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
//
// Copyright (c) 2009-2010 Mikko Mononen memon@inside.org
//
// This software is provided 'as-is', without any express or implied
// warranty.  In no event will the authors be held liable for any damages
// arising from the use of this software.
// Permission is granted to anyone to use this software for any purpose,
// including commercial applications, and to alter it and redistribute it
// freely, subject to the following restrictions:
// 1. The origin of this software must not be misrepresented; you must not
//    claim that you wrote the original software. If you use this software
//    in a product, an acknowledgment in the product documentation would be
//    appreciated but is not required.
// 2. Altered source versions must be plainly marked as such, and must not be
//    misrepresented as being the original software.
// 3. This notice may not be removed or altered from any source distribution.
//

#define _USE_MATH_DEFINES
#include <math.h>
#include <string.h>
#include <stdio.h>
#include <stdlib.h>
#include "Recast.h"
#include "RecastAlloc.h"
#include "RecastAssert.h"


static int getCornerHeight(int x, int y, int i, int dir,
						   const rcCompactHeightfield& chf,
						   bool& isBorderVertex)
{
	const rcCompactSpan& s = chf.spans[i];
	int ch = (int)s.y;
	int dirp = (dir+1) & 0x3;
	
	unsigned int regs[4] = {0,0,0,0};
	
	// Combine region and area codes in order to prevent
	// border vertices which are in between two areas to be removed.
	regs[0] = chf.spans[i].reg | (chf.areas[i] << 16);
	
	if (rcGetCon(s, dir) != RC_NOT_CONNECTED)
	{
		const int ax = x + rcGetDirOffsetX(dir);
		const int ay = y + rcGetDirOffsetY(dir);
		const int ai = (int)chf.cells[ax+ay*chf.width].index + rcGetCon(s, dir);
		const rcCompactSpan& as = chf.spans[ai];
		ch = rcMax(ch, (int)as.y);
		regs[1] = chf.spans[ai].reg | (chf.areas[ai] << 16);
		if (rcGetCon(as, dirp) != RC_NOT_CONNECTED)
		{
			const int ax2 = ax + rcGetDirOffsetX(dirp);
			const int ay2 = ay + rcGetDirOffsetY(dirp);
			const int ai2 = (int)chf.cells[ax2+ay2*chf.width].index + rcGetCon(as, dirp);
			const rcCompactSpan& as2 = chf.spans[ai2];
			ch = rcMax(ch, (int)as2.y);
			regs[2] = chf.spans[ai2].reg | (chf.areas[ai2] << 16);
		}
	}
	if (rcGetCon(s, dirp) != RC_NOT_CONNECTED)
	{
		const int ax = x + rcGetDirOffsetX(dirp);
		const int ay = y + rcGetDirOffsetY(dirp);
		const int ai = (int)chf.cells[ax+ay*chf.width].index + rcGetCon(s, dirp);
		const rcCompactSpan& as = chf.spans[ai];
		ch = rcMax(ch, (int)as.y);
		regs[3] = chf.spans[ai].reg | (chf.areas[ai] << 16);
		if (rcGetCon(as, dir) != RC_NOT_CONNECTED)
		{
			const int ax2 = ax + rcGetDirOffsetX(dir);
			const int ay2 = ay + rcGetDirOffsetY(dir);
			const int ai2 = (int)chf.cells[ax2+ay2*chf.width].index + rcGetCon(as, dir);
			const rcCompactSpan& as2 = chf.spans[ai2];
			ch = rcMax(ch, (int)as2.y);
			regs[2] = chf.spans[ai2].reg | (chf.areas[ai2] << 16);
		}
	}

	// Check if the vertex is special edge vertex, these vertices will be removed later.
	for (int j = 0; j < 4; ++j)
	{
		const int a = j;
		const int b = (j+1) & 0x3;
		const int c = (j+2) & 0x3;
		const int d = (j+3) & 0x3;
		
		// The vertex is a border vertex there are two same exterior cells in a row,
		// followed by two interior cells and none of the regions are out of bounds.
		const bool twoSameExts = (regs[a] & regs[b] & RC_BORDER_REG) != 0 && regs[a] == regs[b];
		const bool twoInts = ((regs[c] | regs[d]) & RC_BORDER_REG) == 0;
		const bool intsSameArea = (regs[c]>>16) == (regs[d]>>16);
		const bool noZeros = regs[a] != 0 && regs[b] != 0 && regs[c] != 0 && regs[d] != 0;
		if (twoSameExts && twoInts && intsSameArea && noZeros)
		{
			isBorderVertex = true;
			break;
		}
	}
	
	return ch;
}

static void walkContour(int x, int y, int i,
						rcCompactHeightfield& chf,
						unsigned char* flags, rcIntArray& points)
{
	// Choose the first non-connected edge
	unsigned char dir = 0;
	while ((flags[i] & (1 << dir)) == 0)
		dir++;
	
	unsigned char startDir = dir;
	int starti = i;
	
	const unsigned char area = chf.areas[i];
	
	int iter = 0;
	while (++iter < 40000)
	{
		if (flags[i] & (1 << dir))
		{
			// Choose the edge corner
			bool isBorderVertex = false;
			bool isAreaBorder = false;
			int px = x;
			int py = getCornerHeight(x, y, i, dir, chf, isBorderVertex);
			int pz = y;
			switch(dir)
			{
				case 0: pz++; break;
				case 1: px++; pz++; break;
				case 2: px++; break;
			}
			int r = 0;
			const rcCompactSpan& s = chf.spans[i];
			if (rcGetCon(s, dir) != RC_NOT_CONNECTED)
			{
				const int ax = x + rcGetDirOffsetX(dir);
				const int ay = y + rcGetDirOffsetY(dir);
				const int ai = (int)chf.cells[ax+ay*chf.width].index + rcGetCon(s, dir);
				r = (int)chf.spans[ai].reg;
				if (area != chf.areas[ai])
					isAreaBorder = true;
			}
			if (isBorderVertex)
				r |= RC_BORDER_VERTEX;
			if (isAreaBorder)
				r |= RC_AREA_BORDER;
			points.push(px);
			points.push(py);
			points.push(pz);
			points.push(r);
			
			flags[i] &= ~(1 << dir); // Remove visited edges
			dir = (dir+1) & 0x3;  // Rotate CW
		}
		else
		{
			int ni = -1;
			const int nx = x + rcGetDirOffsetX(dir);
			const int ny = y + rcGetDirOffsetY(dir);
			const rcCompactSpan& s = chf.spans[i];
			if (rcGetCon(s, dir) != RC_NOT_CONNECTED)
			{
				const rcCompactCell& nc = chf.cells[nx+ny*chf.width];
				ni = (int)nc.index + rcGetCon(s, dir);
			}
			if (ni == -1)
			{
				// Should not happen.
				return;
			}
			x = nx;
			y = ny;
			i = ni;
			dir = (dir+3) & 0x3;	// Rotate CCW
		}
		
		if (starti == i && startDir == dir)
		{
			break;
		}
	}
}

static float distancePtSeg(const int x, const int z,
						   const int px, const int pz,
						   const int qx, const int qz)
{
	float pqx = (float)(qx - px);
	float pqz = (float)(qz - pz);
	float dx = (float)(x - px);
	float dz = (float)(z - pz);
	float d = pqx*pqx + pqz*pqz;
	float t = pqx*dx + pqz*dz;
	if (d > 0)
		t /= d;
	if (t < 0)
		t = 0;
	else if (t > 1)
		t = 1;
	
	dx = px + t*pqx - x;
	dz = pz + t*pqz - z;
	
	return dx*dx + dz*dz;
}

static void simplifyContour(rcIntArray& points, rcIntArray& simplified,
							const float maxError, const int maxEdgeLen, const int buildFlags)
{
	// Add initial points.
	bool hasConnections = false;
	for (int i = 0; i < points.size(); i += 4)
	{
		if ((points[i+3] & RC_CONTOUR_REG_MASK) != 0)
		{
			hasConnections = true;
			break;
		}
	}
	
	if (hasConnections)
	{
		// The contour has some portals to other regions.
		// Add a new point to every location where the region changes.
		for (int i = 0, ni = points.size()/4; i < ni; ++i)
		{
			int ii = (i+1) % ni;
			const bool differentRegs = (points[i*4+3] & RC_CONTOUR_REG_MASK) != (points[ii*4+3] & RC_CONTOUR_REG_MASK);
			const bool areaBorders = (points[i*4+3] & RC_AREA_BORDER) != (points[ii*4+3] & RC_AREA_BORDER);
			if (differentRegs || areaBorders)
			{
				simplified.push(points[i*4+0]);
				simplified.push(points[i*4+1]);
				simplified.push(points[i*4+2]);
				simplified.push(i);
			}
		}
	}
	
	if (simplified.size() == 0)
	{
		// If there is no connections at all,
		// create some initial points for the simplification process.
		// Find lower-left and upper-right vertices of the contour.
		int llx = points[0];
		int lly = points[1];
		int llz = points[2];
		int lli = 0;
		int urx = points[0];
		int ury = points[1];
		int urz = points[2];
		int uri = 0;
		for (int i = 0; i < points.size(); i += 4)
		{
			int x = points[i+0];
			int y = points[i+1];
			int z = points[i+2];
			if (x < llx || (x == llx && z < llz))
			{
				llx = x;
				lly = y;
				llz = z;
				lli = i/4;
			}
			if (x > urx || (x == urx && z > urz))
			{
				urx = x;
				ury = y;
				urz = z;
				uri = i/4;
			}
		}
		simplified.push(llx);
		simplified.push(lly);
		simplified.push(llz);
		simplified.push(lli);
		
		simplified.push(urx);
		simplified.push(ury);
		simplified.push(urz);
		simplified.push(uri);
	}
	
	// Add points until all raw points are within
	// error tolerance to the simplified shape.
	const int pn = points.size()/4;
	for (int i = 0; i < simplified.size()/4; )
	{
		int ii = (i+1) % (simplified.size()/4);
		
		int ax = simplified[i*4+0];
		int az = simplified[i*4+2];
		int ai = simplified[i*4+3];

		int bx = simplified[ii*4+0];
		int bz = simplified[ii*4+2];
		int bi = simplified[ii*4+3];

		// Find maximum deviation from the segment.
		float maxd = 0;
		int maxi = -1;
		int ci, cinc, endi;

		// Traverse the segment in lexilogical order so that the
		// max deviation is calculated similarly when traversing
		// opposite segments.
		if (bx > ax || (bx == ax && bz > az))
		{
			cinc = 1;
			ci = (ai+cinc) % pn;
			endi = bi;
		}
		else
		{
			cinc = pn-1;
			ci = (bi+cinc) % pn;
			endi = ai;
			rcSwap(ax, bx);
			rcSwap(az, bz);
		}
		
		// Tessellate only outer edges or edges between areas.
		if ((points[ci*4+3] & RC_CONTOUR_REG_MASK) == 0 ||
			(points[ci*4+3] & RC_AREA_BORDER))
		{
			while (ci != endi)
			{
				float d = distancePtSeg(points[ci*4+0], points[ci*4+2], ax, az, bx, bz);
				if (d > maxd)
				{
					maxd = d;
					maxi = ci;
				}
				ci = (ci+cinc) % pn;
			}
		}
		
		
		// If the max deviation is larger than accepted error,
		// add new point, else continue to next segment.
		if (maxi != -1 && maxd > (maxError*maxError))
		{
			// Add space for the new point.
			simplified.resize(simplified.size()+4);
			const int n = simplified.size()/4;
			for (int j = n-1; j > i; --j)
			{
				simplified[j*4+0] = simplified[(j-1)*4+0];
				simplified[j*4+1] = simplified[(j-1)*4+1];
				simplified[j*4+2] = simplified[(j-1)*4+2];
				simplified[j*4+3] = simplified[(j-1)*4+3];
			}
			// Add the point.
			simplified[(i+1)*4+0] = points[maxi*4+0];
			simplified[(i+1)*4+1] = points[maxi*4+1];
			simplified[(i+1)*4+2] = points[maxi*4+2];
			simplified[(i+1)*4+3] = maxi;
		}
		else
		{
			++i;
		}
	}
	
	// Split too long edges.
	if (maxEdgeLen > 0 && (buildFlags & (RC_CONTOUR_TESS_WALL_EDGES|RC_CONTOUR_TESS_AREA_EDGES)) != 0)
	{
		for (int i = 0; i < simplified.size()/4; )
		{
			const int ii = (i+1) % (simplified.size()/4);
			
			const int ax = simplified[i*4+0];
			const int az = simplified[i*4+2];
			const int ai = simplified[i*4+3];
			
			const int bx = simplified[ii*4+0];
			const int bz = simplified[ii*4+2];
			const int bi = simplified[ii*4+3];
			
			// Find maximum deviation from the segment.
			int maxi = -1;
			int ci = (ai+1) % pn;
			
			// Tessellate only outer edges or edges between areas.
			bool tess = false;
			// Wall edges.
			if ((buildFlags & RC_CONTOUR_TESS_WALL_EDGES) && (points[ci*4+3] & RC_CONTOUR_REG_MASK) == 0)
				tess = true;
			// Edges between areas.
			if ((buildFlags & RC_CONTOUR_TESS_AREA_EDGES) && (points[ci*4+3] & RC_AREA_BORDER))
				tess = true;
			
			if (tess)
			{
				int dx = bx - ax;
				int dz = bz - az;
				if (dx*dx + dz*dz > maxEdgeLen*maxEdgeLen)
				{
					// Round based on the segments in lexilogical order so that the
					// max tesselation is consistent regardles in which direction
					// segments are traversed.
					const int n = bi < ai ? (bi+pn - ai) : (bi - ai);
					if (n > 1)
					{
						if (bx > ax || (bx == ax && bz > az))
							maxi = (ai + n/2) % pn;
						else
							maxi = (ai + (n+1)/2) % pn;
					}
				}
			}
			
			// If the max deviation is larger than accepted error,
			// add new point, else continue to next segment.
			if (maxi != -1)
			{
				// Add space for the new point.
				simplified.resize(simplified.size()+4);
				const int n = simplified.size()/4;
				for (int j = n-1; j > i; --j)
				{
					simplified[j*4+0] = simplified[(j-1)*4+0];
					simplified[j*4+1] = simplified[(j-1)*4+1];
					simplified[j*4+2] = simplified[(j-1)*4+2];
					simplified[j*4+3] = simplified[(j-1)*4+3];
				}
				// Add the point.
				simplified[(i+1)*4+0] = points[maxi*4+0];
				simplified[(i+1)*4+1] = points[maxi*4+1];
				simplified[(i+1)*4+2] = points[maxi*4+2];
				simplified[(i+1)*4+3] = maxi;
			}
			else
			{
				++i;
			}
		}
	}
	
	for (int i = 0; i < simplified.size()/4; ++i)
	{
		// The edge vertex flag is take from the current raw point,
		// and the neighbour region is take from the next raw point.
		const int ai = (simplified[i*4+3]+1) % pn;
		const int bi = simplified[i*4+3];
		simplified[i*4+3] = (points[ai*4+3] & (RC_CONTOUR_REG_MASK|RC_AREA_BORDER)) | (points[bi*4+3] & RC_BORDER_VERTEX);
	}
	
}

static int calcAreaOfPolygon2D(const int* verts, const int nverts)
{
	int area = 0;
	for (int i = 0, j = nverts-1; i < nverts; j=i++)
	{
		const int* vi = &verts[i*4];
		const int* vj = &verts[j*4];
		area += vi[0] * vj[2] - vj[0] * vi[2];
	}
	return (area+1) / 2;
}

// TODO: these are the same as in RecastMesh.cpp, consider using the same.
// Last time I checked the if version got compiled using cmov, which was a lot faster than module (with idiv).
inline int prev(int i, int n) { return i-1 >= 0 ? i-1 : n-1; }
inline int next(int i, int n) { return i+1 < n ? i+1 : 0; }

inline int area2(const int* a, const int* b, const int* c)
{
	return (b[0] - a[0]) * (c[2] - a[2]) - (c[0] - a[0]) * (b[2] - a[2]);
}

//	Exclusive or: true iff exactly one argument is true.
//	The arguments are negated to ensure that they are 0/1
//	values.  Then the bitwise Xor operator may apply.
//	(This idea is due to Michael Baldwin.)
inline bool xorb(bool x, bool y)
{
	return !x ^ !y;
}

// Returns true iff c is strictly to the left of the directed
// line through a to b.
inline bool left(const int* a, const int* b, const int* c)
{
	return area2(a, b, c) < 0;
}

inline bool leftOn(const int* a, const int* b, const int* c)
{
	return area2(a, b, c) <= 0;
}

inline bool collinear(const int* a, const int* b, const int* c)
{
	return area2(a, b, c) == 0;
}

//	Returns true iff ab properly intersects cd: they share
//	a point interior to both segments.  The properness of the
//	intersection is ensured by using strict leftness.
static bool intersectProp(const int* a, const int* b, const int* c, const int* d)
{
	// Eliminate improper cases.
	if (collinear(a,b,c) || collinear(a,b,d) ||
		collinear(c,d,a) || collinear(c,d,b))
		return false;
	
	return xorb(left(a,b,c), left(a,b,d)) && xorb(left(c,d,a), left(c,d,b));
}

// Returns T iff (a,b,c) are collinear and point c lies
// on the closed segement ab.
static bool between(const int* a, const int* b, const int* c)
{
	if (!collinear(a, b, c))
		return false;
	// If ab not vertical, check betweenness on x; else on y.
	if (a[0] != b[0])
		return	((a[0] <= c[0]) && (c[0] <= b[0])) || ((a[0] >= c[0]) && (c[0] >= b[0]));
	else
		return	((a[2] <= c[2]) && (c[2] <= b[2])) || ((a[2] >= c[2]) && (c[2] >= b[2]));
}

// Returns true iff segments ab and cd intersect, properly or improperly.
static bool intersect(const int* a, const int* b, const int* c, const int* d)<--- Shadowed declaration
{
	if (intersectProp(a, b, c, d))
		return true;
	else if (between(a, b, c) || between(a, b, d) ||
			 between(c, d, a) || between(c, d, b))
		return true;
	else
		return false;
}

static bool vequal(const int* a, const int* b)
{
	return a[0] == b[0] && a[2] == b[2];
}

static bool intersectSegCountour(const int* d0, const int* d1, int i, int n, const int* verts)
{
	// For each edge (k,k+1) of P
	for (int k = 0; k < n; k++)
	{
		int k1 = next(k, n);
		// Skip edges incident to i.
		if (i == k || i == k1)
			continue;
		const int* p0 = &verts[k * 4];
		const int* p1 = &verts[k1 * 4];
		if (vequal(d0, p0) || vequal(d1, p0) || vequal(d0, p1) || vequal(d1, p1))
			continue;
		
		if (intersect(d0, d1, p0, p1))
			return true;
	}
	return false;
}

static bool	inCone(int i, int n, const int* verts, const int* pj)
{
	const int* pi = &verts[i * 4];
	const int* pi1 = &verts[next(i, n) * 4];
	const int* pin1 = &verts[prev(i, n) * 4];
	
	// If P[i] is a convex vertex [ i+1 left or on (i-1,i) ].
	if (leftOn(pin1, pi, pi1))
		return left(pi, pj, pin1) && left(pj, pi, pi1);
	// Assume (i-1,i,i+1) not collinear.
	// else P[i] is reflex.
	return !(leftOn(pi, pj, pi1) && leftOn(pj, pi, pin1));
}


static void removeDegenerateSegments(rcIntArray& simplified)
{
	// Remove adjacent vertices which are equal on xz-plane,
	// or else the triangulator will get confused.
	int npts = simplified.size()/4;
	for (int i = 0; i < npts; ++i)
	{
		int ni = next(i, npts);
		
		if (vequal(&simplified[i*4], &simplified[ni*4]))
		{
			// Degenerate segment, remove.
			for (int j = i; j < simplified.size()/4-1; ++j)
			{
				simplified[j*4+0] = simplified[(j+1)*4+0];
				simplified[j*4+1] = simplified[(j+1)*4+1];
				simplified[j*4+2] = simplified[(j+1)*4+2];
				simplified[j*4+3] = simplified[(j+1)*4+3];
			}
			simplified.resize(simplified.size()-4);
			npts--;
		}
	}
}


static bool mergeContours(rcContour& ca, rcContour& cb, int ia, int ib)
{
	const int maxVerts = ca.nverts + cb.nverts + 2;
	int* verts = (int*)rcAlloc(sizeof(int)*maxVerts*4, RC_ALLOC_PERM);
	if (!verts)
		return false;
	
	int nv = 0;
	
	// Copy contour A.
	for (int i = 0; i <= ca.nverts; ++i)
	{
		int* dst = &verts[nv*4];
		const int* src = &ca.verts[((ia+i)%ca.nverts)*4];
		dst[0] = src[0];
		dst[1] = src[1];
		dst[2] = src[2];
		dst[3] = src[3];
		nv++;
	}

	// Copy contour B
	for (int i = 0; i <= cb.nverts; ++i)
	{
		int* dst = &verts[nv*4];
		const int* src = &cb.verts[((ib+i)%cb.nverts)*4];
		dst[0] = src[0];
		dst[1] = src[1];
		dst[2] = src[2];
		dst[3] = src[3];
		nv++;
	}
	
	rcFree(ca.verts);
	ca.verts = verts;
	ca.nverts = nv;
	
	rcFree(cb.verts);
	cb.verts = 0;
	cb.nverts = 0;
	
	return true;
}

struct rcContourHole
{
	rcContour* contour;
	int minx, minz, leftmost;
};

struct rcContourRegion
{
	rcContour* outline;
	rcContourHole* holes;
	int nholes;
};

struct rcPotentialDiagonal
{
	int vert;
	int dist;
};

// Finds the lowest leftmost vertex of a contour.
static void findLeftMostVertex(rcContour* contour, int* minx, int* minz, int* leftmost)
{
	*minx = contour->verts[0];
	*minz = contour->verts[2];
	*leftmost = 0;
	for (int i = 1; i < contour->nverts; i++)
	{
		const int x = contour->verts[i*4+0];
		const int z = contour->verts[i*4+2];
		if (x < *minx || (x == *minx && z < *minz))
		{
			*minx = x;
			*minz = z;
			*leftmost = i;
		}
	}
}

static int compareHoles(const void* va, const void* vb)
{
	const rcContourHole* a = (const rcContourHole*)va;
	const rcContourHole* b = (const rcContourHole*)vb;
	if (a->minx == b->minx)
	{
		if (a->minz < b->minz)
			return -1;
		if (a->minz > b->minz)
			return 1;
	}
	else
	{
		if (a->minx < b->minx)
			return -1;
		if (a->minx > b->minx)
			return 1;
	}
	return 0;
}


static int compareDiagDist(const void* va, const void* vb)
{
	const rcPotentialDiagonal* a = (const rcPotentialDiagonal*)va;
	const rcPotentialDiagonal* b = (const rcPotentialDiagonal*)vb;
	if (a->dist < b->dist)
		return -1;
	if (a->dist > b->dist)
		return 1;
	return 0;
}


static void mergeRegionHoles(rcContext* ctx, rcContourRegion& region)
{
	// Sort holes from left to right.
	for (int i = 0; i < region.nholes; i++)
		findLeftMostVertex(region.holes[i].contour, &region.holes[i].minx, &region.holes[i].minz, &region.holes[i].leftmost);
	
	qsort(region.holes, region.nholes, sizeof(rcContourHole), compareHoles);
	
	int maxVerts = region.outline->nverts;
	for (int i = 0; i < region.nholes; i++)
		maxVerts += region.holes[i].contour->nverts;
	
	rcScopedDelete<rcPotentialDiagonal> diags((rcPotentialDiagonal*)rcAlloc(sizeof(rcPotentialDiagonal)*maxVerts, RC_ALLOC_TEMP));
	if (!diags)
	{
		ctx->log(RC_LOG_WARNING, "mergeRegionHoles: Failed to allocated diags %d.", maxVerts);
		return;
	}
	
	rcContour* outline = region.outline;
	
	// Merge holes into the outline one by one.
	for (int i = 0; i < region.nholes; i++)
	{
		rcContour* hole = region.holes[i].contour;
		
		int index = -1;
		int bestVertex = region.holes[i].leftmost;
		for (int iter = 0; iter < hole->nverts; iter++)
		{
			// Find potential diagonals.
			// The 'best' vertex must be in the cone described by 3 cosequtive vertices of the outline.
			// ..o j-1
			//   |
			//   |   * best
			//   |
			// j o-----o j+1
			//         :
			int ndiags = 0;
			const int* corner = &hole->verts[bestVertex*4];
			for (int j = 0; j < outline->nverts; j++)
			{
				if (inCone(j, outline->nverts, outline->verts, corner))
				{
					int dx = outline->verts[j*4+0] - corner[0];
					int dz = outline->verts[j*4+2] - corner[2];
					diags[ndiags].vert = j;
					diags[ndiags].dist = dx*dx + dz*dz;
					ndiags++;
				}
			}
			// Sort potential diagonals by distance, we want to make the connection as short as possible.
			qsort(diags, ndiags, sizeof(rcPotentialDiagonal), compareDiagDist);
			
			// Find a diagonal that is not intersecting the outline not the remaining holes.
			index = -1;
			for (int j = 0; j < ndiags; j++)
			{
				const int* pt = &outline->verts[diags[j].vert*4];
				bool intersect = intersectSegCountour(pt, corner, diags[i].vert, outline->nverts, outline->verts);<--- Shadow variable
				for (int k = i; k < region.nholes && !intersect; k++)
					intersect |= intersectSegCountour(pt, corner, -1, region.holes[k].contour->nverts, region.holes[k].contour->verts);
				if (!intersect)
				{
					index = diags[j].vert;
					break;
				}
			}
			// If found non-intersecting diagonal, stop looking.
			if (index != -1)
				break;
			// All the potential diagonals for the current vertex were intersecting, try next vertex.
			bestVertex = (bestVertex + 1) % hole->nverts;
		}
		
		if (index == -1)
		{
			ctx->log(RC_LOG_WARNING, "mergeHoles: Failed to find merge points for %p and %p.", region.outline, hole);
			continue;
		}
		if (!mergeContours(*region.outline, *hole, index, bestVertex))
		{
			ctx->log(RC_LOG_WARNING, "mergeHoles: Failed to merge contours %p and %p.", region.outline, hole);
			continue;
		}
	}
}


/// @par
///
/// The raw contours will match the region outlines exactly. The @p maxError and @p maxEdgeLen
/// parameters control how closely the simplified contours will match the raw contours.
///
/// Simplified contours are generated such that the vertices for portals between areas match up.
/// (They are considered mandatory vertices.)
///
/// Setting @p maxEdgeLength to zero will disabled the edge length feature.
///
/// See the #rcConfig documentation for more information on the configuration parameters.
///
/// @see rcAllocContourSet, rcCompactHeightfield, rcContourSet, rcConfig
bool rcBuildContours(rcContext* ctx, rcCompactHeightfield& chf,
					 const float maxError, const int maxEdgeLen,
					 rcContourSet& cset, const int buildFlags)
{
	rcAssert(ctx);
	
	const int w = chf.width;
	const int h = chf.height;
	const int borderSize = chf.borderSize;
	
	rcScopedTimer timer(ctx, RC_TIMER_BUILD_CONTOURS);
	
	rcVcopy(cset.bmin, chf.bmin);
	rcVcopy(cset.bmax, chf.bmax);
	if (borderSize > 0)
	{
		// If the heightfield was build with bordersize, remove the offset.
		const float pad = borderSize*chf.cs;
		cset.bmin[0] += pad;
		cset.bmin[2] += pad;
		cset.bmax[0] -= pad;
		cset.bmax[2] -= pad;
	}
	cset.cs = chf.cs;
	cset.ch = chf.ch;
	cset.width = chf.width - chf.borderSize*2;
	cset.height = chf.height - chf.borderSize*2;
	cset.borderSize = chf.borderSize;
	cset.maxError = maxError;
	
	int maxContours = rcMax((int)chf.maxRegions, 8);
	cset.conts = (rcContour*)rcAlloc(sizeof(rcContour)*maxContours, RC_ALLOC_PERM);
	if (!cset.conts)
		return false;
	cset.nconts = 0;
	
	rcScopedDelete<unsigned char> flags((unsigned char*)rcAlloc(sizeof(unsigned char)*chf.spanCount, RC_ALLOC_TEMP));
	if (!flags)
	{
		ctx->log(RC_LOG_ERROR, "rcBuildContours: Out of memory 'flags' (%d).", chf.spanCount);
		return false;
	}
	
	ctx->startTimer(RC_TIMER_BUILD_CONTOURS_TRACE);
	
	// Mark boundaries.
	for (int y = 0; y < h; ++y)
	{
		for (int x = 0; x < w; ++x)
		{
			const rcCompactCell& c = chf.cells[x+y*w];
			for (int i = (int)c.index, ni = (int)(c.index+c.count); i < ni; ++i)
			{
				unsigned char res = 0;
				const rcCompactSpan& s = chf.spans[i];
				if (!chf.spans[i].reg || (chf.spans[i].reg & RC_BORDER_REG))
				{
					flags[i] = 0;
					continue;
				}
				for (int dir = 0; dir < 4; ++dir)
				{
					unsigned short r = 0;
					if (rcGetCon(s, dir) != RC_NOT_CONNECTED)
					{
						const int ax = x + rcGetDirOffsetX(dir);
						const int ay = y + rcGetDirOffsetY(dir);
						const int ai = (int)chf.cells[ax+ay*w].index + rcGetCon(s, dir);
						r = chf.spans[ai].reg;
					}
					if (r == chf.spans[i].reg)
						res |= (1 << dir);
				}
				flags[i] = res ^ 0xf; // Inverse, mark non connected edges.
			}
		}
	}
	
	ctx->stopTimer(RC_TIMER_BUILD_CONTOURS_TRACE);
	
	rcIntArray verts(256);
	rcIntArray simplified(64);
	
	for (int y = 0; y < h; ++y)
	{
		for (int x = 0; x < w; ++x)
		{
			const rcCompactCell& c = chf.cells[x+y*w];
			for (int i = (int)c.index, ni = (int)(c.index+c.count); i < ni; ++i)
			{
				if (flags[i] == 0 || flags[i] == 0xf)
				{
					flags[i] = 0;
					continue;
				}
				const unsigned short reg = chf.spans[i].reg;
				if (!reg || (reg & RC_BORDER_REG))
					continue;
				const unsigned char area = chf.areas[i];
				
				verts.resize(0);
				simplified.resize(0);
				
				ctx->startTimer(RC_TIMER_BUILD_CONTOURS_TRACE);
				walkContour(x, y, i, chf, flags, verts);
				ctx->stopTimer(RC_TIMER_BUILD_CONTOURS_TRACE);
				
				ctx->startTimer(RC_TIMER_BUILD_CONTOURS_SIMPLIFY);
				simplifyContour(verts, simplified, maxError, maxEdgeLen, buildFlags);
				removeDegenerateSegments(simplified);
				ctx->stopTimer(RC_TIMER_BUILD_CONTOURS_SIMPLIFY);
				
				
				// Store region->contour remap info.
				// Create contour.
				if (simplified.size()/4 >= 3)
				{
					if (cset.nconts >= maxContours)
					{
						// Allocate more contours.
						// This happens when a region has holes.
						const int oldMax = maxContours;
						maxContours *= 2;
						rcContour* newConts = (rcContour*)rcAlloc(sizeof(rcContour)*maxContours, RC_ALLOC_PERM);
						for (int j = 0; j < cset.nconts; ++j)
						{
							newConts[j] = cset.conts[j];
							// Reset source pointers to prevent data deletion.
							cset.conts[j].verts = 0;
							cset.conts[j].rverts = 0;
						}
						rcFree(cset.conts);
						cset.conts = newConts;
						
						ctx->log(RC_LOG_WARNING, "rcBuildContours: Expanding max contours from %d to %d.", oldMax, maxContours);
					}
					
					rcContour* cont = &cset.conts[cset.nconts++];
					
					cont->nverts = simplified.size()/4;
					cont->verts = (int*)rcAlloc(sizeof(int)*cont->nverts*4, RC_ALLOC_PERM);
					if (!cont->verts)
					{
						ctx->log(RC_LOG_ERROR, "rcBuildContours: Out of memory 'verts' (%d).", cont->nverts);
						return false;
					}
					memcpy(cont->verts, &simplified[0], sizeof(int)*cont->nverts*4);
					if (borderSize > 0)
					{
						// If the heightfield was build with bordersize, remove the offset.
						for (int j = 0; j < cont->nverts; ++j)
						{
							int* v = &cont->verts[j*4];
							v[0] -= borderSize;
							v[2] -= borderSize;
						}
					}
					
					cont->nrverts = verts.size()/4;
					cont->rverts = (int*)rcAlloc(sizeof(int)*cont->nrverts*4, RC_ALLOC_PERM);
					if (!cont->rverts)
					{
						ctx->log(RC_LOG_ERROR, "rcBuildContours: Out of memory 'rverts' (%d).", cont->nrverts);
						return false;
					}
					memcpy(cont->rverts, &verts[0], sizeof(int)*cont->nrverts*4);
					if (borderSize > 0)
					{
						// If the heightfield was build with bordersize, remove the offset.
						for (int j = 0; j < cont->nrverts; ++j)
						{
							int* v = &cont->rverts[j*4];
							v[0] -= borderSize;
							v[2] -= borderSize;
						}
					}
					
					cont->reg = reg;
					cont->area = area;
				}
			}
		}
	}
	
	// Merge holes if needed.
	if (cset.nconts > 0)
	{
		// Calculate winding of all polygons.
		rcScopedDelete<signed char> winding((signed char*)rcAlloc(sizeof(signed char)*cset.nconts, RC_ALLOC_TEMP));
		if (!winding)
		{
			ctx->log(RC_LOG_ERROR, "rcBuildContours: Out of memory 'hole' (%d).", cset.nconts);
			return false;
		}
		int nholes = 0;
		for (int i = 0; i < cset.nconts; ++i)
		{
			rcContour& cont = cset.conts[i];
			// If the contour is wound backwards, it is a hole.
			winding[i] = calcAreaOfPolygon2D(cont.verts, cont.nverts) < 0 ? -1 : 1;
			if (winding[i] < 0)
				nholes++;
		}
		
		if (nholes > 0)
		{
			// Collect outline contour and holes contours per region.
			// We assume that there is one outline and multiple holes.
			const int nregions = chf.maxRegions+1;
			rcScopedDelete<rcContourRegion> regions((rcContourRegion*)rcAlloc(sizeof(rcContourRegion)*nregions, RC_ALLOC_TEMP));
			if (!regions)
			{
				ctx->log(RC_LOG_ERROR, "rcBuildContours: Out of memory 'regions' (%d).", nregions);
				return false;
			}
			memset(regions, 0, sizeof(rcContourRegion)*nregions);
			
			rcScopedDelete<rcContourHole> holes((rcContourHole*)rcAlloc(sizeof(rcContourHole)*cset.nconts, RC_ALLOC_TEMP));
			if (!holes)
			{
				ctx->log(RC_LOG_ERROR, "rcBuildContours: Out of memory 'holes' (%d).", cset.nconts);
				return false;
			}
			memset(holes, 0, sizeof(rcContourHole)*cset.nconts);
			
			for (int i = 0; i < cset.nconts; ++i)
			{
				rcContour& cont = cset.conts[i];
				// Positively would contours are outlines, negative holes.
				if (winding[i] > 0)
				{
					if (regions[cont.reg].outline)
						ctx->log(RC_LOG_ERROR, "rcBuildContours: Multiple outlines for region %d.", cont.reg);
					regions[cont.reg].outline = &cont;
				}
				else
				{
					regions[cont.reg].nholes++;
				}
			}
			int index = 0;
			for (int i = 0; i < nregions; i++)
			{
				if (regions[i].nholes > 0)
				{
					regions[i].holes = &holes[index];
					index += regions[i].nholes;
					regions[i].nholes = 0;
				}
			}
			for (int i = 0; i < cset.nconts; ++i)
			{
				rcContour& cont = cset.conts[i];
				rcContourRegion& reg = regions[cont.reg];
				if (winding[i] < 0)
					reg.holes[reg.nholes++].contour = &cont;
			}
			
			// Finally merge each regions holes into the outline.
			for (int i = 0; i < nregions; i++)
			{
				rcContourRegion& reg = regions[i];
				if (!reg.nholes) continue;
				
				if (reg.outline)
				{
					mergeRegionHoles(ctx, reg);
				}
				else
				{
					// The region does not have an outline.
					// This can happen if the contour becaomes selfoverlapping because of
					// too aggressive simplification settings.
					ctx->log(RC_LOG_ERROR, "rcBuildContours: Bad outline for region %d, contour simplification is likely too aggressive.", i);
				}
			}
		}
		
	}
	
	return true;
}