/usr/include/CGAL/Alpha_shape_3.h is in libcgal-dev 4.7-4.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142 1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188 1189 1190 1191 1192 1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216 1217 1218 1219 1220 1221 1222 1223 1224 1225 1226 1227 1228 1229 1230 1231 1232 1233 1234 1235 1236 1237 1238 1239 1240 1241 1242 1243 1244 1245 1246 1247 1248 1249 1250 1251 1252 1253 1254 1255 1256 1257 1258 1259 1260 1261 1262 1263 1264 1265 1266 1267 1268 1269 1270 1271 1272 1273 1274 1275 1276 1277 1278 1279 1280 1281 1282 1283 1284 1285 1286 1287 1288 1289 1290 1291 1292 1293 1294 1295 1296 1297 1298 1299 1300 1301 1302 1303 1304 1305 1306 1307 1308 1309 1310 1311 1312 1313 1314 1315 1316 1317 1318 1319 1320 1321 1322 1323 1324 1325 1326 1327 1328 1329 1330 1331 1332 1333 1334 1335 1336 1337 1338 1339 1340 1341 1342 1343 1344 1345 1346 1347 1348 1349 1350 1351 1352 1353 1354 1355 1356 1357 1358 1359 1360 1361 1362 1363 1364 1365 1366 1367 1368 1369 1370 1371 1372 1373 1374 1375 1376 1377 1378 1379 1380 1381 1382 1383 1384 1385 1386 1387 1388 1389 1390 1391 1392 1393 1394 1395 1396 1397 1398 1399 1400 1401 1402 1403 1404 1405 1406 1407 1408 1409 1410 1411 1412 1413 1414 1415 1416 1417 1418 1419 1420 1421 1422 1423 1424 1425 1426 1427 1428 1429 1430 1431 1432 1433 1434 1435 1436 1437 1438 1439 1440 1441 1442 1443 1444 1445 1446 1447 1448 1449 1450 1451 1452 1453 1454 1455 1456 1457 1458 1459 1460 1461 1462 1463 1464 1465 1466 1467 1468 1469 1470 1471 1472 1473 1474 1475 1476 1477 1478 1479 1480 1481 1482 1483 1484 1485 1486 1487 1488 1489 1490 1491 1492 1493 1494 1495 1496 1497 1498 1499 1500 1501 1502 1503 1504 1505 1506 1507 1508 1509 1510 1511 1512 1513 1514 1515 1516 1517 1518 1519 1520 1521 1522 1523 1524 1525 1526 1527 1528 1529 1530 1531 1532 1533 1534 1535 1536 1537 1538 1539 1540 1541 1542 1543 1544 1545 1546 1547 1548 1549 1550 1551 1552 1553 1554 1555 1556 1557 1558 1559 1560 1561 1562 1563 1564 1565 1566 1567 1568 1569 1570 1571 1572 1573 1574 1575 1576 1577 1578 1579 1580 1581 1582 1583 1584 1585 1586 1587 1588 1589 1590 1591 1592 1593 1594 1595 1596 1597 1598 1599 1600 1601 1602 1603 1604 1605 1606 1607 1608 1609 1610 1611 1612 1613 1614 1615 1616 1617 1618 1619 1620 1621 1622 1623 1624 1625 1626 1627 1628 1629 1630 1631 1632 1633 1634 1635 1636 1637 1638 1639 1640 1641 1642 1643 1644 1645 1646 1647 1648 1649 1650 1651 1652 1653 1654 1655 1656 1657 1658 1659 1660 1661 1662 1663 1664 1665 1666 1667 1668 1669 1670 1671 1672 1673 1674 1675 1676 1677 1678 1679 1680 1681 1682 1683 1684 1685 1686 1687 1688 1689 1690 1691 1692 1693 1694 1695 1696 1697 1698 1699 1700 1701 1702 1703 1704 1705 1706 1707 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 | // Copyright (c) 1997, 2012 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org).
// You can redistribute it and/or modify it under the terms of the GNU
// General Public License as published by the Free Software Foundation,
// either version 3 of the License, or (at your option) any later version.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the so
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL$
// $Id$
//
//
// Author(s) : Tran Kai Frank DA <Frank.Da@sophia.inria.fr>
// Andreas Fabri <Andreas.Fabri@geometryfactory.com>
// Mariette Yvinec <Mariette.Yvinec@sophia.inria.fr>
#ifndef CGAL_ALPHA_SHAPE_3_H
#define CGAL_ALPHA_SHAPE_3_H
#include <CGAL/basic.h>
#include <set>
#include <map>
#include <list>
#include <vector>
#include <algorithm>
#include <utility>
#include <iostream>
#include <CGAL/Triangulation_utils_3.h>
#include <CGAL/Object.h>
#include <CGAL/Unique_hash_map.h>
#include <CGAL/Compact_container.h>
#include <CGAL/Alpha_shape_vertex_base_3.h>
#include <CGAL/Alpha_shape_cell_base_3.h>
#include <CGAL/internal/Lazy_alpha_nt_3.h>
#include <CGAL/iterator.h>
#ifdef CGAL_USE_GEOMVIEW
#include <CGAL/IO/Geomview_stream.h> // TBC
#endif
//-------------------------------------------------------------------
namespace CGAL {
//-------------------------------------------------------------------
template < class Dt, class ExactAlphaComparisonTag = Tag_false >
class Alpha_shape_3 : public Dt
{
// DEFINITION The class Alpha_shape_3<Dt> represents the family
// of alpha-shapes for a set of points (or a set of weighted points)
// for all possible values of alpha. The alphashape is defined through
// the Delaunay tetrahedralization of the points
// (or the Regular tetrahedralization in case of weighted points)
// and depends on the value of a parameter called alpha.
// The alpha_shape is the domain of a subcomplex of this triangulation
// called the Alpha_complex. The alpha_complex includes any simplex
// having a circumscribing sphere (an orthogonal sphere
// in case of weighted points) empty of other points
// (or suborthogonal to other sites in case of weighted points)
// with squared radius equal or less than alpha
// The alpha_shapes comes in two versions : GENERAL or REGULARIZED
// where the REGULARIZED version is onbtaining by restricting the
// alpha complex ti is pure 3D component.
// The cells of the triangulation are classified as INTERIOR
// or EXTERIOR according to the value alpha_cell of their circumsphere
// squared radius compared to alpha.
// In GENERAL mode each k-dimensional simplex of the triangulation
// for (k=0,1,2)
// can be classified as EXTERIOR, SINGULAR, REGULAR
// or INTERIOR with respect to the alpha shape.
// In GENERAL mode a $k$ simplex is REGULAR if it is on the boundary
// of the alpha_complex and belongs to a $k+1$ simplex in the complex
// and it is SINGULAR simplex if it is a boundary simplex tht is not
// included in a $k+1$ simplex of the complex.
// In REGULARIZED mode each k-dimensional simplex of the triangulation
// for (k=0,1,2)
// can be classified as EXTERIOR, REGULAR
// or INTERIOR with respect to the alpha shape.
// A $k$ simplex is REGULAR if it is on the boundary of alpha complex
// and belong to a tetrahedral cell of the complex.
// Roughly, the Alpha_shapes data structure computes and stores,
// for each simplex
// the at most three critical value (alpha_min, alpha_mid and alpha_max)
// which compared to the actual alpha value
// determine the classification of the simplex.
//------------------------- TYPES ------------------------------------
public:
typedef Dt Triangulation;
typedef typename Dt::Geom_traits Gt;
typedef typename Dt::Triangulation_data_structure Tds;
//extra the type used for representing alpha according to ExactAlphaComparisonTag
typedef typename internal::Alpha_nt_selector_3<Gt,ExactAlphaComparisonTag,typename Dt::Weighted_tag>::Type_of_alpha NT;
typedef typename internal::Alpha_nt_selector_3<Gt,ExactAlphaComparisonTag,typename Dt::Weighted_tag>::Compute_squared_radius_3 Compute_squared_radius_3;
typedef NT FT;
typedef typename Gt::FT Coord_type;
//checks whether tags are correctly set in Vertex and Cell classes
CGAL_static_assertion( (boost::is_same<NT,typename Dt::Cell::NT>::value) );
CGAL_static_assertion( (boost::is_same<NT,typename Dt::Vertex::Alpha_status::NT>::value) );
typedef typename Gt::Point_3 Point;
typedef typename Dt::Cell_handle Cell_handle;
typedef typename Dt::Vertex_handle Vertex_handle;
typedef typename Dt::Facet Facet;
typedef typename Dt::Edge Edge;
typedef typename Dt::Cell_circulator Cell_circulator;
typedef typename Dt::Facet_circulator Facet_circulator;
typedef typename Dt::Cell_iterator Cell_iterator;
typedef typename Dt::Facet_iterator Facet_iterator;
typedef typename Dt::Edge_iterator Edge_iterator;
typedef typename Dt::Vertex_iterator Vertex_iterator;
typedef typename Dt::Finite_cells_iterator Finite_cells_iterator;
typedef typename Dt::Finite_facets_iterator Finite_facets_iterator;
typedef typename Dt::Finite_edges_iterator Finite_edges_iterator;
typedef typename Dt::Finite_vertices_iterator Finite_vertices_iterator;
typedef typename Dt::size_type size_type;
typedef typename Dt::Locate_type Locate_type;
typedef typename Dt::Weighted_tag Weighted_tag;
using Dt::dimension;
using Dt::finite_facets_begin;
using Dt::finite_facets_end;
using Dt::finite_edges_begin;
using Dt::finite_edges_end;
using Dt::finite_vertices_begin;
using Dt::finite_vertices_end;
using Dt::finite_cells_begin;
using Dt::finite_cells_end;
using Dt::VERTEX;
using Dt::EDGE;
using Dt::FACET;
using Dt::CELL;
using Dt::OUTSIDE_CONVEX_HULL;
using Dt::OUTSIDE_AFFINE_HULL;
using Dt::vertex_triple_index;
using Dt::is_infinite;
using Dt::is_Gabriel;
using Dt::incident_cells;
using Dt::incident_vertices;
using Dt::incident_facets;
using Dt::locate;
enum Classification_type {EXTERIOR,
SINGULAR,
REGULAR,
INTERIOR};
enum Mode {GENERAL, REGULARIZED};
typedef CGAL::Alpha_status< NT > Alpha_status;
typedef Compact_container<Alpha_status> Alpha_status_container;
typedef typename Alpha_status_container::const_iterator
Alpha_status_const_iterator;
typedef typename Alpha_status_container::iterator
Alpha_status_iterator;
typedef std::vector< NT > Alpha_spectrum;
typedef std::multimap< NT, Cell_handle > Alpha_cell_map;
typedef std::multimap< NT, Facet> Alpha_facet_map;
typedef std::multimap< NT, Edge > Alpha_edge_map;
typedef std::multimap< NT, Vertex_handle> Alpha_vertex_map;
typedef std::pair<Vertex_handle, Vertex_handle> Vertex_handle_pair;
typedef std::map<Vertex_handle_pair,Alpha_status_iterator> Edge_alpha_map;
typedef typename std::list< Vertex_handle >::iterator
Alpha_shape_vertices_iterator;
typedef typename std::list< Facet >::iterator
Alpha_shape_facets_iterator;
//test if a cell is exterior to the alphashape
class Exterior_cell_test{
const Alpha_shape_3 * _as;
public:
Exterior_cell_test() {}
Exterior_cell_test(const Alpha_shape_3 * as) {_as = as;}
bool operator() ( const Finite_cells_iterator& fci) const {
return _as->classify(fci) == EXTERIOR ;
}
};
typedef Filter_iterator< Finite_cells_iterator, Exterior_cell_test>
Alpha_shape_cells_iterator;
typedef typename Alpha_spectrum::const_iterator Alpha_iterator;
// An iterator that allow to traverse the sorted sequence of
// different alpha-values. The iterator is bidirectional and
// non-mutable. Its value-type is NT
private:
typedef Unique_hash_map<Cell_handle, bool > Marked_cell_set;
private:
NT _alpha;
NT _alpha_solid;
Mode _mode;
mutable bool use_vertex_cache;
mutable bool use_facet_cache;
// only finite facets and simplices are inserted into the maps
Alpha_cell_map alpha_cell_map;
Alpha_facet_map alpha_min_facet_map;
Alpha_edge_map alpha_min_edge_map;
Alpha_vertex_map alpha_min_vertex_map;
Alpha_spectrum alpha_spectrum;
Alpha_status_container alpha_status_container;
Edge_alpha_map edge_alpha_map;
//deprecated - for backward compatibility
mutable std::list< Vertex_handle > alpha_shape_vertices_list;
mutable std::list< Facet > alpha_shape_facets_list;
//------------------------- CONSTRUCTORS ------------------------------
public:
// Introduces an empty alpha-shape `A' for a
// alpha-value `alpha'.
Alpha_shape_3(NT alpha = 0,
Mode m = REGULARIZED)
: _alpha(alpha), _mode(m),
use_vertex_cache(false), use_facet_cache(false)
{}
Alpha_shape_3(Dt& dt, NT alpha = 0, Mode m = REGULARIZED)
:_alpha(alpha), _mode(m),
use_vertex_cache(false), use_facet_cache(false)
{
Dt::swap(dt);
if (dimension() == 3) initialize_alpha();
}
// Introduces an alpha-shape `A' for the alpha-value
// `alpha' that is initialized with the points in the range
// from first to last
template < class InputIterator >
Alpha_shape_3(const InputIterator& first,
const InputIterator& last,
const NT& alpha = 0,
Mode m = REGULARIZED)
: _alpha(alpha), _mode(m),
use_vertex_cache(false), use_facet_cache(false)
{
Dt::insert(first, last);
if (dimension() == 3) initialize_alpha();
}
public:
//----------------------- OPERATIONS ---------------------------------
template < class InputIterator >
std::ptrdiff_t make_alpha_shape(const InputIterator& first,
const InputIterator& last)
{
clear();
size_type n = Dt::insert(first, last);
if (dimension() == 3){
initialize_alpha();
}
return n;
}
// Introduces an alpha-shape `A'
// that is initialized with the points in the range
// from first to last
private :
//--------------------- INITIALIZATION OF PRIVATE MEMBERS -----------
// called with reinitialize=false on first initialization
// reinitialize=true when switching the mode.
void initialize_alpha_cell_map();
void initialize_alpha_facet_maps(bool reinitialize = false);
void initialize_alpha_edge_maps(bool reinitialize = false);
void initialize_alpha_vertex_maps(bool reinitialize = false);
void initialize_alpha_spectrum();
void initialize_alpha(bool reinitialize = false) {
if (reinitialize == false) initialize_alpha_cell_map();
initialize_alpha_facet_maps(reinitialize);
initialize_alpha_edge_maps(reinitialize);
initialize_alpha_vertex_maps(reinitialize);
initialize_alpha_spectrum();
}
private :
Vertex_handle_pair
make_vertex_handle_pair( Vertex_handle v1, Vertex_handle v2) const {
return v1 < v2 ? std::make_pair(v1,v2)
: std::make_pair(v2,v1);
}
Vertex_handle_pair
make_vertex_handle_pair(const Edge& e) const {
return make_vertex_handle_pair(e.first->vertex(e.second),
e.first->vertex(e.third));
}
// the version to be used with Tag_true is templated to avoid
// instanciation through explicit instantiation of the whole class
void set_alpha_min_of_vertices(Tag_false)
{
for( Finite_vertices_iterator vit = finite_vertices_begin();
vit != finite_vertices_end(); ++vit){
Alpha_status* as = vit->get_alpha_status();
as->set_is_Gabriel(true);
as->set_alpha_min(NT(0));
}
// insert a single vertex into the map because they all have the
// same alpha_min value
alpha_min_vertex_map.insert(typename Alpha_vertex_map::value_type
( NT(0), finite_vertices_begin()));
}
template <class Tag>
void set_alpha_min_of_vertices(Tag)
{
for( Finite_vertices_iterator vit = finite_vertices_begin();
vit != finite_vertices_end(); ++vit) {
if (is_Gabriel(vit)) {
Alpha_status* as = vit->get_alpha_status();
as->set_is_Gabriel(true);
as->set_alpha_min(squared_radius(vit));
alpha_min_vertex_map.insert(typename Alpha_vertex_map::value_type
(as->alpha_min(),vit));
}
}
return;
}
//---------------------------------------------------------------------
public:
void clear()
{
// clears the structure
alpha_status_container.clear();
Dt::clear();
alpha_cell_map.clear();
alpha_min_facet_map.clear();
alpha_min_edge_map.clear();
alpha_min_vertex_map.clear();
alpha_spectrum.clear();
alpha_shape_vertices_list.clear();
alpha_shape_facets_list.clear();
use_vertex_cache = false;
use_facet_cache = false;
}
//---------------------------------------------------------------------
public:
NT set_alpha(const NT& alpha)
// Sets the alpha-value to `alpha'. Precondition: `alpha' >= 0.
// Returns the previous alpha
{
NT previous_alpha = _alpha;
_alpha = alpha;
use_vertex_cache = false;
use_facet_cache = false;
return previous_alpha;
}
const NT& get_alpha() const
// Returns the current alpha-value.
{
return _alpha;
}
const NT& get_nth_alpha(int n) const
// Returns the n-th alpha-value.
// n < size()
{
CGAL_triangulation_assertion( n > 0 &&
n <= static_cast<int>(alpha_spectrum.size()) );
return alpha_spectrum[n-1];
}
size_type number_of_alphas() const
// Returns the number of different alpha-values
{
return alpha_spectrum.size();
}
const Edge_alpha_map* get_edge_alpha_map() const
{
return &edge_alpha_map;
}
//---------------------------------------------------------------------
private:
// the dynamic version is not yet implemented
// desactivate the tetrahedralization member functions
void insert(const Point& /*p*/) {}
// Inserts point `p' in the alpha shape and returns the
// corresponding vertex of the underlying Delaunay tetrahedralization.
// If point `p' coincides with an already existing vertex, this
// vertex is returned and the alpha shape remains unchanged.
// Otherwise, the vertex is inserted in the underlying Delaunay
// tetrahedralization and the associated intervals are updated.
void remove(Vertex_handle /*v*/) {}
// Removes the vertex from the underlying Delaunay tetrahedralization.
// The created hole is retriangulated and the associated intervals
// are updated.
//---------------------------------------------------------------------
public:
Mode set_mode(Mode mode = REGULARIZED )
// Sets `A' to its general or regularized version. Returns the
// previous mode.
{
Mode previous_mode = _mode;
_mode = mode;
if (previous_mode != _mode) {
initialize_alpha(true);
use_vertex_cache = false;
use_facet_cache = false;
}
return previous_mode;
}
Mode get_mode() const
// Returns whether `A' is general or regularized.
{
return _mode;
}
//---------------------------------------------------------------------
private:
void update_alpha_shape_vertex_list() const;
void update_alpha_shape_facet_list() const;
//---------------------------------------------------------------------
public:
Alpha_shape_vertices_iterator alpha_shape_vertices_begin() const
{
if(!use_vertex_cache) update_alpha_shape_vertex_list();
return alpha_shape_vertices_list.begin();
}
Alpha_shape_vertices_iterator Alpha_shape_vertices_begin() const
{
return alpha_shape_vertices_begin();
}
//---------------------------------------------------------------------
Alpha_shape_vertices_iterator alpha_shape_vertices_end() const
{
return alpha_shape_vertices_list.end();
}
Alpha_shape_vertices_iterator Alpha_shape_vertices_end() const
{
return alpha_shape_vertices_end();
}
//---------------------------------------------------------------------
Alpha_shape_facets_iterator alpha_shape_facets_begin() const
{
if(! use_facet_cache) update_alpha_shape_facet_list();
return alpha_shape_facets_list.begin();
}
Alpha_shape_facets_iterator Alpha_shape_facets_begin() const
{
return alpha_shape_facets_begin();
}
//---------------------------------------------------------------------
Alpha_shape_facets_iterator alpha_shape_facets_end() const
{
return alpha_shape_facets_list.end();
}
Alpha_shape_facets_iterator Alpha_shape_facets_end() const
{
return alpha_shape_facets_end();
}
Alpha_shape_cells_iterator alpha_shape_cells_begin() const
{
return CGAL::filter_iterator(finite_cells_end(),
Exterior_cell_test(this),
finite_cells_begin());
}
Alpha_shape_cells_iterator alpha_shape_cells_end() const
{
return CGAL::filter_iterator(finite_cells_end(),
Exterior_cell_test(this));
}
public:
// Traversal of the alpha-Values
//
// The alpha shape class defines an iterator that allows to
// visit the sorted sequence of alpha-values. This iterator is
// non-mutable and bidirectional. Its value type is NT.
Alpha_iterator alpha_begin() const { return alpha_spectrum.begin(); }
Alpha_iterator alpha_end() const {return alpha_spectrum.end();}
Alpha_iterator alpha_find(const NT& alpha) const
// Returns an iterator pointing to an element with alpha-value
// `alpha', or the corresponding past-the-end iterator if such an
// element is not found.
{
return std::find(alpha_spectrum.begin(),
alpha_spectrum.end(),
alpha);
}
Alpha_iterator alpha_lower_bound(const NT& alpha) const
// Returns an iterator pointing to the first element with
// alpha-value not less than `alpha'.
{
return std::lower_bound(alpha_spectrum.begin(),
alpha_spectrum.end(),
alpha);
}
Alpha_iterator alpha_upper_bound(const NT& alpha) const
// Returns an iterator pointing to the first element with
// alpha-value greater than `alpha'.
{
return std::upper_bound(alpha_spectrum.begin(),
alpha_spectrum.end(),
alpha);
}
//--------------------- PREDICATES -----------------------------------
public:
void compute_edge_status( const Cell_handle& c,
int i,
int j,
Alpha_status& as) const;
Classification_type classify(const Alpha_status& as, const NT& alpha) const;
Classification_type classify(const Alpha_status* as, const NT& alpha) const;
Classification_type classify(const Alpha_status_const_iterator as,
const NT& alpha) const;
public:
Classification_type classify(const Point& p) const
{
return classify(p, get_alpha());
}
Classification_type classify(const Point& p,
const NT& alpha) const
// Classifies a point `p' with respect to `A'.
{
Locate_type type;
int i, j;
Cell_handle pCell = locate(p, type, i, j);
switch (type)
{
case VERTEX : return classify(pCell->vertex(i), alpha);
case EDGE : return classify(pCell, i, j, alpha);
case FACET : return classify(pCell, i, alpha);
case CELL : return classify(pCell, alpha);
case OUTSIDE_CONVEX_HULL : return EXTERIOR;
case OUTSIDE_AFFINE_HULL : return EXTERIOR;
default : return EXTERIOR;
};
}
//---------------------------------------------------------------------
Classification_type classify(const Cell_handle& s) const
// Classifies the cell `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
return classify(s, get_alpha());
}
Classification_type classify(const Cell_handle& s,
const NT& alpha) const
// Classifies the cell `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
// s->radius == alpha => f interior
{
if (is_infinite(s)) return EXTERIOR;
return (s->get_alpha() <= alpha) ? INTERIOR : EXTERIOR;
}
//---------------------------------------------------------------------
Classification_type classify(const Facet& f) const
{
return classify(f.first, f.second, get_alpha());
}
Classification_type classify(const Cell_handle& s, int i) const
{
return classify(s, i, get_alpha());
}
Classification_type classify(const Facet& f, const NT& alpha) const
{
return classify(f.first, f.second, alpha);
}
Classification_type classify(const Cell_handle& s,
int i,
const NT& alpha) const;
// Classifies the face `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
//---------------------------------------------------------------------
Classification_type classify(const Edge& e) const
{
return classify(e.first, e.second, e.third, get_alpha());
}
Classification_type classify(const Cell_handle& s,
int i,
int j) const
{
return classify(s, i, j, get_alpha());
}
Classification_type classify(const Edge& e,
const NT& alpha ) const
{
return classify(e.first, e.second, e.third, alpha);
}
Classification_type classify(const Cell_handle& s,
int i,
int j,
const NT& alpha) const;
// Classifies the edge `e' of the underlying Delaunay
// tetrahedralization with respect to `A'.
//---------------------------------------------------------------------
Classification_type classify(const Vertex_handle& v) const
{
return classify(v, get_alpha());
}
Classification_type classify(const Vertex_handle& v,
const NT& alpha) const;
// Classifies the vertex `v' of the underlying Delaunay
// tetrahedralization with respect to `A'.
//--------------------- NB COMPONENTS ---------------------------------
size_type
number_solid_components() const
{
return number_of_solid_components(get_alpha());
}
size_type
number_of_solid_components() const
{
return number_of_solid_components(get_alpha());
}
size_type
number_solid_components(const NT& alpha) const
{
return number_of_solid_components(alpha);
}
size_type
number_of_solid_components(const NT& alpha) const;
// Determine the number of connected solid components
// takes time O(#alpha_shape) amortized if STL_HASH_TABLES
// O(#alpha_shape log n) otherwise
private:
void traverse(Cell_handle pCell,
Marked_cell_set& marked_cell_set,
const NT alpha) const;
//----------------------------------------------------------------------
public:
Alpha_iterator find_optimal_alpha(size_type nb_components) const;
// find the minimum alpha that satisfies the properties
// (1) all data points are on the boundary of some 3d component
// or in its interior
// (2) the nb of solid components is equal or less than nb_component
NT find_alpha_solid() const;
// compute the minumum alpha such that all data points
// are either on the boundary or in the interior
// not necessarily connected
// starting point for searching
// takes O(#alpha_shape) time
//------------------- GEOMETRIC PRIMITIVES ----------------------------
private:
NT squared_radius(const Cell_handle& s) const
{
return Compute_squared_radius_3()(*this)(
this->point(s,0), this->point(s,1),
this->point(s,2), this->point(s,3));
}
NT squared_radius(const Cell_handle& s, const int& i) const
{
return Compute_squared_radius_3()(*this) (
this->point(s,vertex_triple_index(i,0)),
this->point(s,vertex_triple_index(i,1)),
this->point(s,vertex_triple_index(i,2)) );
}
NT squared_radius(const Facet& f) const {
return squared_radius(f.first, f.second);
}
NT squared_radius(const Cell_handle& s,
const int& i, const int& j) const
{
return Compute_squared_radius_3()(*this)(
this->point(s,i), this->point(s,j));
}
NT squared_radius(const Edge& e) const {
return squared_radius(e.first,e.second,e.third);
}
NT squared_radius(const Vertex_handle& v) const {
return Compute_squared_radius_3()(*this)(v->point());
}
//---------------------------------------------------------------------
private:
// prevent default copy constructor and default assigment
Alpha_shape_3(const Alpha_shape_3&);
void operator=(const Alpha_shape_3&);
//---------------------------------------------------------------------
public:
#ifdef CGAL_USE_GEOMVIEW
void show_alpha_shape_faces(Geomview_stream &gv) const;
#endif
// to Debug
void print_maps() const;
void print_alphas() const;
void print_alpha_status( const Alpha_status& as) const;
// To extract the alpha_shape faces for a given alpha value
template<class OutputIterator>
OutputIterator get_alpha_shape_cells(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_cells_iterator cit = finite_cells_begin();
for( ; cit != finite_cells_end() ; ++cit){
if (classify(cit, alpha) == type) *it++ = Cell_handle(cit);
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_facets(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_facets_iterator fit = finite_facets_begin();
for( ; fit != finite_facets_end() ; ++fit){
if (classify(*fit, alpha) == type) *it++ = *fit;
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_edges(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_edges_iterator eit = finite_edges_begin();
for( ; eit != finite_edges_end() ; ++eit){
if (classify(*eit, alpha) == type) *it++ = *eit;
}
return it;
}
template<class OutputIterator>
OutputIterator get_alpha_shape_vertices(OutputIterator it,
Classification_type type,
const NT& alpha) const
{
Finite_vertices_iterator vit = finite_vertices_begin();
for( ; vit != finite_vertices_end() ; ++vit){
if (classify(vit, alpha) == type) *it++ = Vertex_handle(vit);
}
return it;
}
Alpha_status
get_alpha_status(const Edge& e) const
{
return *edge_alpha_map.find(make_vertex_handle_pair(e))->second;
}
Alpha_status
get_alpha_status(const Facet& f) const
{
return *(f.first->get_facet_status(f.second));
}
template<class OutputIterator>
OutputIterator get_alpha_shape_cells(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_cells(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator get_alpha_shape_facets(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_facets(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator get_alpha_shape_edges(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_edges(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator get_alpha_shape_vertices(OutputIterator it,
Classification_type type) const
{ return get_alpha_shape_vertices(it, type, get_alpha());}
template<class OutputIterator>
OutputIterator filtration_with_alpha_values(OutputIterator it) const
// scan the alpha_cell_map, alpha_min_facet_map, alpha_min_edge_map
// and alpha_min_vertex in GENERAL mode
// only alpha_cell_map in REGULARIZED mode
// and output all the faces in order of alpha value of their appearing
// in the alpha complexe
{
typename Alpha_cell_map::const_iterator cit ;
typename Alpha_facet_map::const_iterator fit ;
typename Alpha_edge_map::const_iterator eit ;
typename Alpha_vertex_map::const_iterator vit;
if (get_mode() == GENERAL) {
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.begin();
eit = alpha_min_edge_map.begin();
vit = alpha_min_vertex_map.begin();
}
else { //mode==REGULARIZED do not scan maps of Gabriel elements
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.end();
eit = alpha_min_edge_map.end();
vit = alpha_min_vertex_map.end();
}
// sets to avoid multiple output of the same face
// as a regular subfaces of different faces
std::set<Facet> facet_set;
std::set<Vertex_handle_pair> edge_set;
std::set<Vertex_handle> vertex_set;
NT alpha_current = 0;
while (cit != alpha_cell_map.end()) {
if ( vit != alpha_min_vertex_map.end()
&& (eit == alpha_min_edge_map.end() || (vit->first <= eit->first))
&& (fit == alpha_min_facet_map.end()|| (vit->first <= fit->first))
&& (cit == alpha_cell_map.end() || (vit->first <= cit->first)))
{
//advance on vit
filtration_set_management(vit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(vit->first, vit->second, it);
vit++;
}
if ( eit != alpha_min_edge_map.end()
&& ( fit == alpha_min_facet_map.end() || (eit->first <= fit->first) )
&& ( cit == alpha_cell_map.end() || (eit->first <= cit->first) )
&& ( vit == alpha_min_vertex_map.end()|| (vit->first > eit->first) )
) { //advance on eit
filtration_set_management(eit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(eit->first, eit->second, it, vertex_set);
eit++;
}
if ( fit != alpha_min_facet_map.end()
&& (cit == alpha_cell_map.end() || (fit->first <= cit->first))
&& (eit == alpha_min_edge_map.end() || (eit->first > fit->first))
&& (vit == alpha_min_vertex_map.end()|| (vit->first > fit->first))
) { //advance on fit
filtration_set_management(fit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(fit->first, fit->second, it,
edge_set, vertex_set);
fit++;
}
if ( cit != alpha_cell_map.end()
&& (fit == alpha_min_facet_map.end() || (fit->first > cit->first) )
&& (eit == alpha_min_edge_map.end() || (eit->first > cit->first) )
&& (vit == alpha_min_vertex_map.end()|| (vit->first > cit->first) )
) { //advance on cit
filtration_set_management(cit, alpha_current,
facet_set, edge_set, vertex_set);
filtration_output(cit->first, cit->second, it,
facet_set, edge_set, vertex_set);
cit++;
}
}
return it;
}
template<class OutputIterator>
OutputIterator filtration(OutputIterator it) const
{
Dispatch_or_drop_output_iterator<cpp11::tuple<CGAL::Object>, cpp11::tuple<OutputIterator> > out(it);
return cpp11::template get<0>( filtration_with_alpha_values(out) );
}
private:
template<class Alpha_face_iterator>
void
filtration_set_management ( Alpha_face_iterator afit,
NT& alpha_current,
std::set<Facet>& facet_set,
std::set<Vertex_handle_pair>& edge_set,
std::set<Vertex_handle>& vertex_set) const
{
if (afit->first != alpha_current) { //new alpha_value
alpha_current = afit->first;
facet_set.clear();
edge_set.clear();
vertex_set.clear();
}
return;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT & alpha,
Vertex_handle vh,
OutputIterator it,
Tag_true) const
{
*it++ = make_object(vh);
*it++ = alpha;
//std::cerr << "filtration " << alpha << " \t VERTEX " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Vertex_handle vh,
OutputIterator it,
Tag_false) const
{
// when Delaunay, the alpha_min_vertex_map contains a single vertex
// because all vertices are Gabriel with the same alpha_min=0
// this affects only the GENERAL mode
if (get_mode() == GENERAL){
Finite_vertices_iterator vit=finite_vertices_begin();
for( ; vit != finite_vertices_end(); vit++) {
*it++ = make_object( Vertex_handle(vit));
*it++ = alpha;
}
}
else {
*it++ = make_object(vh);
*it++ = alpha;
}
//std::cerr << "filtration " << alpha << " \t VERTEX " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Vertex_handle vh,
OutputIterator it) const
{
return filtration_output(alpha, vh, it, Weighted_tag());
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Edge e,
OutputIterator it,
std::set<Vertex_handle>& vertex_set) const
{
Vertex_handle vh[] = {e.first->vertex(e.second),
e.first->vertex(e.third)};
for(int i=0; i<2; i++) {
Alpha_status* as = vh[i]->get_alpha_status();
if ( (get_mode()== REGULARIZED || !as->is_Gabriel())
&& as->alpha_mid() == alpha
&& vertex_set.find(vh[i]) == vertex_set.end() ) {
filtration_output( alpha, vh[i], it);
vertex_set.insert(vh[i]);
}
}
*it++ = make_object(e);
*it++ = alpha;
//std::cerr << "filtration " << alpha << " \t EDGE " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Facet f,
OutputIterator it,
std::set<Vertex_handle_pair>& edge_set,
std::set<Vertex_handle>& vertex_set ) const
{
Cell_handle c = f.first;
int facet_index = f.second;
for(int k=0; k<3; k++) {
int i = vertex_triple_index(facet_index, k );
int j = vertex_triple_index(facet_index, this->ccw(k));
Alpha_status as;
Vertex_handle_pair
vhp = make_vertex_handle_pair(c->vertex(i),c->vertex(j));
if (get_mode() == GENERAL) {
as = *(edge_alpha_map.find(vhp)->second);
}
else{ //no edge map in REGULARIZED mode - classify on the fly
compute_edge_status( c, i, j, as);
}
if ( (get_mode()== REGULARIZED || !as.is_Gabriel())
&& as.alpha_mid() == alpha
&& edge_set.find(vhp)== edge_set.end() ) {
filtration_output( alpha, make_triple(c,i,j), it, vertex_set);
edge_set.insert(vhp);
}
}
*it++ = make_object(f);
*it++ = alpha;
//std::cerr << "filtration " << alpha << " \t FACET " << std::endl;
return it;
}
template<class OutputIterator>
OutputIterator
filtration_output( const NT& alpha,
Cell_handle c,
OutputIterator it,
std::set<Facet>& facet_set,
std::set<Vertex_handle_pair>& edge_set,
std::set<Vertex_handle>& vertex_set) const
{
for(int i=0; i<4; i++) {
Alpha_status_iterator as = c->get_facet_status(i);
Facet f = std::make_pair(c,i);
if ((get_mode()== REGULARIZED || !as->is_Gabriel())
&& as->alpha_mid() == alpha
&& facet_set.find(f) == facet_set.end()
&& facet_set.find(std::make_pair(c->neighbor(i),
this->mirror_index(c, i)))
== facet_set.end()) {
filtration_output( alpha, f, it, edge_set, vertex_set);
facet_set.insert(f);
}
}
*it++ = make_object(c);
*it++ = alpha;
//std::cerr << "filtration " << alpha << " \t CELL " << std::endl;
return it;
}
};
//---------------------------------------------------------------------
//--------------------- MEMBER FUNCTIONS-------------------------------
//---------------------------------------------------------------------
//--------------------- INITIALIZATION OF PRIVATE MEMBERS -------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_cell_map()
{
Finite_cells_iterator cell_it, done = finite_cells_end();
NT alpha ;
for( cell_it = finite_cells_begin(); cell_it != done; ++cell_it) {
alpha = squared_radius(cell_it);
alpha_cell_map.insert(typename Alpha_cell_map::value_type(alpha, cell_it));
// cross references
cell_it->set_alpha(alpha);
}
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_facet_maps(bool reinitialize)
{
Finite_facets_iterator fit;
Cell_handle pCell, pNeighbor ;
int i, iNeigh;
Alpha_status_iterator as;
if (!reinitialize) {
NT alpha_max, alpha_mid;
for( fit = finite_facets_begin();
fit != finite_facets_end(); ++fit) {
as = alpha_status_container.insert(Alpha_status());
pCell = fit->first;
i = fit->second;
pNeighbor = pCell->neighbor(i);
iNeigh = pNeighbor->index(pCell);
// not on the convex hull
if(!is_infinite(pCell) && !is_infinite(pNeighbor)) {
NT alpha_Cell = pCell->get_alpha();
NT alpha_Neighbor = pNeighbor->get_alpha();
if ( alpha_Cell < alpha_Neighbor) {
alpha_mid = alpha_Cell;
alpha_max = alpha_Neighbor;
}
else {
alpha_mid = alpha_Neighbor;
alpha_max = alpha_Cell;
}
as->set_is_on_chull(false);
as->set_alpha_mid(alpha_mid);
as->set_alpha_max(alpha_max);
// alpha_mid_facet_map.insert(typename
// Alpha_facet_map::value_type(alpha_mid, *fit));
}
else { // on the convex hull
alpha_mid = !is_infinite(pCell) ? pCell->get_alpha()
: pNeighbor->get_alpha();
as->set_alpha_mid(alpha_mid);
as->set_is_on_chull(true);
}
//cross links
pCell->set_facet_status(i, as);
pNeighbor->set_facet_status(iNeigh,as);
}
}
// initialize alpha_min if mode GENERAL
if(get_mode() == GENERAL && alpha_min_facet_map.empty()) {
//already done if !alpha_min_facet_map.empty()
NT alpha_min;
for( fit = finite_facets_begin();
fit != finite_facets_end(); ++fit) {
as = fit->first->get_facet_status(fit->second);
if (is_Gabriel(*fit)) {
as->set_is_Gabriel(true);
alpha_min = squared_radius(*fit);
as->set_alpha_min(alpha_min);
alpha_min_facet_map.insert(typename
Alpha_facet_map::value_type(alpha_min, *fit));
}
else{
as->set_is_Gabriel(false);
as->set_alpha_min(as->alpha_mid());
}
}
}
return;
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_edge_maps(bool )
{
// alpha_status for edges, edge_alpha_map
// and alpha_mid_edge and alpha_min_edge
// are initialized only in GENERAL mode
if(get_mode() == REGULARIZED) {return;} //no_edge_map in REGULARIZED mode
if ( !edge_alpha_map.empty()) return; // already done
Finite_edges_iterator eit;
Alpha_status_iterator as;
for (eit = finite_edges_begin();
eit != finite_edges_end(); ++eit) {
as = alpha_status_container.insert(Alpha_status());
compute_edge_status(eit->first, eit->second, eit->third, *as);
if ( as->is_Gabriel()) {
alpha_min_edge_map.insert(typename
Alpha_edge_map::value_type(as->alpha_min(),
*eit));
}
//cross links
Vertex_handle_pair
vhp = make_vertex_handle_pair( eit->first->vertex(eit->second),
eit->first->vertex(eit->third));
edge_alpha_map.insert(std::make_pair(vhp, as));
}
return;
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_vertex_maps(bool reinitialize)
{
//for a vertex
// alpha_max = max of alpha values of incident cells
// alpha_mid = min of alpha values of incident cells in REGULAR mode
// = min of alpha values of incidents faces in GENERAL mode
// alpha_min = -squared_radius of weighted point,
// if the vertex is Gabriel set only in GENERAL mode
NT alpha, alpha_mid;
Finite_vertices_iterator vit;
if (reinitialize == false) _alpha_solid = alpha_cell_map.begin()->first;
for( vit = finite_vertices_begin();
vit != finite_vertices_end(); ++vit) {
Alpha_status* as = vit->get_alpha_status();
if (reinitialize == false) {
// set is_on_chull, compute alpha_max
// and alpha_mid (version REGULAR)
// compute _alpha_solid (max of alpha_mid of vertices in REGULAR mode)
as->set_is_on_chull(false);
std::list<Cell_handle> incidents;
incident_cells(static_cast<Vertex_handle>(vit),
back_inserter(incidents));
typename std::list<Cell_handle>::iterator chit=incidents.begin();
if (is_infinite(*chit)) as->set_is_on_chull(true);
while (is_infinite(*chit)) ++chit; //skip infinte cells
alpha = (*chit)->get_alpha();
as->set_alpha_mid(alpha);
as->set_alpha_max(alpha);
++chit;
for( ; chit != incidents.end(); ++chit) {
if (is_infinite(*chit)) as->set_is_on_chull(true);
else {
alpha = (*chit)->get_alpha();
if (alpha < as->alpha_mid()) as->set_alpha_mid(alpha);
if (alpha > as->alpha_max()) as->set_alpha_max(alpha);
}
}
if (as->alpha_mid() > _alpha_solid) _alpha_solid = as->alpha_mid();
}
if (get_mode() == GENERAL) { //reset alpha_mid, set alph_min
std::list<Vertex_handle> incidentv;
incident_vertices(static_cast<Vertex_handle>(vit),
back_inserter(incidentv));
typename std::list<Vertex_handle>::iterator vvit=incidentv.begin();
for( ; vvit != incidentv.end(); ++vvit) {
if (!is_infinite(*vvit)) {
Vertex_handle_pair vhp = make_vertex_handle_pair( *vvit, vit);
Alpha_status_iterator asedge = edge_alpha_map[vhp];
alpha_mid = asedge->is_Gabriel() ? asedge->alpha_min()
: asedge->alpha_mid();
if ( alpha_mid < as->alpha_mid()) as->set_alpha_mid(alpha_mid);
}
}
}
if (get_mode()== REGULARIZED && reinitialize == true) {
// reset alpha_mid
std::list<Cell_handle> incidents;
incident_cells(static_cast<Vertex_handle>(vit),
back_inserter(incidents));
typename std::list<Cell_handle>::iterator chit=incidents.begin();
while (is_infinite(*chit)) ++chit; //skip infinte cells
alpha = (*chit)->get_alpha();
as->set_alpha_mid(alpha);
for( ; chit != incidents.end(); ++chit) {
if (is_infinite(*chit)) as->set_is_on_chull(true);
else {
alpha = (*chit)->get_alpha();
if (alpha < as->alpha_mid()) as->set_alpha_mid(alpha);
}
}
}
}
// set alpha_min in case GENERAL
if (get_mode() == GENERAL && alpha_min_vertex_map.empty()) {
set_alpha_min_of_vertices(Weighted_tag());
}
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::initialize_alpha_spectrum()
// merges the alpha values of alpha_cell_map
// and alpha_min_facet_map alpha_min_edge_map alpha_min_vertex in GENERAL mode
// only alpha_cell_map in REGULARIZED mode
{
typename Alpha_cell_map::iterator cit ;
typename Alpha_facet_map::iterator fit ;
typename Alpha_edge_map::iterator eit ;
typename Alpha_vertex_map::iterator vit;
alpha_spectrum.clear();
if (get_mode() == GENERAL) {
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.begin();
eit = alpha_min_edge_map.begin();
vit = alpha_min_vertex_map.begin();
alpha_spectrum.reserve(alpha_cell_map.size() +
alpha_min_facet_map.size() +
alpha_min_edge_map.size() +
alpha_min_vertex_map.size());
}
else {
alpha_spectrum.reserve(alpha_cell_map.size());
cit = alpha_cell_map.begin();
fit = alpha_min_facet_map.end();
eit = alpha_min_edge_map.end();
vit = alpha_min_vertex_map.end();
}
while (cit != alpha_cell_map.end() ||
fit != alpha_min_facet_map.end() ||
eit != alpha_min_edge_map.end() ) {
if ( cit != alpha_cell_map.end()
&& ( fit == alpha_min_facet_map.end() || !(fit->first < cit->first) )
&& ( eit == alpha_min_edge_map.end() || !(eit->first < cit->first) )
&& ( vit == alpha_min_vertex_map.end() || !(vit->first < cit->first) )
) { //advance on cit
if (alpha_spectrum.empty() || alpha_spectrum.back() < cit->first){
alpha_spectrum.push_back(cit->first);
}
cit++;
}
if ( fit != alpha_min_facet_map.end()
&& ( cit == alpha_cell_map.end() || !(cit->first < fit->first) )
&& ( eit == alpha_min_edge_map.end() || !(eit->first < fit->first) )
&& ( vit == alpha_min_vertex_map.end() || !(vit->first < fit->first) )
) { //advance on fit
if (alpha_spectrum.empty() || alpha_spectrum.back() < fit->first){
alpha_spectrum.push_back(fit->first);
}
fit++;
}
if ( eit != alpha_min_edge_map.end()
&& ( fit == alpha_min_facet_map.end() || !(fit->first < eit->first) )
&& ( cit == alpha_cell_map.end() || !(cit->first < eit->first) )
&& ( vit == alpha_min_vertex_map.end() || !(vit->first < eit->first) )
) { //advance on eit
if (alpha_spectrum.empty() || alpha_spectrum.back() < eit->first) {
alpha_spectrum.push_back(eit->first);
}
eit++;
}
if ( vit != alpha_min_vertex_map.end()
&& ( fit == alpha_min_facet_map.end() || !(fit->first < vit->first) )
&& ( cit == alpha_cell_map.end() || !(cit->first < vit->first) )
&& ( eit == alpha_min_edge_map.end() || !(eit->first < vit->first) )
) { //advance on vit
if (alpha_spectrum.empty() || alpha_spectrum.back() < vit->first) {
alpha_spectrum.push_back(vit->first);
}
vit++;
}
}
}
//---------------------------------------------------------------------
#if 0
// Obviously not ready yet
template <class Dt,class EACT>
std::istream& operator>>(std::istream& is, const Alpha_shape_3<Dt,EACT>& A)
// Reads a alpha shape from stream `is' and assigns it to
// Unknown creationvariable. Precondition: The extract operator must
// be defined for `Point'.
{}
#endif
//---------------------------------------------------------------------
template <class Dt,class EACT>
std::ostream& operator<<(std::ostream& os, const Alpha_shape_3<Dt,EACT>& A)
// Inserts the alpha shape into the stream `os' as an indexed face set.
// Precondition: The insert operator must be defined for `Point'
{
typedef Alpha_shape_3<Dt,EACT> AS;
typedef typename AS::size_type size_type;
typedef typename AS::Vertex_handle Vertex_handle;
typedef typename AS::Cell_handle Cell_handle;
typedef typename AS::Alpha_shape_vertices_iterator
Alpha_shape_vertices_iterator;
typedef typename AS::Alpha_shape_facets_iterator
Alpha_shape_facets_iterator;
Unique_hash_map< Vertex_handle, size_type > V;
size_type number_of_vertices = 0;
Alpha_shape_vertices_iterator vit;
for( vit = A.alpha_shape_vertices_begin();
vit != A.alpha_shape_vertices_end();
++vit) {
V[*vit] = number_of_vertices++;
os << (*vit)->point() << std::endl;
}
Cell_handle c;
int i;
Alpha_shape_facets_iterator fit;
for( fit = A.alpha_shape_facets_begin();
fit != A.alpha_shape_facets_end();
++fit) {
c = fit->first;
i = fit->second;
// the following ensures that regular facets are output
// in ccw order
if (A.classify(*fit) == AS::REGULAR && (A.classify(c) == AS::INTERIOR)){
c = c->neighbor(i);
i = c->index(fit->first);
}
int i0 = Triangulation_utils_3::vertex_triple_index(i,0);
int i1 = Triangulation_utils_3::vertex_triple_index(i,1);
int i2 = Triangulation_utils_3::vertex_triple_index(i,2);
os << V[c->vertex(i0)] << ' '
<< V[c->vertex(i1)] << ' '
<< V[c->vertex(i2)] << std::endl;
}
return os;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::update_alpha_shape_vertex_list() const
{
alpha_shape_vertices_list.clear();
use_vertex_cache = true;
std::back_insert_iterator<std::list< Vertex_handle > >
it = back_inserter(alpha_shape_vertices_list);
get_alpha_shape_vertices(it, REGULAR);
if (get_mode()==GENERAL) get_alpha_shape_vertices(it, SINGULAR);
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::update_alpha_shape_facet_list() const
{
alpha_shape_facets_list.clear();
use_facet_cache = true;
// Writes the faces of the alpha shape `A' for the current 'alpha'-value
// to the container where 'out' refers to.
std::back_insert_iterator<std::list< Facet> >
it = back_inserter(alpha_shape_facets_list);
get_alpha_shape_facets(it, REGULAR);
if (get_mode()==GENERAL) get_alpha_shape_facets(it, SINGULAR);
return;
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Alpha_status& as,
const NT& alpha) const
{
//tetrahedra with circumradius=alpha are considered inside
if ( !as.is_on_chull() && alpha >= as.alpha_max()) return INTERIOR;
else if ( alpha >= as.alpha_mid()) return REGULAR;
else if ( get_mode() == GENERAL &&
as.is_Gabriel() &&
alpha >= as.alpha_min()) return SINGULAR;
else return EXTERIOR;
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Alpha_status* as,
const NT& alpha) const
{
//tetrahedra with circumradius=alpha are considered inside
if ( !as->is_on_chull() && alpha >= as->alpha_max()) return INTERIOR;
else if ( alpha >= as->alpha_mid()) return REGULAR;
else if ( get_mode() == GENERAL &&
as->is_Gabriel() &&
alpha >= as->alpha_min()) return SINGULAR;
else return EXTERIOR;
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(Alpha_status_const_iterator as,
const NT& alpha) const
{
return classify(&(*as), alpha);
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Cell_handle& s,
int i,
const NT& alpha) const
// Classifies the face `f' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
if (is_infinite(s,i)) return EXTERIOR;
Alpha_status_iterator as = s->get_facet_status(i);
return classify(as, alpha);
}
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Cell_handle& c,
int i,
int j,
const NT& alpha) const
// Classifies the edge `e' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
if (is_infinite(c, i, j)) return EXTERIOR;
if (get_mode() == GENERAL) {
Alpha_status_iterator asit;
Vertex_handle_pair
vhp=make_vertex_handle_pair(c->vertex(i),c->vertex(j));
asit = edge_alpha_map.find(vhp)->second;
return classify(asit,alpha);
}
//no edge map in REGULARIZED mode - classify on the fly
Alpha_status as;
compute_edge_status( c, i, j, as);
return classify(as, alpha);
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::
compute_edge_status( const Cell_handle& c,
int i,
int j,
Alpha_status& as) const
{
Facet_circulator fcirc, done;
Alpha_status_iterator asf;
NT alpha;
as.set_is_on_chull(false);
Cell_circulator ccirc, last;
ccirc = incident_cells(c,i,j);
last=ccirc;
while (is_infinite(ccirc) ) ++ccirc; //skip infinite incident cells
alpha = (*ccirc).get_alpha();
as.set_alpha_mid(alpha); // initialise as.alpha_mid to alpha value of an incident cell
as.set_alpha_max(alpha); // same for as.alpha_max
while (++ccirc != last)
{
if (!is_infinite(ccirc)) {
alpha = (*ccirc).get_alpha();
if (alpha < as.alpha_mid())
as.set_alpha_mid(alpha);
if ( ! as.is_on_chull()) {
if( as.alpha_max() < alpha)
as.set_alpha_max( alpha );
}
}
}
fcirc = incident_facets(c,i,j);
done = fcirc;
do {
if (!is_infinite(*fcirc)) {
asf = (*fcirc).first->get_facet_status((*fcirc).second);
if (get_mode() == GENERAL && asf->is_Gabriel()){
alpha = asf->alpha_min();
if (alpha < as.alpha_mid()) as.set_alpha_mid(alpha);
}
if (asf->is_on_chull())
as.set_is_on_chull(true);
}
} while (++fcirc != done);
// initialize alphamin
if ( get_mode() == GENERAL){
if (is_Gabriel(c,i,j)) {
alpha = squared_radius(c,i,j);
as.set_is_Gabriel(true);
as.set_alpha_min(alpha);
}
else{
as.set_is_Gabriel(false);
as.set_alpha_min(as.alpha_mid());
}
}
}
//---------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Classification_type
Alpha_shape_3<Dt,EACT>::classify(const Vertex_handle& v,
const NT& alpha) const
// Classifies the vertex `v' of the underlying Delaunay
// tetrahedralization with respect to `A'.
{
if (is_infinite(v)) return EXTERIOR;
Alpha_status* as = v->get_alpha_status();
return classify(as, alpha);
}
//--------------------- NB COMPONENTS ---------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::size_type
Alpha_shape_3<Dt,EACT>::number_of_solid_components(const NT& alpha) const
// Determine the number of connected solid components
// takes time O(#alpha_shape) amortized if STL_HASH_TABLES
// O(#alpha_shape log n) otherwise
{
typedef typename Marked_cell_set::Data Data;
Marked_cell_set marked_cell_set(false);
Finite_cells_iterator cell_it, done = finite_cells_end();
size_type nb_solid_components = 0;
// only finite simplices
for( cell_it = finite_cells_begin(); cell_it != done; ++cell_it)
{
Cell_handle pCell = cell_it;
CGAL_triangulation_assertion(pCell != NULL);
if (classify(pCell, alpha) == INTERIOR){
Data& data = marked_cell_set[pCell];
if(data == false) {
// we traverse only interior simplices
data = true;
traverse(pCell, marked_cell_set, alpha);
nb_solid_components++;
}
}
}
return nb_solid_components;
}
template <class Dt,class EACT>
void Alpha_shape_3<Dt,EACT>::traverse(Cell_handle pCell,
Marked_cell_set& marked_cell_set,
const NT alpha) const
{
typedef typename Marked_cell_set::Data Data;
std::list<Cell_handle> cells;
cells.push_back(pCell);
Cell_handle pNeighbor;
while(! cells.empty()){
pCell = cells.back();
cells.pop_back();
for (int i=0; i<=3; i++)
{
pNeighbor = pCell->neighbor(i);
CGAL_triangulation_assertion(pNeighbor != NULL);
if (classify(pNeighbor, alpha) == INTERIOR){
Data& data = marked_cell_set[pNeighbor];
if(data == false){
data = true;
cells.push_back(pNeighbor);
}
}
}
}
}
//----------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::Alpha_iterator
Alpha_shape_3<Dt,EACT>::find_optimal_alpha(size_type nb_components) const
// find the minimum alpha that satisfies the properties
// (1) nb_components solid components <= nb_components
// (2) all data points on the boundary or in its interior
{
NT alpha = find_alpha_solid();
// from this alpha on the alpha_solid satisfies property (2)
Alpha_iterator first = alpha_lower_bound(alpha);
if (number_of_solid_components(alpha) == nb_components)
{
// if ((first+1) < alpha_end())
// return (first+1);
// else
return first;
}
// do binary search on the alpha values
// number_of_solid_components() is a monotone function
// if we start with find_alpha_solid
Alpha_iterator last = alpha_end();
Alpha_iterator middle;
std::ptrdiff_t len = last - first - 1;
std::ptrdiff_t half;
while (len > 0)
{
half = len / 2;
middle = first + half;
/* //#ifdef DEBUG */
/* std::cerr << "first : " << *first */
/* << " last : " */
/* << ((first+len != last) ? *(first+len) : *(last-1)) */
/* << " mid : " << *middle */
/* << " nb comps : " << number_of_solid_components(*middle) */
/* << std::endl; */
/* //#endif // DEBUG */
if (number_of_solid_components(*middle) > nb_components)
{
first = middle + 1;
len = len - half -1;
}
else // number_of_solid_components(*middle) <= nb_components
{
len = half;
}
}
/* std::cerr << "a la fin " << std::endl */
/* << "first : " << *first */
/* << " nb comps : " << number_of_solid_components(*first) */
/* << std::endl; */
/* if ((first+1) < alpha_end()) */
/* std::cerr << "first+1 " << *(first+1) */
/* << " nb comps : " << number_of_solid_components(*(first+1)) */
/* << std::endl; */
/* std::cerr << std::endl; */
if (number_of_solid_components(*first) <= nb_components ) return first;
else return first+1;
}
//----------------------------------------------------------------------
template <class Dt,class EACT>
typename Alpha_shape_3<Dt,EACT>::NT
Alpha_shape_3<Dt,EACT>::find_alpha_solid() const
// compute the minumum alpha such that all data points
// are either on the boundary or in the interior
// not necessarily connected
{
return _alpha_solid;
}
// TO DEBUG
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::print_maps() const
{
typename Alpha_cell_map::const_iterator cit ;
typename Alpha_facet_map::const_iterator fit ;
typename Alpha_edge_map::const_iterator eit ;
typename Alpha_vertex_map::const_iterator vit;
std::cerr << "size of cell map " << alpha_cell_map.size()
<< std::endl;
std::cerr << "size of facet map " << alpha_min_facet_map.size() <<
std::endl;
std::cerr << "size of edge map " << alpha_min_edge_map.size() <<
std::endl;
std::cerr << "size of vertex map " << alpha_min_vertex_map.size() <<
std::endl;
std::cerr << std::endl;
std::cerr << "alpha_cell_map " << std::endl;
for(cit = alpha_cell_map.begin();
cit != alpha_cell_map.end(); ++cit) {
std::cerr << cit->first << std::endl;
}
std::cerr << std::endl;
std::cerr << "alpha_min_facet_map " << std::endl;
for(fit = alpha_min_facet_map.begin();
fit != alpha_min_facet_map.end(); ++fit) {
std::cerr << fit->first << std::endl;
}
std::cerr << std::endl;
std::cerr << "alpha_min_edge_map " << std::endl;
for(eit = alpha_min_edge_map.begin();
eit != alpha_min_edge_map.end(); ++eit) {
std::cerr << eit->first << std::endl;
}
std::cerr << std::endl;
std::cerr << "alpha_min_vertex_map " << std::endl;
for(vit = alpha_min_vertex_map.begin();
vit != alpha_min_vertex_map.end(); ++vit) {
std::cerr << vit->first << std::endl;
}
std::cerr << std::endl;
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::print_alphas() const
{
std::cerr << std::endl;
std::cerr << " alpha values of facets" << std::endl;
for(Finite_facets_iterator fit = finite_facets_begin();
fit != finite_facets_end();
++fit) {
Alpha_status_iterator as = fit->first->get_facet_status(fit->second);
print_alpha_status(*as);
}
std::cerr << std::endl;
std::cerr << " alpha values of edges " << std::endl;
if (get_mode() == GENERAL) {
for(Finite_edges_iterator eit = finite_edges_begin();
eit != finite_edges_end();
++eit) {
Vertex_handle_pair
vhp = make_vertex_handle_pair(eit->first->vertex(eit->second),
eit->first->vertex(eit->third));
Alpha_status_iterator as = edge_alpha_map.find(vhp)->second;
print_alpha_status(*as);
}
}
std::cerr << std::endl;
std::cerr << " alpha values of vertices " << std::endl;
for(Finite_vertices_iterator vit = finite_vertices_begin();
vit != finite_vertices_end();
++vit) {
Alpha_status* as = vit->get_alpha_status();
print_alpha_status(*as);
}
}
template <class Dt,class EACT>
void
Alpha_shape_3<Dt,EACT>::print_alpha_status(const Alpha_status& as) const
{
if ( get_mode() == GENERAL && as.is_Gabriel())
std::cerr << as.alpha_min() ;
else std::cerr << "--- " ;
std::cerr << "\t";
std::cerr << as.alpha_mid() << "\t";
if(as.is_on_chull()) std::cerr << "--- ";
else std::cerr << as.alpha_max();
std::cerr << std::endl;
}
} //namespace CGAL
#ifdef CGAL_USE_GEOMVIEW
#include <CGAL/IO/alpha_shape_geomview_ostream_3.h>
#endif
#endif //CGAL_ALPHA_SHAPE_3_H
|