
boolT waserror= False;
realT dist;
if (facetlist == qh facet_list)
zzval_(Zflippedfacets)= 0;
FORALLfacet_(facetlist) {
if (facet->normal && !qh_checkflipped (facet, &dist, !qh_ALL)) {
fprintf(qh ferr, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
facet->id, dist);
if (!qh FORCEoutput) {
qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
waserror= True;
}
}
}
if (waserror) {
fprintf (qh ferr, "\n\
A flipped facet occurs when its distance to the interior point is\n\
greater than %2.2g, the maximum roundoff error.\n", -qh DISTround);
qh_errexit(qh_ERRprec, NULL, NULL);
}
} /* checkflipped_all */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="checkpolygon">-</a>
qh_checkpolygon( facetlist )
checks the correctness of the structure
notes:
call with either qh.facet_list or qh.newfacet_list
checks num_facets and num_vertices if qh.facet_list
design:
for each facet
checks facet and outside set
initializes vertexlist
for each facet
checks vertex set
if checking all facets (qh.facetlist)
check facet count
if qh.VERTEXneighbors
check vertex neighbors and count
check vertex count
*/
void qh_checkpolygon(facetT *facetlist) {
facetT *facet;
vertexT *vertex, **vertexp, *vertexlist;
int numfacets= 0, numvertices= 0, numridges= 0;
int totvneighbors= 0, totvertices= 0;
boolT waserror= False, nextseen= False, visibleseen= False;
trace1((qh ferr, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
if (facetlist != qh facet_list || qh ONLYgood)
nextseen= True;
FORALLfacet_(facetlist) {
if (facet == qh visible_list)
visibleseen= True;
if (!facet->visible) {
if (!nextseen) {
if (facet == qh facet_next)
nextseen= True;
else if (qh_setsize (facet->outsideset)) {
if (!qh NARROWhull
#if !qh_COMPUTEfurthest
|| facet->furthestdist >= qh MINoutside
#endif
) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
}
}
numfacets++;
qh_checkfacet(facet, False, &waserror);
}
}
if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
qh_printlists();
qh_errexit (qh_ERRqhull, qh visible_list, NULL);
}
if (facetlist == qh facet_list)
vertexlist= qh vertex_list;
else if (facetlist == qh newfacet_list)
vertexlist= qh newvertex_list;
else
vertexlist= NULL;
FORALLvertex_(vertexlist) {
vertex->seen= False;
vertex->visitid= 0;
}
FORALLfacet_(facetlist) {
if (facet->visible)
continue;
if (facet->simplicial)
numridges += qh hull_dim;
else
numridges += qh_setsize (facet->ridges);
FOREACHvertex_(facet->vertices) {
vertex->visitid++;
if (!vertex->seen) {
vertex->seen= True;
numvertices++;
if (qh_pointid (vertex->point) == -1) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
vertex->point, vertex->id, qh first_point);
waserror= True;
}
}
}
}
qh vertex_visit += numfacets;
if (facetlist == qh facet_list) {
if (numfacets != qh num_facets - qh num_visible) {
fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
numfacets, qh num_facets, qh num_visible);
waserror= True;
}
qh vertex_visit++;
if (qh VERTEXneighbors) {
FORALLvertices {
qh_setcheck (vertex->neighbors, "neighbors for v", vertex->id);
if (vertex->deleted)
continue;
totvneighbors += qh_setsize (vertex->neighbors);
}
FORALLfacet_(facetlist)
totvertices += qh_setsize (facet->vertices);
if (totvneighbors != totvertices) {
fprintf(qh ferr, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent. Totvneighbors %d, totvertices %d\n",
totvneighbors, totvertices);
waserror= True;
}
}
if (numvertices != qh num_vertices - qh_setsize(qh del_vertices)) {
fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
numvertices, qh num_vertices - qh_setsize(qh del_vertices));
waserror= True;
}
if (qh hull_dim == 2 && numvertices != numfacets) {
fprintf (qh ferr, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
numvertices, numfacets);
waserror= True;
}
if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
fprintf (qh ferr, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
A vertex appears twice in a edge list. May occur during merging.",
numvertices, numfacets, numridges/2);
/* occurs if lots of merging and a vertex ends up twice in an edge list. e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
}
}
if (waserror)
qh_errexit(qh_ERRqhull, NULL, NULL);
} /* checkpolygon */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="checkvertex">-</a>
qh_checkvertex( vertex )
check vertex for consistency
checks vertex->neighbors
notes:
neighbors checked efficiently in checkpolygon
*/
void qh_checkvertex (vertexT *vertex) {
boolT waserror= False;
facetT *neighbor, **neighborp, *errfacet=NULL;
if (qh_pointid (vertex->point) == -1) {
fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
waserror= True;
}
if (vertex->id >= qh vertex_id) {
fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
waserror= True;
}
if (!waserror && !vertex->deleted) {
if (qh_setsize (vertex->neighbors)) {
FOREACHneighbor_(vertex) {
if (!qh_setin (neighbor->vertices, vertex)) {
fprintf (qh ferr, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
errfacet= neighbor;
waserror= True;
}
}
}
}
if (waserror) {
qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
qh_errexit (qh_ERRqhull, errfacet, NULL);
}
} /* checkvertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="clearcenters">-</a>
qh_clearcenters( type )
clear old data from facet->center
notes:
sets new centertype
nop if CENTERtype is the same
*/
void qh_clearcenters (qh_CENTER type) {
facetT *facet;
if (qh CENTERtype != type) {
FORALLfacets {
if (qh CENTERtype == qh_ASvoronoi){
if (facet->center) {
qh_memfree (facet->center, qh center_size);
facet->center= NULL;
}
}else /* qh CENTERtype == qh_AScentrum */ {
if (facet->center) {
qh_memfree (facet->center, qh normal_size);
facet->center= NULL;
}
}
}
qh CENTERtype= type;
}
trace2((qh ferr, "qh_clearcenters: switched to center type %d\n", type));
} /* clearcenters */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="createsimplex">-</a>
qh_createsimplex( vertices )
creates a simplex from a set of vertices
returns:
initializes qh.facet_list to the simplex
initializes qh.newfacet_list, .facet_tail
initializes qh.vertex_list, .newvertex_list, .vertex_tail
design:
initializes lists
for each vertex
create a new facet
for each new facet
create its neighbor set
*/
void qh_createsimplex(setT *vertices) {
facetT *facet= NULL, *newfacet;
boolT toporient= True;
int vertex_i, vertex_n, nth;
setT *newfacets= qh_settemp (qh hull_dim+1);
vertexT *vertex;
qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
qh num_facets= qh num_vertices= qh num_visible= 0;
qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
FOREACHvertex_i_(vertices) {
newfacet= qh_newfacet();
newfacet->vertices= qh_setnew_delnthsorted (vertices, vertex_n,
vertex_i, 0);
newfacet->toporient= toporient;
qh_appendfacet(newfacet);
newfacet->newfacet= True;
qh_appendvertex (vertex);
qh_setappend (&newfacets, newfacet);
toporient ^= True;
}
FORALLnew_facets {
nth= 0;
FORALLfacet_(qh newfacet_list) {
if (facet != newfacet)
SETelem_(newfacet->neighbors, nth++)= facet;
}
qh_settruncate (newfacet->neighbors, qh hull_dim);
}
qh_settempfree (&newfacets);
trace1((qh ferr, "qh_createsimplex: created simplex\n"));
} /* createsimplex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="delridge">-</a>
qh_delridge( ridge )
deletes ridge from data structures it belongs to
frees up its memory
notes:
in merge.c, caller sets vertex->delridge for each vertex
ridges also freed in qh_freeqhull
*/
void qh_delridge(ridgeT *ridge) {
void **freelistp; /* used !qh_NOmem */
qh_setdel(ridge->top->ridges, ridge);
qh_setdel(ridge->bottom->ridges, ridge);
qh_setfree(&(ridge->vertices));
qh_memfree_(ridge, sizeof(ridgeT), freelistp);
} /* delridge */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="delvertex">-</a>
qh_delvertex( vertex )
deletes a vertex and frees its memory
notes:
assumes vertex->adjacencies have been updated if needed
unlinks from vertex_list
*/
void qh_delvertex (vertexT *vertex) {
if (vertex == qh tracevertex)
qh tracevertex= NULL;
qh_removevertex (vertex);
qh_setfree (&vertex->neighbors);
qh_memfree(vertex, sizeof(vertexT));
} /* delvertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="facet3vertex">-</a>
qh_facet3vertex( )
return temporary set of 3-d vertices in qh_ORIENTclock order
design:
if simplicial facet
build set from facet->vertices with facet->toporient
else
for each ridge in order
build set from ridge's vertices
*/
setT *qh_facet3vertex (facetT *facet) {
ridgeT *ridge, *firstridge;
vertexT *vertex;
int cntvertices, cntprojected=0;
setT *vertices;
cntvertices= qh_setsize(facet->vertices);
vertices= qh_settemp (cntvertices);
if (facet->simplicial) {
if (cntvertices != 3) {
fprintf (qh ferr, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
cntvertices, facet->id);
qh_errexit(qh_ERRqhull, facet, NULL);
}
qh_setappend (&vertices, SETfirst_(facet->vertices));
if (facet->toporient ^ qh_ORIENTclock)
qh_setappend (&vertices, SETsecond_(facet->vertices));
else
qh_setaddnth (&vertices, 0, SETsecond_(facet->vertices));
qh_setappend (&vertices, SETelem_(facet->vertices, 2));
}else {
ridge= firstridge= SETfirstt_(facet->ridges, ridgeT); /* no infinite */
while ((ridge= qh_nextridge3d (ridge, facet, &vertex))) {
qh_setappend (&vertices, vertex);
if (++cntprojected > cntvertices || ridge == firstridge)
break;
}
if (!ridge || cntprojected != cntvertices) {
fprintf (qh ferr, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up. got at least %d\n",
facet->id, cntprojected);
qh_errexit(qh_ERRqhull, facet, ridge);
}
}
return vertices;
} /* facet3vertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="findbestfacet">-</a>
qh_findbestfacet( point, bestoutside, bestdist, isoutside )
find facet that is furthest below a point
for Delaunay triangulations,
Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
returns:
if bestoutside is set (e.g., qh_ALL)
returns best facet that is not upperdelaunay
if Delaunay and inside, point is outside circumsphere of bestfacet
else
returns first facet below point
if point is inside, returns nearest, !upperdelaunay facet
distance to facet
isoutside set if outside of facet
notes:
this works for all distributions
if inside, qh_findbestfacet performs an exhaustive search
this may be too conservative. Sometimes it is clearly required.
qh_findbestfacet is not used by qhull.
uses qh.visit_id and qh.coplanarset
see:
<a href="geom.c#findbest">qh_findbest</a>
*/
facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
realT *bestdist, boolT *isoutside) {
facetT *bestfacet= NULL;
int numpart, totpart= 0;
bestfacet= qh_findbest (point, qh facet_list,
bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
bestdist, isoutside, &totpart);
if (*bestdist < -qh DISTround) {
bestfacet= qh_findfacet_all (point, bestdist, isoutside, &numpart);
totpart += numpart;
if ((isoutside && bestoutside)
|| (!isoutside && bestfacet->upperdelaunay)) {
bestfacet= qh_findbest (point, bestfacet,
bestoutside, False, bestoutside,
bestdist, isoutside, &totpart);
totpart += numpart;
}
}
trace3((qh ferr, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
bestfacet->id, *bestdist, *isoutside, totpart));
return bestfacet;
} /* findbestfacet */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="findfacet_all">-</a>
qh_findfacet_all( point, bestdist, isoutside, numpart )
exhaustive search for facet below a point
for Delaunay triangulations,
Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
returns:
returns first facet below point
if point is inside,
returns nearest facet
distance to facet
isoutside if point is outside of the hull
number of distance tests
*/
facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
int *numpart) {
facetT *bestfacet= NULL, *facet;
realT dist;
int totpart= 0;
*bestdist= REALmin;
*isoutside= False;
FORALLfacets {
if (facet->flipped || !facet->normal)
continue;
totpart++;
qh_distplane (point, facet, &dist);
if (dist > *bestdist) {
*bestdist= dist;
bestfacet= facet;
if (dist > qh MINoutside) {
*isoutside= True;
break;
}
}
}
*numpart= totpart;
trace3((qh ferr, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
getid_(bestfacet), *bestdist, *isoutside, totpart));
return bestfacet;
} /* findfacet_all */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="findgood">-</a>
qh_findgood( facetlist, goodhorizon )
identify good facets for qh.PRINTgood
if qh.GOODvertex>0
facet includes point as vertex
if !match, returns goodhorizon
inactive if qh.MERGING
if qh.GOODpoint
facet is visible or coplanar (>0) or not visible (<0)
if qh.GOODthreshold
facet->normal matches threshold
if !goodhorizon and !match,
selects facet with closest angle
sets GOODclosest
returns:
number of new, good facets found
determines facet->good
may update qh.GOODclosest
notes:
qh_findgood_all further reduces the good region
design:
count good facets
mark good facets for qh.GOODpoint
mark good facets for qh.GOODthreshold
if necessary
update qh.GOODclosest
*/
int qh_findgood (facetT *facetlist, int goodhorizon) {
facetT *facet, *bestfacet= NULL;
realT angle, bestangle= REALmax, dist;
int numgood=0;
FORALLfacet_(facetlist) {
if (facet->good)
numgood++;
}
if (qh GOODvertex>0 && !qh MERGING) {
FORALLfacet_(facetlist) {
if (!qh_isvertex (qh GOODvertexp, facet->vertices)) {
facet->good= False;
numgood--;
}
}
}
if (qh GOODpoint && numgood) {
FORALLfacet_(facetlist) {
if (facet->good && facet->normal) {
zinc_(Zdistgood);
qh_distplane (qh GOODpointp, facet, &dist);
if ((qh GOODpoint > 0) ^ (dist > 0.0)) {
facet->good= False;
numgood--;
}
}
}
}
if (qh GOODthreshold && (numgood || goodhorizon || qh GOODclosest)) {
FORALLfacet_(facetlist) {
if (facet->good && facet->normal) {
if (!qh_inthresholds (facet->normal, &angle)) {
facet->good= False;
numgood--;
if (angle < bestangle) {
bestangle= angle;
bestfacet= facet;
}
}
}
}
if (!numgood && (!goodhorizon || qh GOODclosest)) {
if (qh GOODclosest) {
if (qh GOODclosest->visible)
qh GOODclosest= NULL;
else {
qh_inthresholds (qh GOODclosest->normal, &angle);
if (angle < bestangle)
bestfacet= qh GOODclosest;
}
}
if (bestfacet && bestfacet != qh GOODclosest) {
if (qh GOODclosest)
qh GOODclosest->good= False;
qh GOODclosest= bestfacet;
bestfacet->good= True;
numgood++;
trace2((qh ferr, "qh_findgood: f%d is closest (%2.2g) to thresholds\n",
bestfacet->id, bestangle));
return numgood;
}
}else if (qh GOODclosest) { /* numgood > 0 */
qh GOODclosest->good= False;
qh GOODclosest= NULL;
}
}
zadd_(Zgoodfacet, numgood);
trace2((qh ferr, "qh_findgood: found %d good facets with %d good horizon\n",
numgood, goodhorizon));
if (!numgood && qh GOODvertex>0 && !qh MERGING)
return goodhorizon;
return numgood;
} /* findgood */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="findgood_all">-</a>
qh_findgood_all( facetlist )
apply other constraints for good facets (used by qh.PRINTgood)
if qh.GOODvertex
facet includes (>0) or doesn't include (<0) point as vertex
if last good facet and ONLYgood, prints warning and continues
if qh.SPLITthresholds
facet->normal matches threshold, or if none, the closest one
calls qh_findgood
nop if good not used
returns:
clears facet->good if not good
sets qh.num_good
notes:
this is like qh_findgood but more restrictive
design:
uses qh_findgood to mark good facets
marks facets for qh.GOODvertex
marks facets for qh.SPLITthreholds
*/
void qh_findgood_all (facetT *facetlist) {
facetT *facet, *bestfacet=NULL;
realT angle, bestangle= REALmax;
int numgood=0, startgood;
if (!qh GOODvertex && !qh GOODthreshold && !qh GOODpoint
&& !qh SPLITthresholds)
return;
if (!qh ONLYgood)
qh_findgood (qh facet_list, 0);
FORALLfacet_(facetlist) {
if (facet->good)
numgood++;
}
if (qh GOODvertex <0 || (qh GOODvertex > 0 && qh MERGING)) {
FORALLfacet_(facetlist) {
if (facet->good && ((qh GOODvertex > 0) ^ !!qh_isvertex (qh GOODvertexp, facet->vertices))) {
if (!--numgood) {
if (qh ONLYgood) {
fprintf (qh ferr, "qhull warning: good vertex p%d does not match last good facet f%d. Ignored.\n",
qh_pointid(qh GOODvertexp), facet->id);
return;
}else if (qh GOODvertex > 0)
fprintf (qh ferr, "qhull warning: point p%d is not a vertex ('QV%d').\n",
qh GOODvertex-1, qh GOODvertex-1);
else
fprintf (qh ferr, "qhull warning: point p%d is a vertex for every facet ('QV-%d').\n",
-qh GOODvertex - 1, -qh GOODvertex - 1);
}
facet->good= False;
}
}
}
startgood= numgood;
if (qh SPLITthresholds) {
FORALLfacet_(facetlist) {
if (facet->good) {
if (!qh_inthresholds (facet->normal, &angle)) {
facet->good= False;
numgood--;
if (angle < bestangle) {
bestangle= angle;
bestfacet= facet;
}
}
}
}
if (!numgood && bestfacet) {
bestfacet->good= True;
numgood++;
trace0((qh ferr, "qh_findgood_all: f%d is closest (%2.2g) to thresholds\n",
bestfacet->id, bestangle));
return;
}
}
qh num_good= numgood;
trace0((qh ferr, "qh_findgood_all: %d good facets remain out of %d facets\n",
numgood, startgood));
} /* findgood_all */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="furthestnext">-</a>
qh_furthestnext()
set qh.facet_next to facet with furthest of all furthest points
searches all facets on qh.facet_list
notes:
this may help avoid precision problems
*/
void qh_furthestnext (void /* qh facet_list */) {
facetT *facet, *bestfacet= NULL;
realT dist, bestdist= -REALmax;
FORALLfacets {
if (facet->outsideset) {
#if qh_COMPUTEfurthest
pointT *furthest;
furthest= (pointT*)qh_setlast (facet->outsideset);
zinc_(Zcomputefurthest);
qh_distplane (furthest, facet, &dist);
#else
dist= facet->furthestdist;
#endif
if (dist > bestdist) {
bestfacet= facet;
bestdist= dist;
}
}
}
if (bestfacet) {
qh_removefacet (bestfacet);
qh_prependfacet (bestfacet, &qh facet_next);
trace1((qh ferr, "qh_furthestnext: made f%d next facet (dist %.2g)\n",
bestfacet->id, bestdist));
}
} /* furthestnext */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="furthestout">-</a>
qh_furthestout( facet )
make furthest outside point the last point of outsideset
returns:
updates facet->outsideset
clears facet->notfurthest
sets facet->furthestdist
design:
determine best point of outsideset
make it the last point of outsideset
*/
void qh_furthestout (facetT *facet) {
pointT *point, **pointp, *bestpoint= NULL;
realT dist, bestdist= -REALmax;
FOREACHpoint_(facet->outsideset) {
qh_distplane (point, facet, &dist);
zinc_(Zcomputefurthest);
if (dist > bestdist) {
bestpoint= point;
bestdist= dist;
}
}
if (bestpoint) {
qh_setdel (facet->outsideset, point);
qh_setappend (&facet->outsideset, point);
#if !qh_COMPUTEfurthest
facet->furthestdist= bestdist;
#endif
}
facet->notfurthest= False;
trace3((qh ferr, "qh_furthestout: p%d is furthest outside point of f%d\n",
qh_pointid (point), facet->id));
} /* furthestout */
/*-<a href="qh-qhull.htm#TOC"
>-------------------------------</a><a name="infiniteloop">-</a>
qh_infiniteloop( facet )
report infinite loop error due to facet
*/
void qh_infiniteloop (facetT *facet) {
fprintf (qh ferr, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
qh_errexit (qh_ERRqhull, facet, NULL);
} /* qh_infiniteloop */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="initbuild">-</a>
qh_initbuild()
initialize hull and outside sets with point array
qh.FIRSTpoint/qh.NUMpoints is point array
if qh.GOODpoint
adds qh.GOODpoint to initial hull
returns:
qh_facetlist with initial hull
points partioned into outside sets, coplanar sets, or inside
initializes qh.GOODpointp, qh.GOODvertexp,
design:
initialize global variables used during qh_buildhull
determine precision constants and points with max/min coordinate values
if qh.SCALElast, scale last coordinate (for 'd')
build initial simplex
partition input points into facets of initial simplex
set up lists
if qh.ONLYgood
check consistency
add qh.GOODvertex if defined
*/
void qh_initbuild( void) {
setT *maxpoints, *vertices;
facetT *facet;
int i, numpart;
realT dist;
boolT isoutside;
qh furthest_id= -1;
qh lastreport= 0;
qh facet_id= qh vertex_id= qh ridge_id= 0;
qh visit_id= qh vertex_visit= 0;
qh maxoutdone= False;
if (qh GOODpoint > 0)
qh GOODpointp= qh_point (qh GOODpoint-1);
else if (qh GOODpoint < 0)
qh GOODpointp= qh_point (-qh GOODpoint-1);
if (qh GOODvertex > 0)
qh GOODvertexp= qh_point (qh GOODvertex-1);
else if (qh GOODvertex < 0)
qh GOODvertexp= qh_point (-qh GOODvertex-1);
if ((qh GOODpoint
&& (qh GOODpointp < qh first_point /* also catches !GOODpointp */
|| qh GOODpointp > qh_point (qh num_points-1)))
|| (qh GOODvertex
&& (qh GOODvertexp < qh first_point /* also catches !GOODvertexp */
|| qh GOODvertexp > qh_point (qh num_points-1)))) {
fprintf (qh ferr, "qhull input error: either QGn or QVn point is > p%d\n",
qh num_points-1);
qh_errexit (qh_ERRinput, NULL, NULL);
}
maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
if (qh SCALElast)
qh_scalelast (qh first_point, qh num_points, qh hull_dim,
qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
qh_detroundoff();
if (qh DELAUNAY && qh upper_threshold[qh hull_dim-1] > REALmax/2
&& qh lower_threshold[qh hull_dim-1] < -REALmax/2) {
for (i= qh_PRINTEND; i--; ) {
if (qh PRINTout[i] == qh_PRINTgeom && qh DROPdim < 0
&& !qh GOODthreshold && !qh SPLITthresholds)
break; /* in this case, don't set upper_threshold */
}
if (i < 0) {
if (qh UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
qh lower_threshold[qh hull_dim-1]= qh ANGLEround * qh_ZEROdelaunay;
qh GOODthreshold= True;
}else {
qh upper_threshold[qh hull_dim-1]= -qh ANGLEround * qh_ZEROdelaunay;
if (!qh GOODthreshold)
qh SPLITthresholds= True; /* build upper-convex hull even if Qg */
/* qh_initqhull_globals errors if Qg without Pdk/etc. */
}
}
}
vertices= qh_initialvertices(qh hull_dim, maxpoints, qh first_point, qh num_points);
qh_initialhull (vertices); /* initial qh facet_list */
qh_partitionall (vertices, qh first_point, qh num_points);
if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
if (qh TRACElevel || qh IStracing)
fprintf (qh ferr, "\nTrace level %d for %s | %s\n",
qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
fprintf (qh ferr, "Options selected for Qhull %s:\n%s\n", qh_VERSION, qh qhull_options);
}
qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
qh facet_next= qh facet_list;
qh_furthestnext (/* qh facet_list */);
if (qh PREmerge) {
qh cos_max= qh premerge_cos;
qh centrum_radius= qh premerge_centrum;
}
if (qh ONLYgood) {
if (qh GOODvertex > 0 && qh MERGING) {
fprintf (qh ferr, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
qh_errexit (qh_ERRinput, NULL, NULL);
}
if (!(qh GOODthreshold || qh GOODpoint
|| (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
fprintf (qh ferr, "qhull input error: 'Qg' (ONLYgood) needs a good threshold ('Pd0D0'), a\n\
good point (QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
qh_errexit (qh_ERRinput, NULL, NULL);
}
if (qh GOODvertex > 0 && !qh MERGING /* matches qh_partitionall */
&& !qh_isvertex (qh GOODvertexp, vertices)) {
facet= qh_findbestnew (qh GOODvertexp, qh facet_list,
&dist, !qh_ALL, &isoutside, &numpart);
zadd_(Zdistgood, numpart);
if (!isoutside) {
fprintf (qh ferr, "qhull input error: point for QV%d is inside initial simplex. It can not be made a vertex.\n",
qh_pointid(qh GOODvertexp));
qh_errexit (qh_ERRinput, NULL, NULL);
}
if (!qh_addpoint (qh GOODvertexp, facet, False)) {
qh_settempfree(&vertices);
qh_settempfree(&maxpoints);
return;
}
}
qh_findgood (qh facet_list, 0);
}
qh_settempfree(&vertices);
qh_settempfree(&maxpoints);
trace1((qh ferr, "qh_initbuild: initial hull created and points partitioned\n"));
} /* initbuild */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="initialhull">-</a>
qh_initialhull( vertices )
constructs the initial hull as a DIM3 simplex of vertices
design:
creates a simplex (initializes lists)
determines orientation of simplex
sets hyperplanes for facets
doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
checks for flipped facets and qh.NARROWhull
checks the result
*/
void qh_initialhull(setT *vertices) {
facetT *facet, *firstfacet, *neighbor, **neighborp;
realT dist, angle, minangle= REALmax;
#ifndef qh_NOtrace
int k;
#endif
qh_createsimplex(vertices); /* qh facet_list */
qh_resetlists (False, qh_RESETvisible);
qh facet_next= qh facet_list; /* advance facet when processed */
qh interior_point= qh_getcenter(vertices);
firstfacet= qh facet_list;
qh_setfacetplane(firstfacet);
zinc_(Znumvisibility); /* needs to be in printsummary */
qh_distplane(qh interior_point, firstfacet, &dist);
if (dist > 0) {
FORALLfacets
facet->toporient ^= True;
}
FORALLfacets
qh_setfacetplane(facet);
FORALLfacets {
if (!qh_checkflipped (facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
trace1((qh ferr, "qh_initialhull: initial orientation incorrect. Correct all facets\n"));
facet->flipped= False;
FORALLfacets {
facet->toporient ^= True;
qh_orientoutside (facet);
}
break;
}
}
FORALLfacets {
if (!qh_checkflipped (facet, NULL, !qh_ALL)) { /* can happen with 'R0.1' */
qh_precision ("initial facet is coplanar with interior point");
fprintf (qh ferr, "qhull precision error: initial facet %d is coplanar with the interior point\n",
facet->id);
qh_errexit (qh_ERRsingular, facet, NULL);
}
FOREACHneighbor_(facet) {
angle= qh_getangle (facet->normal, neighbor->normal);
minimize_( minangle, angle);
}
}
if (minangle < qh_MAXnarrow && !qh NOnarrow) {
realT diff= 1.0 + minangle;
qh NARROWhull= True;
qh_option ("_narrow-hull", NULL, &diff);
if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
fprintf (qh ferr, "qhull precision warning: \n\
The initial hull is narrow (cosine of min. angle is %.16f).\n\
A coplanar point may lead to a wide facet. Options 'QbB' (scale to unit box)\n\
or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp' to skip\n\
this warning. See 'Limitations' in qh-impre.htm.\n",
-minangle); /* convert from angle between normals to angle between facets */
}
zzval_(Zprocessed)= qh hull_dim+1;
qh_checkpolygon (qh facet_list);
qh_checkconvex(qh facet_list, qh_DATAfault);
#ifndef qh_NOtrace
if (qh IStracing >= 1) {
fprintf(qh ferr, "qh_initialhull: simplex constructed, interior point:");
for (k=0; k < qh hull_dim; k++)
fprintf (qh ferr, " %6.4g", qh interior_point[k]);
fprintf (qh ferr, "\n");
}
#endif
} /* initialhull */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="initialvertices">-</a>
qh_initialvertices( dim, maxpoints, points, numpoints )
determines a non-singular set of initial vertices
maxpoints may include duplicate points
returns:
temporary set of dim+1 vertices in descending order by vertex id
if qh.RANDOMoutside && !qh.ALLpoints
picks random points
if dim >= qh_INITIALmax,
uses min/max x and max points with non-zero determinants
notes:
unless qh.ALLpoints,
uses maxpoints as long as determinate is non-zero
*/
setT *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints) {
pointT *point, **pointp;
setT *vertices, *simplex, *tested;
realT randr;
int index, point_i, point_n, k;
boolT nearzero= False;
vertices= qh_settemp (dim + 1);
simplex= qh_settemp (dim+1);
if (qh ALLpoints)
qh_maxsimplex (dim, NULL, points, numpoints, &simplex);
else if (qh RANDOMoutside) {
while (qh_setsize (simplex) != dim+1) {
randr= qh_RANDOMint;
randr= randr/(qh_RANDOMmax+1);
index= (int)floor(qh num_points * randr);
while (qh_setin (simplex, qh_point (index))) {
index++; /* in case qh_RANDOMint always returns the same value */
index= index < qh num_points ? index : 0;
}
qh_setappend (&simplex, qh_point (index));
}
}else if (qh hull_dim >= qh_INITIALmax) {
tested= qh_settemp (dim+1);
qh_setappend (&simplex, SETfirst_(maxpoints)); /* max and min X coord */
qh_setappend (&simplex, SETsecond_(maxpoints));
qh_maxsimplex (fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
k= qh_setsize (simplex);
FOREACHpoint_i_(maxpoints) {
if (point_i & 0x1) { /* first pick up max. coord. points */
if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
qh_detsimplex(point, simplex, k, &nearzero);
if (nearzero)
qh_setappend (&tested, point);
else {
qh_setappend (&simplex, point);
if (++k == dim) /* use search for last point */
break;
}
}
}
}
while (k != dim && (point= (pointT*)qh_setdellast (maxpoints))) {
if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
qh_detsimplex (point, simplex, k, &nearzero);
if (nearzero)
qh_setappend (&tested, point);
else {
qh_setappend (&simplex, point);
k++;
}
}
}
index= 0;
while (k != dim && (point= qh_point (index++))) {
if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
qh_detsimplex (point, simplex, k, &nearzero);
if (!nearzero){
qh_setappend (&simplex, point);
k++;
}
}
}
qh_settempfree (&tested);
qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
}else
qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
FOREACHpoint_(simplex)
qh_setaddnth (&vertices, 0, qh_newvertex(point)); /* descending order */
qh_settempfree (&simplex);
return vertices;
} /* initialvertices */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="isvertex">-</a>
qh_isvertex( )
returns vertex if point is in vertex set, else returns NULL
notes:
for qh.GOODvertex
*/
vertexT *qh_isvertex (pointT *point, setT *vertices) {
vertexT *vertex, **vertexp;
FOREACHvertex_(vertices) {
if (vertex->point == point)
return vertex;
}
return NULL;
} /* isvertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="makenewfacets">-</a>
qh_makenewfacets( point )
make new facets from point and qh.visible_list
returns:
qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
qh.newvertex_list= list of vertices in new facets with ->newlist set
if (qh.ONLYgood)
newfacets reference horizon facets, but not vice versa
ridges reference non-simplicial horizon ridges, but not vice versa
does not change existing facets
else
sets qh.NEWfacets
new facets attached to horizon facets and ridges
for visible facets,
visible->r.replace is corresponding new facet
see also:
qh_makenewplanes() -- make hyperplanes for facets
qh_attachnewfacets() -- attachnewfacets if not done here (qh ONLYgood)
qh_matchnewfacets() -- match up neighbors
qh_updatevertices() -- update vertex neighbors and delvertices
qh_deletevisible() -- delete visible facets
qh_checkpolygon() --check the result
qh_triangulate() -- triangulate a non-simplicial facet
design:
for each visible facet
make new facets to its horizon facets
update its f.replace
clear its neighbor set
*/
vertexT *qh_makenewfacets (pointT *point /*visible_list*/) {
facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
vertexT *apex;
int numnew=0;
qh newfacet_list= qh facet_tail;
qh newvertex_list= qh vertex_tail;
apex= qh_newvertex(point);
qh_appendvertex (apex);
qh visit_id++;
if (!qh ONLYgood)
qh NEWfacets= True;
FORALLvisible_facets {
FOREACHneighbor_(visible)
neighbor->seen= False;
if (visible->ridges) {
visible->visitid= qh visit_id;
newfacet2= qh_makenew_nonsimplicial (visible, apex, &numnew);
}
if (visible->simplicial)
newfacet= qh_makenew_simplicial (visible, apex, &numnew);
if (!qh ONLYgood) {
if (newfacet2) /* newfacet is null if all ridges defined */
newfacet= newfacet2;
if (newfacet)
visible->f.replace= newfacet;
else
zinc_(Zinsidevisible);
SETfirst_(visible->neighbors)= NULL;
}
}
trace1((qh ferr, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
numnew, qh_pointid(point)));
if (qh IStracing >= 4)
qh_printfacetlist (qh newfacet_list, NULL, qh_ALL);
return apex;
} /* makenewfacets */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="matchduplicates">-</a>
qh_matchduplicates( atfacet, atskip, hashsize, hashcount )
match duplicate ridges in qh.hash_table for atfacet/atskip
duplicates marked with ->dupridge and qh_DUPLICATEridge
returns:
picks match with worst merge (min distance apart)
updates hashcount
see also:
qh_matchneighbor
notes:
design:
compute hash value for atfacet and atskip
repeat twice -- once to make best matches, once to match the rest
for each possible facet in qh.hash_table
if it is a matching facet and pass 2
make match
unless tricoplanar, mark match for merging (qh_MERGEridge)
[e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
if it is a matching facet and pass 1
test if this is a better match
if pass 1,
make best match (it will not be merged)
*/
#ifndef qh_NOmerge
void qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount) {
boolT same, ismatch;
int hash, scan;
facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
realT maxdist= -REALmax, mindist, dist2, low, high;
hash= (int)qh_gethash (hashsize, atfacet->vertices, qh hull_dim, 1,
SETelem_(atfacet->vertices, atskip));
trace2((qh ferr, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
atfacet->id, atskip, hash, *hashcount));
for (makematch= 0; makematch < 2; makematch++) {
qh visit_id++;
for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
zinc_(Zhashlookup);
nextfacet= NULL;
newfacet->visitid= qh visit_id;
for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
scan= (++scan >= hashsize ? 0 : scan)) {
if (!facet->dupridge || facet->visitid == qh visit_id)
continue;
zinc_(Zhashtests);
if (qh_matchvertices (1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
ismatch= (same == (newfacet->toporient ^ facet->toporient));
if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
if (!makematch) {
fprintf (qh ferr, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
facet->id, skip, newfacet->id, newskip, hash);
qh_errexit2 (qh_ERRqhull, facet, newfacet);
}
}else if (ismatch && makematch) {
if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
SETelem_(facet->neighbors, skip)= newfacet;
if (newfacet->tricoplanar)
SETelem_(newfacet->neighbors, newskip)= facet;
else
SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
*hashcount -= 2; /* removed two unmatched facets */
trace4((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
facet->id, skip, newfacet->id, newskip));
}
}else if (ismatch) {
mindist= qh_getdistance (facet, newfacet, &low, &high);
dist2= qh_getdistance (newfacet, facet, &low, &high);
minimize_(mindist, dist2);
if (mindist > maxdist) {
maxdist= mindist;
maxmatch= facet;
maxskip= skip;
maxmatch2= newfacet;
maxskip2= newskip;
}
trace3((qh ferr, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
facet->id, skip, newfacet->id, newskip, mindist,
maxmatch->id, maxmatch2->id));
}else { /* !ismatch */
nextfacet= facet;
nextskip= skip;
}
}
if (makematch && !facet
&& SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
fprintf (qh ferr, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
newfacet->id, newskip, hash);
qh_errexit (qh_ERRqhull, newfacet, NULL);
}
}
} /* end of for each new facet at hash */
if (!makematch) {
if (!maxmatch) {
fprintf (qh ferr, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
atfacet->id, atskip, hash);
qh_errexit (qh_ERRqhull, atfacet, NULL);
}
SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
*hashcount -= 2; /* removed two unmatched facets */
zzinc_(Zmultiridge);
trace0((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
maxmatch->id, maxskip, maxmatch2->id, maxskip2));
qh_precision ("ridge with multiple neighbors");
if (qh IStracing >= 4)
qh_errprint ("DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
}
}
} /* matchduplicates */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="nearcoplanar">-</a>
qh_nearcoplanar()
for all facets, remove near-inside points from facet->coplanarset</li>
coplanar points defined by innerplane from qh_outerinner()
returns:
if qh KEEPcoplanar && !qh KEEPinside
facet->coplanarset only contains coplanar points
if qh.JOGGLEmax
drops inner plane by another qh.JOGGLEmax diagonal since a
vertex could shift out while a coplanar point shifts in
notes:
used for qh.PREmerge and qh.JOGGLEmax
must agree with computation of qh.NEARcoplanar in qh_detroundoff()
design:
if not keeping coplanar or inside points
free all coplanar sets
else if not keeping both coplanar and inside points
remove !coplanar or !inside points from coplanar sets
*/
void qh_nearcoplanar ( void /* qh.facet_list */) {
facetT *facet;
pointT *point, **pointp;
int numpart;
realT dist, innerplane;
if (!qh KEEPcoplanar && !qh KEEPinside) {
FORALLfacets {
if (facet->coplanarset)
qh_setfree( &facet->coplanarset);
}
}else if (!qh KEEPcoplanar || !qh KEEPinside) {
qh_outerinner (NULL, NULL, &innerplane);
if (qh JOGGLEmax < REALmax/2)
innerplane -= qh JOGGLEmax * sqrt (qh hull_dim);
numpart= 0;
FORALLfacets {
if (facet->coplanarset) {
FOREACHpoint_(facet->coplanarset) {
numpart++;
qh_distplane (point, facet, &dist);
if (dist < innerplane) {
if (!qh KEEPinside)
SETref_(point)= NULL;
}else if (!qh KEEPcoplanar)
SETref_(point)= NULL;
}
qh_setcompact (facet->coplanarset);
}
}
zzadd_(Zcheckpart, numpart);
}
} /* nearcoplanar */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="nearvertex">-</a>
qh_nearvertex( facet, point, bestdist )
return nearest vertex in facet to point
returns:
vertex and its distance
notes:
if qh.DELAUNAY
distance is measured in the input set
searches neighboring tricoplanar facets (requires vertexneighbors)
Slow implementation. Recomputes vertex set for each point.
The vertex set could be stored in the qh.keepcentrum facet.
*/
vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp) {
realT bestdist= REALmax, dist;
vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
coordT *center;
facetT *neighbor, **neighborp;
setT *vertices;
int dim= qh hull_dim;
if (qh DELAUNAY)
dim--;
if (facet->tricoplanar) {
if (!qh VERTEXneighbors || !facet->center) {
fprintf(qh ferr, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
qh_errexit(qh_ERRqhull, NULL, NULL);
}
vertices= qh_settemp (qh TEMPsize);
apex= SETfirst_(facet->vertices);
center= facet->center;
FOREACHneighbor_(apex) {
if (neighbor->center == center) {
FOREACHvertex_(neighbor->vertices)
qh_setappend(&vertices, vertex);
}
}
}else
vertices= facet->vertices;
FOREACHvertex_(vertices) {
dist= qh_pointdist (vertex->point, point, -dim);
if (dist < bestdist) {
bestdist= dist;
bestvertex= vertex;
}
}
if (facet->tricoplanar)
qh_settempfree (&vertices);
*bestdistp= sqrt (bestdist);
return bestvertex;
} /* nearvertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="newhashtable">-</a>
qh_newhashtable( newsize )
returns size of qh.hash_table of at least newsize slots
notes:
assumes qh.hash_table is NULL
qh_HASHfactor determines the number of extra slots
size is not divisible by 2, 3, or 5
*/
int qh_newhashtable(int newsize) {
int size;
size= ((newsize+1)*qh_HASHfactor) | 0x1; /* odd number */
while (True) {
if ((size%3) && (size%5))
break;
size += 2;
/* loop terminates because there is an infinite number of primes */
}
qh hash_table= qh_setnew (size);
qh_setzero (qh hash_table, 0, size);
return size;
} /* newhashtable */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="newvertex">-</a>
qh_newvertex( point )
returns a new vertex for point
*/
vertexT *qh_newvertex(pointT *point) {
vertexT *vertex;
zinc_(Ztotvertices);
vertex= (vertexT *)qh_memalloc(sizeof(vertexT));
memset ((char *) vertex, 0, sizeof (vertexT));
if (qh vertex_id == 0xFFFFFF) {
fprintf(qh ferr, "qhull input error: more than %d vertices. ID field overflows and two vertices\n\
may have the same identifier. Vertices not sorted correctly.\n", 0xFFFFFF);
qh_errexit(qh_ERRinput, NULL, NULL);
}
if (qh vertex_id == qh tracevertex_id)
qh tracevertex= vertex;
vertex->id= qh vertex_id++;
vertex->point= point;
trace4((qh ferr, "qh_newvertex: vertex p%d (v%d) created\n", qh_pointid(vertex->point),
vertex->id));
return (vertex);
} /* newvertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="nextridge3d">-</a>
qh_nextridge3d( atridge, facet, vertex )
return next ridge and vertex for a 3d facet
notes:
in qh_ORIENTclock order
this is a O(n^2) implementation to trace all ridges
be sure to stop on any 2nd visit
design:
for each ridge
exit if it is the ridge after atridge
*/
ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp) {
vertexT *atvertex, *vertex, *othervertex;
ridgeT *ridge, **ridgep;
if ((atridge->top == facet) ^ qh_ORIENTclock)
atvertex= SETsecondt_(atridge->vertices, vertexT);
else
atvertex= SETfirstt_(atridge->vertices, vertexT);
FOREACHridge_(facet->ridges) {
if (ridge == atridge)
continue;
if ((ridge->top == facet) ^ qh_ORIENTclock) {
othervertex= SETsecondt_(ridge->vertices, vertexT);
vertex= SETfirstt_(ridge->vertices, vertexT);
}else {
vertex= SETsecondt_(ridge->vertices, vertexT);
othervertex= SETfirstt_(ridge->vertices, vertexT);
}
if (vertex == atvertex) {
if (vertexp)
*vertexp= othervertex;
return ridge;
}
}
return NULL;
} /* nextridge3d */
#else /* qh_NOmerge */
void qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount) {
}
ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp) {
return NULL;
}
#endif /* qh_NOmerge */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="outcoplanar">-</a>
qh_outcoplanar()
move points from all facets' outsidesets to their coplanarsets
notes:
for post-processing under qh.NARROWhull
design:
for each facet
for each outside point for facet
partition point into coplanar set
*/
void qh_outcoplanar (void /* facet_list */) {
pointT *point, **pointp;
facetT *facet;
realT dist;
trace1((qh ferr, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
FORALLfacets {
FOREACHpoint_(facet->outsideset) {
qh num_outside--;
if (qh KEEPcoplanar || qh KEEPnearinside) {
qh_distplane (point, facet, &dist);
zinc_(Zpartition);
qh_partitioncoplanar (point, facet, &dist);
}
}
qh_setfree (&facet->outsideset);
}
} /* outcoplanar */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="point">-</a>
qh_point( id )
return point for a point id, or NULL if unknown
alternative code:
return ((pointT *)((unsigned long)qh.first_point
+ (unsigned long)((id)*qh.normal_size)));
*/
pointT *qh_point (int id) {
if (id < 0)
return NULL;
if (id < qh num_points)
return qh first_point + id * qh hull_dim;
id -= qh num_points;
if (id < qh_setsize (qh other_points))
return SETelemt_(qh other_points, id, pointT);
return NULL;
} /* point */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="point_add">-</a>
qh_point_add( set, point, elem )
stores elem at set[point.id]
returns:
access function for qh_pointfacet and qh_pointvertex
notes:
checks point.id
*/
void qh_point_add (setT *set, pointT *point, void *elem) {
int id, size;
SETreturnsize_(set, size);
if ((id= qh_pointid(point)) < 0)
fprintf (qh ferr, "qhull internal warning (point_add): unknown point %p id %d\n",
point, id);
else if (id >= size) {
fprintf (qh ferr, "qhull internal errror (point_add): point p%d is out of bounds (%d)\n",
id, size);
qh_errexit (qh_ERRqhull, NULL, NULL);
}else
SETelem_(set, id)= elem;
} /* point_add */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="pointfacet">-</a>
qh_pointfacet()
return temporary set of facet for each point
the set is indexed by point id
notes:
vertices assigned to one of the facets
coplanarset assigned to the facet
outside set assigned to the facet
NULL if no facet for point (inside)
includes qh.GOODpointp
access:
FOREACHfacet_i_(facets) { ... }
SETelem_(facets, i)
design:
for each facet
add each vertex
add each coplanar point
add each outside point
*/
setT *qh_pointfacet (void /*qh facet_list*/) {
int numpoints= qh num_points + qh_setsize (qh other_points);
setT *facets;
facetT *facet;
vertexT *vertex, **vertexp;
pointT *point, **pointp;
facets= qh_settemp (numpoints);
qh_setzero (facets, 0, numpoints);
qh vertex_visit++;
FORALLfacets {
FOREACHvertex_(facet->vertices) {
if (vertex->visitid != qh vertex_visit) {
vertex->visitid= qh vertex_visit;
qh_point_add (facets, vertex->point, facet);
}
}
FOREACHpoint_(facet->coplanarset)
qh_point_add (facets, point, facet);
FOREACHpoint_(facet->outsideset)
qh_point_add (facets, point, facet);
}
return facets;
} /* pointfacet */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="pointvertex">-</a>
qh_pointvertex( )
return temporary set of vertices indexed by point id
entry is NULL if no vertex for a point
this will include qh.GOODpointp
access:
FOREACHvertex_i_(vertices) { ... }
SETelem_(vertices, i)
*/
setT *qh_pointvertex (void /*qh facet_list*/) {
int numpoints= qh num_points + qh_setsize (qh other_points);
setT *vertices;
vertexT *vertex;
vertices= qh_settemp (numpoints);
qh_setzero (vertices, 0, numpoints);
FORALLvertices
qh_point_add (vertices, vertex->point, vertex);
return vertices;
} /* pointvertex */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="prependfacet">-</a>
qh_prependfacet( facet, facetlist )
prepend facet to the start of a facetlist
returns:
increments qh.numfacets
updates facetlist, qh.facet_list, facet_next
notes:
be careful of prepending since it can lose a pointer.
e.g., can lose _next by deleting and then prepending before _next
*/
void qh_prependfacet(facetT *facet, facetT **facetlist) {
facetT *prevfacet, *list;
trace4((qh ferr, "qh_prependfacet: prepend f%d before f%d\n",
facet->id, getid_(*facetlist)));
if (!*facetlist)
(*facetlist)= qh facet_tail;
list= *facetlist;
prevfacet= list->previous;
facet->previous= prevfacet;
if (prevfacet)
prevfacet->next= facet;
list->previous= facet;
facet->next= *facetlist;
if (qh facet_list == list) /* this may change *facetlist */
qh facet_list= facet;
if (qh facet_next == list)
qh facet_next= facet;
*facetlist= facet;
qh num_facets++;
} /* prependfacet */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="printhashtable">-</a>
qh_printhashtable( fp )
print hash table to fp
notes:
not in I/O to avoid bringing io.c in
design:
for each hash entry
if defined
if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
print entry and neighbors
*/
void qh_printhashtable(FILE *fp) {
facetT *facet, *neighbor;
int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
vertexT *vertex, **vertexp;
FOREACHfacet_i_(qh hash_table) {
if (facet) {
FOREACHneighbor_i_(facet) {
if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
break;
}
if (neighbor_i == neighbor_n)
continue;
fprintf (fp, "hash %d f%d ", facet_i, facet->id);
FOREACHvertex_(facet->vertices)
fprintf (fp, "v%d ", vertex->id);
fprintf (fp, "\n neighbors:");
FOREACHneighbor_i_(facet) {
if (neighbor == qh_MERGEridge)
id= -3;
else if (neighbor == qh_DUPLICATEridge)
id= -2;
else
id= getid_(neighbor);
fprintf (fp, " %d", id);
}
fprintf (fp, "\n");
}
}
} /* printhashtable */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="printlists">-</a>
qh_printlists( fp )
print out facet and vertex list for debugging (without 'f/v' tags)
*/
void qh_printlists (void) {
facetT *facet;
vertexT *vertex;
int count= 0;
fprintf (qh ferr, "qh_printlists: facets:");
FORALLfacets {
if (++count % 100 == 0)
fprintf (qh ferr, "\n ");
fprintf (qh ferr, " %d", facet->id);
}
fprintf (qh ferr, "\n new facets %d visible facets %d next facet for qh_addpoint %d\n vertices (new %d):",
getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
getid_(qh newvertex_list));
count = 0;
FORALLvertices {
if (++count % 100 == 0)
fprintf (qh ferr, "\n ");
fprintf (qh ferr, " %d", vertex->id);
}
fprintf (qh ferr, "\n");
} /* printlists */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="resetlists">-</a>
qh_resetlists( stats, qh_RESETvisible )
reset newvertex_list, newfacet_list, visible_list
if stats,
maintains statistics
returns:
visible_list is empty if qh_deletevisible was called
*/
void qh_resetlists (boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/) {
vertexT *vertex;
facetT *newfacet, *visible;
int totnew=0, totver=0;
if (stats) {
FORALLvertex_(qh newvertex_list)
totver++;
FORALLnew_facets
totnew++;
zadd_(Zvisvertextot, totver);
zmax_(Zvisvertexmax, totver);
zadd_(Znewfacettot, totnew);
zmax_(Znewfacetmax, totnew);
}
FORALLvertex_(qh newvertex_list)
vertex->newlist= False;
qh newvertex_list= NULL;
FORALLnew_facets
newfacet->newfacet= False;
qh newfacet_list= NULL;
if (resetVisible) {
FORALLvisible_facets {
visible->f.replace= NULL;
visible->visible= False;
}
qh num_visible= 0;
}
qh visible_list= NULL; /* may still have visible facets via qh_triangulate */
qh NEWfacets= False;
} /* resetlists */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="setvoronoi_all">-</a>
qh_setvoronoi_all()
compute Voronoi centers for all facets
includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
returns:
facet->center is the Voronoi center
notes:
this is unused/untested code
please email bradb@shore.net if this works ok for you
use:
FORALLvertices {...} to locate the vertex for a point.
FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
*/
void qh_setvoronoi_all (void) {
facetT *facet;
qh_clearcenters (qh_ASvoronoi);
qh_vertexneighbors();
FORALLfacets {
if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
if (!facet->center)
facet->center= qh_facetcenter (facet->vertices);
}
}
} /* setvoronoi_all */
#ifndef qh_NOmerge
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="triangulate">-</a>
qh_triangulate()
triangulate non-simplicial facets on qh.facet_list,
if qh.CENTERtype=qh_ASvoronoi, sets Voronoi centers of non-simplicial facets
returns:
all facets simplicial
each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
notes:
call after qh_check_output since may switch to Voronoi centers
Output may overwrite ->f.triowner with ->f.area
*/
void qh_triangulate (void /*qh facet_list*/) {
facetT *facet, *nextfacet, *owner;
int onlygood= qh ONLYgood;
facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
facetT *orig_neighbor= NULL, *otherfacet;
vertexT *new_vertex_list= NULL;
mergeT *merge;
mergeType mergetype;
int neighbor_i, neighbor_n;
trace1((qh ferr, "qh_triangulate: triangulate non-simplicial facets\n"));
if (qh hull_dim == 2)
return;
if (qh VORONOI) { /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
qh_clearcenters (qh_ASvoronoi);
qh_vertexneighbors();
}
qh ONLYgood= False; /* for makenew_nonsimplicial */
qh visit_id++;
qh NEWfacets= True;
qh degen_mergeset= qh_settemp (qh TEMPsize);
qh newvertex_list= qh vertex_tail;
for (facet= qh facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
nextfacet= facet->next;
if (facet->visible || facet->simplicial)
continue;
/* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
if (!new_facet_list)
new_facet_list= facet; /* will be moved to end */
qh_triangulate_facet (facet, &new_vertex_list);
}
trace2((qh ferr, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
nextfacet= facet->next;
if (facet->visible)
continue;
if (facet->ridges) {
if (qh_setsize(facet->ridges) > 0) {
fprintf( qh ferr, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
qh_errexit (qh_ERRqhull, facet, NULL);
}
qh_setfree (&facet->ridges);
}
if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
zinc_(Ztrinull);
qh_triangulate_null (facet);
}
}
trace2((qh ferr, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh degen_mergeset)));
qh visible_list= qh facet_tail;
while ((merge= (mergeT*)qh_setdellast (qh degen_mergeset))) {
facet1= merge->facet1;
facet2= merge->facet2;
mergetype= merge->type;
qh_memfree (merge, sizeof(mergeT));
if (mergetype == MRGmirror) {
zinc_(Ztrimirror);
qh_triangulate_mirror (facet1, facet2);
}
}
qh_settempfree(&qh degen_mergeset);
trace2((qh ferr, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
qh newvertex_list= new_vertex_list; /* all vertices of new facets */
qh visible_list= NULL;
qh_updatevertices(/*qh newvertex_list, empty newfacet_list and visible_list*/);
qh_resetlists (False, !qh_RESETvisible /*qh newvertex_list, empty newfacet_list and visible_list*/);
trace2((qh ferr, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
trace2((qh ferr, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
FORALLfacet_(new_facet_list) {
if (facet->tricoplanar && !facet->visible) {
FOREACHneighbor_i_(facet) {
if (neighbor_i == 0) { /* first iteration */
if (neighbor->tricoplanar)
orig_neighbor= neighbor->f.triowner;
else
orig_neighbor= neighbor;
}else {
if (neighbor->tricoplanar)
otherfacet= neighbor->f.triowner;
else
otherfacet= neighbor;
if (orig_neighbor == otherfacet) {
zinc_(Ztridegen);
facet->degenerate= True;
break;
}
}
}
}
}
trace2((qh ferr, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
owner= NULL;
visible= NULL;
for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
nextfacet= facet->next;
if (facet->visible) {
if (facet->tricoplanar) { /* a null or mirrored facet */
qh_delfacet(facet);
qh num_visible--;
}else { /* a non-simplicial facet followed by its tricoplanars */
if (visible && !owner) {
/* RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
trace2((qh ferr, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
visible->id));
qh_delfacet(visible);
qh num_visible--;
}
visible= facet;
owner= NULL;
}
}else if (facet->tricoplanar) {
if (facet->f.triowner != visible) {
fprintf( qh ferr, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
qh_errexit2 (qh_ERRqhull, facet, visible);
}
if (owner)
facet->f.triowner= owner;
else if (!facet->degenerate) {
owner= facet;
nextfacet= visible->next; /* rescan tricoplanar facets with owner */
facet->keepcentrum= True; /* one facet owns ->normal, etc. */
facet->coplanarset= visible->coplanarset;
facet->outsideset= visible->outsideset;
visible->coplanarset= NULL;
visible->outsideset= NULL;
if (!qh TRInormals) { /* center and normal copied to tricoplanar facets */
visible->center= NULL;
visible->normal= NULL;
}
qh_delfacet(visible);
qh num_visible--;
}
}
}
if (visible && !owner) {
trace2((qh ferr, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
visible->id));
qh_delfacet(visible);
qh num_visible--;
}
qh NEWfacets= False;
qh ONLYgood= onlygood; /* restore value */
if (qh CHECKfrequently)
qh_checkpolygon (qh facet_list);
} /* triangulate */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="triangulate_facet">-</a>
qh_triangulate_facet (facetA)
triangulate a non-simplicial facet
if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
returns:
qh.newfacet_list == simplicial facets
facet->tricoplanar set and ->keepcentrum false
facet->degenerate set if duplicated apex
facet->f.trivisible set to facetA
facet->center copied from facetA (created if qh_ASvoronoi)
qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
facet->normal,offset,maxoutside copied from facetA
notes:
qh_makenew_nonsimplicial uses neighbor->seen for the same
see also:
qh_addpoint() -- add a point
qh_makenewfacets() -- construct a cone of facets for a new vertex
design:
if qh_ASvoronoi,
compute Voronoi center (facet->center)
select first vertex (highest ID to preserve ID ordering of ->vertices)
triangulate from vertex to ridges
copy facet->center, normal, offset
update vertex neighbors
*/
void qh_triangulate_facet (facetT *facetA, vertexT **first_vertex) {
facetT *newfacet;
facetT *neighbor, **neighborp;
vertexT *apex;
int numnew=0;
trace3((qh ferr, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
if (qh IStracing >= 4)
qh_printfacet (qh ferr, facetA);
FOREACHneighbor_(facetA) {
neighbor->seen= False;
neighbor->coplanar= False;
}
if (qh CENTERtype == qh_ASvoronoi && !facetA->center /* matches upperdelaunay in qh_setfacetplane() */
&& fabs_(facetA->normal[qh hull_dim -1]) >= qh ANGLEround * qh_ZEROdelaunay) {
facetA->center= qh_facetcenter (facetA->vertices);
}
qh_willdelete (facetA, NULL);
qh newfacet_list= qh facet_tail;
facetA->visitid= qh visit_id;
apex= SETfirst_(facetA->vertices);
qh_makenew_nonsimplicial (facetA, apex, &numnew);
SETfirst_(facetA->neighbors)= NULL;
FORALLnew_facets {
newfacet->tricoplanar= True;
newfacet->f.trivisible= facetA;
newfacet->degenerate= False;
newfacet->upperdelaunay= facetA->upperdelaunay;
newfacet->good= facetA->good;
if (qh TRInormals) {
newfacet->keepcentrum= True;
newfacet->normal= qh_copypoints (facetA->normal, 1, qh hull_dim);
if (qh CENTERtype == qh_AScentrum)
newfacet->center= qh_getcentrum (newfacet);
else
newfacet->center= qh_copypoints (facetA->center, 1, qh hull_dim);
}else {
newfacet->keepcentrum= False;
newfacet->normal= facetA->normal;
newfacet->center= facetA->center;
}
newfacet->offset= facetA->offset;
#if qh_MAXoutside
newfacet->maxoutside= facetA->maxoutside;
#endif
}
qh_matchnewfacets(/*qh newfacet_list*/);
zinc_(Ztricoplanar);
zadd_(Ztricoplanartot, numnew);
zmax_(Ztricoplanarmax, numnew);
qh visible_list= NULL;
if (!(*first_vertex))
(*first_vertex)= qh newvertex_list;
qh newvertex_list= NULL;
qh_updatevertices(/*qh newfacet_list, empty visible_list and newvertex_list*/);
qh_resetlists (False, !qh_RESETvisible /*qh newfacet_list, empty visible_list and newvertex_list*/);
} /* triangulate_facet */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="triangulate_link">-</a>
qh_triangulate_link (oldfacetA, facetA, oldfacetB, facetB)
relink facetA to facetB via oldfacets
returns:
adds mirror facets to qh degen_mergeset (4-d and up only)
design:
if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_link (facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
int errmirror= False;
trace3((qh ferr, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
if (qh_setin (facetA->neighbors, facetB)) {
if (!qh_setin (facetB->neighbors, facetA))
errmirror= True;
else
qh_appendmergeset (facetA, facetB, MRGmirror, NULL);
}else if (qh_setin (facetB->neighbors, facetA))
errmirror= True;
if (errmirror) {
fprintf( qh ferr, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
qh_errexit2 (qh_ERRqhull, facetA, facetB);
}
qh_setreplace (facetB->neighbors, oldfacetB, facetA);
qh_setreplace (facetA->neighbors, oldfacetA, facetB);
} /* triangulate_link */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="triangulate_mirror">-</a>
qh_triangulate_mirror (facetA, facetB)
delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
a mirrored facet shares the same vertices of a logical ridge
design:
since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_mirror (facetT *facetA, facetT *facetB) {
facetT *neighbor, *neighborB;
int neighbor_i, neighbor_n;
trace3((qh ferr, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
facetA->id, facetB->id));
FOREACHneighbor_i_(facetA) {
neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
if (neighbor == neighborB)
continue; /* occurs twice */
qh_triangulate_link (facetA, neighbor, facetB, neighborB);
}
qh_willdelete (facetA, NULL);
qh_willdelete (facetB, NULL);
} /* triangulate_mirror */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="triangulate_null">-</a>
qh_triangulate_null (facetA)
remove null facetA from qh_triangulate_facet()
a null facet has vertex #1 (apex) == vertex #2
returns:
adds facetA to ->visible for deletion after qh_updatevertices
qh degen_mergeset contains mirror facets (4-d and up only)
design:
since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
if they are already neighbors, the opposing neighbors become MRGmirror facets
*/
void qh_triangulate_null (facetT *facetA) {
facetT *neighbor, *otherfacet;
trace3((qh ferr, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
neighbor= SETfirst_(facetA->neighbors);
otherfacet= SETsecond_(facetA->neighbors);
qh_triangulate_link (facetA, neighbor, facetA, otherfacet);
qh_willdelete (facetA, NULL);
} /* triangulate_null */
#else /* qh_NOmerge */
void qh_triangulate (void) {
}
#endif /* qh_NOmerge */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="vertexintersect">-</a>
qh_vertexintersect( vertexsetA, vertexsetB )
intersects two vertex sets (inverse id ordered)
vertexsetA is a temporary set at the top of qhmem.tempstack
returns:
replaces vertexsetA with the intersection
notes:
could overwrite vertexsetA if currently too slow
*/
void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
setT *intersection;
intersection= qh_vertexintersect_new (*vertexsetA, vertexsetB);
qh_settempfree (vertexsetA);
*vertexsetA= intersection;
qh_settemppush (intersection);
} /* vertexintersect */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="vertexintersect_new">-</a>
qh_vertexintersect_new( )
intersects two vertex sets (inverse id ordered)
returns:
a new set
*/
setT *qh_vertexintersect_new (setT *vertexsetA,setT *vertexsetB) {
setT *intersection= qh_setnew (qh hull_dim - 1);
vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
while (*vertexA && *vertexB) {
if (*vertexA == *vertexB) {
qh_setappend(&intersection, *vertexA);
vertexA++; vertexB++;
}else {
if ((*vertexA)->id > (*vertexB)->id)
vertexA++;
else
vertexB++;
}
}
return intersection;
} /* vertexintersect_new */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="vertexneighbors">-</a>
qh_vertexneighbors()
for each vertex in qh.facet_list,
determine its neighboring facets
returns:
sets qh.VERTEXneighbors
nop if qh.VERTEXneighbors already set
qh_addpoint() will maintain them
notes:
assumes all vertex->neighbors are NULL
design:
for each facet
for each vertex
append facet to vertex->neighbors
*/
void qh_vertexneighbors (void /*qh facet_list*/) {
facetT *facet;
vertexT *vertex, **vertexp;
if (qh VERTEXneighbors)
return;
trace1((qh ferr, "qh_vertexneighbors: determing neighboring facets for each vertex\n"));
qh vertex_visit++;
FORALLfacets {
if (facet->visible)
continue;
FOREACHvertex_(facet->vertices) {
if (vertex->visitid != qh vertex_visit) {
vertex->visitid= qh vertex_visit;
vertex->neighbors= qh_setnew (qh hull_dim);
}
qh_setappend (&vertex->neighbors, facet);
}
}
qh VERTEXneighbors= True;
} /* vertexneighbors */
/*-<a href="qh-poly.htm#TOC"
>-------------------------------</a><a name="vertexsubset">-</a>
qh_vertexsubset( vertexsetA, vertexsetB )
returns True if vertexsetA is a subset of vertexsetB
assumes vertexsets are sorted
note:
empty set is a subset of any other set
*/
boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
while (True) {
if (!*vertexA)
return True;
if (!*vertexB)
return False;
if ((*vertexA)->id > (*vertexB)->id)
return False;
if (*vertexA == *vertexB)
vertexA++;
vertexB++;
}
return False; /* avoid warnings */
} /* vertexsubset */
|
