/*
JWildfire - an image and animation processor written in Java
Copyright (C) 1995-2011 Andreas Maschke
This is free software; you can redistribute it and/or modify it under the terms of the GNU Lesser
General Public License as published by the Free Software Foundation; either version 2.1 of the
License, or (at your option) any later version.
This software is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without
even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
Lesser General Public License for more details.
You should have received a copy of the GNU Lesser General Public License along with this software;
if not, write to the Free Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA
02110-1301 USA, or see the FSF site: http://www.fsf.org.
*/
// Port of Hexes and Crackle plugin by slobo777, see http://slobo777.deviantart.com/art/Apo-Plugins-Hexes-And-Crackle-99243824
// All credits for this wonderful plugin to him!
package org.jwildfire.create.tina.variation;
import static org.jwildfire.base.mathlib.MathLib.floor;
public class NoiseTools {
//This is an implementation of "Simplex Noise" and "Perlin Noise" as invented by Ken Perlin,
//and described by Stefan Gustavson.
private final static int _x_ = 0;
private final static int _y_ = 1;
private final static int _z_ = 2;
//p[] contains "random" hash values used to pick gradients. The structure repeats to prevent
// need to write code to handle wrap-arounds - i.e. it is safe to add two values from
// this list (or anything else modulo 1024) and lookup a third result which will also be
// between 0 and 1023 inclusive.
private static final int p[] = new int[] {
127, 71, 882, 898, 798, 463, 517, 451, 454, 634, 578, 695, 728, 742, 325, 350, 684, 153, 340,
311, 992, 706, 218, 285, 96, 486, 160, 98, 686, 288, 193, 119, 410, 246, 536, 415, 953, 417,
784, 573, 734, 1, 136, 381, 177, 678, 773, 22, 301, 51, 874, 844, 775, 744, 633, 468, 1019,
287, 475, 78, 294, 724, 519, 17, 323, 191, 187, 446, 262, 212, 170, 33, 7, 227, 566, 526, 264,
556, 717, 477, 815, 671, 225, 207, 692, 663, 969, 393, 658, 877, 353, 788, 128, 303, 614, 501,
490, 387, 53, 941, 951, 736, 539, 102, 163, 175, 584, 988, 35, 347, 442, 649, 642, 198, 727,
939, 913, 811, 894, 858, 181, 412, 307, 830, 154, 479, 704, 326, 681, 619, 698, 621, 552, 598,
74, 890, 299, 922, 701, 481, 867, 214, 817, 731, 768, 673, 315, 338, 576, 222, 484, 305, 623,
239, 269, 46, 748, 608, 546, 537, 125, 667, 998, 714, 529, 823, 247, 289, 771, 808, 973, 735,
516, 974, 702, 636, 357, 455, 600, 80, 336, 696, 963, 297, 92, 980, 670, 958, 625, 712, 406,
173, 19, 763, 470, 793, 283, 655, 59, 421, 1016, 219, 13, 105, 840, 111, 38, 408, 945, 242,
559, 206, 443, 331, 737, 580, 767, 1020, 220, 31, 968, 15, 527, 833, 139, 129, 859, 739, 418,
783, 933, 49, 789, 178, 124, 772, 627, 0, 23, 388, 950, 976, 940, 485, 685, 21, 523, 723, 244,
637, 488, 835, 379, 342, 452, 862, 295, 765, 897, 507, 370, 567, 416, 100, 914, 300, 120, 392,
694, 94, 265, 791, 171, 200, 787, 441, 868, 672, 769, 983, 911, 427, 82, 69, 224, 176, 920,
500, 462, 263, 513, 797, 293, 322, 645, 469, 635, 40, 215, 687, 960, 818, 826, 34, 603, 316,
994, 611, 511, 93, 899, 114, 73, 241, 585, 327, 674, 280, 957, 471, 24, 502, 355, 159, 1017,
855, 270, 538, 521, 162, 880, 334, 986, 740, 719, 266, 820, 97, 41, 52, 750, 893, 838, 616, 83,
896, 777, 464, 562, 183, 362, 411, 478, 398, 384, 912, 599, 587, 609, 822, 243, 504, 753, 857,
157, 964, 65, 261, 81, 371, 435, 924, 885, 884, 863, 613, 721, 669, 121, 639, 989, 487, 238,
448, 216, 852, 643, 713, 676, 277, 879, 133, 123, 304, 547, 396, 70, 141, 909, 848, 900, 318,
146, 356, 802, 4, 807, 558, 764, 545, 588, 872, 554, 467, 544, 505, 149, 62, 901, 64, 45, 813,
27, 109, 718, 803, 853, 996, 1014, 476, 575, 28, 199, 688, 6, 482, 703, 560, 395, 66, 341, 794,
422, 376, 601, 76, 14, 569, 480, 39, 1011, 1001, 854, 55, 89, 335, 761, 363, 419, 252, 799,
358, 324, 1012, 152, 312, 496, 235, 916, 582, 615, 979, 1005, 891, 1013, 641, 18, 148, 185,
512, 378, 58, 211, 495, 594, 87, 762, 366, 660, 449, 520, 424, 886, 819, 281, 147, 290, 390,
32, 572, 993, 720, 683, 309, 254, 607, 568, 256, 533, 394, 620, 429, 67, 831, 103, 423, 668,
693, 518, 551, 697, 253, 949, 54, 875, 116, 434, 743, 644, 590, 279, 843, 589, 11, 647, 586,
806, 549, 375, 226, 851, 499, 450, 978, 29, 982, 189, 107, 508, 373, 796, 20, 700, 110, 26,
461, 782, 591, 828, 57, 904, 847, 328, 122, 630, 711, 44, 397, 404, 209, 365, 84, 194, 1021,
675, 135, 965, 329, 557, 691, 79, 352, 498, 629, 869, 90, 921, 233, 622, 871, 755, 439, 955,
228, 63, 825, 43, 943, 438, 144, 961, 359, 330, 682, 626, 425, 259, 249, 801, 754, 1003, 230,
377, 217, 878, 1007, 313, 2, 915, 550, 271, 437, 846, 548, 145, 715, 346, 251, 372, 99, 543,
16, 47, 195, 679, 174, 905, 188, 804, 169, 785, 231, 726, 814, 339, 531, 420, 258, 1009, 134,
972, 458, 234, 690, 260, 666, 646, 142, 184, 91, 628, 987, 10, 210, 926, 348, 386, 161, 60,
409, 680, 204, 164, 444, 708, 276, 68, 383, 491, 382, 42, 816, 483, 699, 150, 9, 565, 555, 433,
593, 86, 952, 839, 618, 751, 889, 108, 361, 595, 677, 407, 856, 255, 604, 85, 648, 928, 824,
213, 192, 267, 902, 792, 656, 631, 403, 389, 493, 333, 756, 602, 925, 113, 632, 354, 37, 873,
577, 56, 278, 930, 367, 428, 332, 317, 530, 364, 800, 774, 497, 1023, 12, 137, 845, 653, 101,
888, 542, 167, 48, 158, 1002, 745, 292, 944, 456, 990, 574, 25, 1018, 937, 298, 966, 430, 400,
349, 860, 689, 320, 117, 778, 104, 314, 786, 205, 606, 440, 936, 457, 932, 934, 948, 168, 445,
931, 757, 291, 571, 919, 360, 284, 509, 296, 245, 836, 166, 3, 257, 50, 282, 151, 810, 344,
947, 236, 946, 865, 752, 77, 610, 967, 795, 131, 302, 760, 781, 190, 938, 61, 1022, 652, 138,
984, 832, 202, 140, 985, 5, 657, 997, 401, 319, 431, 662, 405, 275, 650, 651, 887, 310, 1004,
368, 208, 596, 248, 758, 8, 126, 730, 489, 343, 337, 506, 515, 432, 232, 250, 532, 954, 524,
115, 229, 522, 908, 729, 186, 561, 995, 156, 196, 118, 805, 399, 918, 991, 849, 273, 747, 640,
143, 321, 624, 268, 306, 30, 722, 540, 534, 710, 130, 155, 883, 716, 525, 426, 812, 345, 929,
975, 472, 837, 605, 664, 391, 581, 272, 746, 112, 659, 665, 780, 240, 841, 474, 563, 36, 579,
286, 436, 907, 369, 201, 402, 962, 106, 749, 172, 494, 88, 466, 473, 414, 597, 374, 942, 308,
766, 459, 821, 592, 881, 380, 759, 866, 779, 809, 876, 541, 829, 528, 999, 221, 661, 927, 413,
977, 182, 583, 733, 892, 741, 570, 351, 617, 956, 72, 709, 850, 732, 770, 870, 95, 935, 223,
179, 861, 917, 447, 385, 132, 827, 923, 75, 465, 612, 460, 725, 492, 553, 1008, 910, 981, 503,
165, 895, 834, 1000, 180, 638, 906, 510, 274, 776, 971, 564, 738, 903, 654, 864, 959, 1015,
453, 535, 237, 197, 1006, 790, 514, 842, 970, 705, 707, 1010, 203,
//1k Block repeats here
127, 71, 882, 898, 798, 463, 517, 451, 454, 634, 578, 695, 728, 742, 325, 350, 684, 153, 340,
311, 992, 706, 218, 285, 96, 486, 160, 98, 686, 288, 193, 119, 410, 246, 536, 415, 953, 417,
784, 573, 734, 1, 136, 381, 177, 678, 773, 22, 301, 51, 874, 844, 775, 744, 633, 468, 1019,
287, 475, 78, 294, 724, 519, 17, 323, 191, 187, 446, 262, 212, 170, 33, 7, 227, 566, 526, 264,
556, 717, 477, 815, 671, 225, 207, 692, 663, 969, 393, 658, 877, 353, 788, 128, 303, 614, 501,
490, 387, 53, 941, 951, 736, 539, 102, 163, 175, 584, 988, 35, 347, 442, 649, 642, 198, 727,
939, 913, 811, 894, 858, 181, 412, 307, 830, 154, 479, 704, 326, 681, 619, 698, 621, 552, 598,
74, 890, 299, 922, 701, 481, 867, 214, 817, 731, 768, 673, 315, 338, 576, 222, 484, 305, 623,
239, 269, 46, 748, 608, 546, 537, 125, 667, 998, 714, 529, 823, 247, 289, 771, 808, 973, 735,
516, 974, 702, 636, 357, 455, 600, 80, 336, 696, 963, 297, 92, 980, 670, 958, 625, 712, 406,
173, 19, 763, 470, 793, 283, 655, 59, 421, 1016, 219, 13, 105, 840, 111, 38, 408, 945, 242,
559, 206, 443, 331, 737, 580, 767, 1020, 220, 31, 968, 15, 527, 833, 139, 129, 859, 739, 418,
783, 933, 49, 789, 178, 124, 772, 627, 0, 23, 388, 950, 976, 940, 485, 685, 21, 523, 723, 244,
637, 488, 835, 379, 342, 452, 862, 295, 765, 897, 507, 370, 567, 416, 100, 914, 300, 120, 392,
694, 94, 265, 791, 171, 200, 787, 441, 868, 672, 769, 983, 911, 427, 82, 69, 224, 176, 920,
500, 462, 263, 513, 797, 293, 322, 645, 469, 635, 40, 215, 687, 960, 818, 826, 34, 603, 316,
994, 611, 511, 93, 899, 114, 73, 241, 585, 327, 674, 280, 957, 471, 24, 502, 355, 159, 1017,
855, 270, 538, 521, 162, 880, 334, 986, 740, 719, 266, 820, 97, 41, 52, 750, 893, 838, 616, 83,
896, 777, 464, 562, 183, 362, 411, 478, 398, 384, 912, 599, 587, 609, 822, 243, 504, 753, 857,
157, 964, 65, 261, 81, 371, 435, 924, 885, 884, 863, 613, 721, 669, 121, 639, 989, 487, 238,
448, 216, 852, 643, 713, 676, 277, 879, 133, 123, 304, 547, 396, 70, 141, 909, 848, 900, 318,
146, 356, 802, 4, 807, 558, 764, 545, 588, 872, 554, 467, 544, 505, 149, 62, 901, 64, 45, 813,
27, 109, 718, 803, 853, 996, 1014, 476, 575, 28, 199, 688, 6, 482, 703, 560, 395, 66, 341, 794,
422, 376, 601, 76, 14, 569, 480, 39, 1011, 1001, 854, 55, 89, 335, 761, 363, 419, 252, 799,
358, 324, 1012, 152, 312, 496, 235, 916, 582, 615, 979, 1005, 891, 1013, 641, 18, 148, 185,
512, 378, 58, 211, 495, 594, 87, 762, 366, 660, 449, 520, 424, 886, 819, 281, 147, 290, 390,
32, 572, 993, 720, 683, 309, 254, 607, 568, 256, 533, 394, 620, 429, 67, 831, 103, 423, 668,
693, 518, 551, 697, 253, 949, 54, 875, 116, 434, 743, 644, 590, 279, 843, 589, 11, 647, 586,
806, 549, 375, 226, 851, 499, 450, 978, 29, 982, 189, 107, 508, 373, 796, 20, 700, 110, 26,
461, 782, 591, 828, 57, 904, 847, 328, 122, 630, 711, 44, 397, 404, 209, 365, 84, 194, 1021,
675, 135, 965, 329, 557, 691, 79, 352, 498, 629, 869, 90, 921, 233, 622, 871, 755, 439, 955,
228, 63, 825, 43, 943, 438, 144, 961, 359, 330, 682, 626, 425, 259, 249, 801, 754, 1003, 230,
377, 217, 878, 1007, 313, 2, 915, 550, 271, 437, 846, 548, 145, 715, 346, 251, 372, 99, 543,
16, 47, 195, 679, 174, 905, 188, 804, 169, 785, 231, 726, 814, 339, 531, 420, 258, 1009, 134,
972, 458, 234, 690, 260, 666, 646, 142, 184, 91, 628, 987, 10, 210, 926, 348, 386, 161, 60,
409, 680, 204, 164, 444, 708, 276, 68, 383, 491, 382, 42, 816, 483, 699, 150, 9, 565, 555, 433,
593, 86, 952, 839, 618, 751, 889, 108, 361, 595, 677, 407, 856, 255, 604, 85, 648, 928, 824,
213, 192, 267, 902, 792, 656, 631, 403, 389, 493, 333, 756, 602, 925, 113, 632, 354, 37, 873,
577, 56, 278, 930, 367, 428, 332, 317, 530, 364, 800, 774, 497, 1023, 12, 137, 845, 653, 101,
888, 542, 167, 48, 158, 1002, 745, 292, 944, 456, 990, 574, 25, 1018, 937, 298, 966, 430, 400,
349, 860, 689, 320, 117, 778, 104, 314, 786, 205, 606, 440, 936, 457, 932, 934, 948, 168, 445,
931, 757, 291, 571, 919, 360, 284, 509, 296, 245, 836, 166, 3, 257, 50, 282, 151, 810, 344,
947, 236, 946, 865, 752, 77, 610, 967, 795, 131, 302, 760, 781, 190, 938, 61, 1022, 652, 138,
984, 832, 202, 140, 985, 5, 657, 997, 401, 319, 431, 662, 405, 275, 650, 651, 887, 310, 1004,
368, 208, 596, 248, 758, 8, 126, 730, 489, 343, 337, 506, 515, 432, 232, 250, 532, 954, 524,
115, 229, 522, 908, 729, 186, 561, 995, 156, 196, 118, 805, 399, 918, 991, 849, 273, 747, 640,
143, 321, 624, 268, 306, 30, 722, 540, 534, 710, 130, 155, 883, 716, 525, 426, 812, 345, 929,
975, 472, 837, 605, 664, 391, 581, 272, 746, 112, 659, 665, 780, 240, 841, 474, 563, 36, 579,
286, 436, 907, 369, 201, 402, 962, 106, 749, 172, 494, 88, 466, 473, 414, 597, 374, 942, 308,
766, 459, 821, 592, 881, 380, 759, 866, 779, 809, 876, 541, 829, 528, 999, 221, 661, 927, 413,
977, 182, 583, 733, 892, 741, 570, 351, 617, 956, 72, 709, 850, 732, 770, 870, 95, 935, 223,
179, 861, 917, 447, 385, 132, 827, 923, 75, 465, 612, 460, 725, 492, 553, 1008, 910, 981, 503,
165, 895, 834, 1000, 180, 638, 906, 510, 274, 776, 971, 564, 738, 903, 654, 864, 959, 1015,
453, 535, 237, 197, 1006, 790, 514, 842, 970, 705, 707, 1010, 203,
//2k block overlaps by two items here . . . (to allow for over-runs caused by taking
// "next item in sequence")
127, 71
};
//grad[][] contains gradient values that will be associated with grid points for
// the simplex code to interpolate. They are chosen using the hash codes
// from p[], above
private static final double grad3[][] = new double[][] {
{ 0.79148875, 0.11986299, -0.59931496 }, { 0.51387411, -0.61170974, 0.60145208 }, { -0.95395128, -0.21599571, 0.20814132 }, { 0.59830026, 0.67281067, 0.43515813 },
{ -0.93971346, 0.16019818, -0.30211777 }, { -0.74549699, -0.35758846, 0.56246309 }, { -0.78850321, -0.29060783, 0.54204223 }, { 0.61332339, 0.38915256, 0.68730976 },
{ -0.64370632, -0.40843865, 0.64716307 }, { -0.23922684, 0.70399949, -0.66869667 }, { -0.82882802, -0.00130741, 0.55950192 }, { 0.07987672, 0.62439350, -0.77701510 },
{ -0.46863456, -0.57517073, 0.67049257 }, { 0.30792870, 0.42464616, -0.85138449 }, { -0.06972001, 0.30439513, 0.94999091 }, { 0.58798450, -0.00151777, 0.80887077 },
{ -0.32757867, 0.51578941, 0.79161449 }, { -0.44745031, 0.86883688, 0.21192142 }, { -0.38042636, 0.71222019, 0.58993066 }, { -0.32616370, 0.61421101, -0.71858339 },
{ 0.45483340, 0.19928843, -0.86799234 }, { -0.81020233, -0.05930352, 0.58314259 }, { 0.81994145, 0.39825895, 0.41120046 }, { 0.49257662, 0.74240487, 0.45409612 },
{ 0.95124863, -0.26667257, -0.15495734 }, { -0.95745656, 0.09203090, -0.27350914 }, { 0.20842499, -0.82482150, -0.52557446 }, { 0.46829293, -0.47740985, -0.74349282 },
{ -0.65000311, -0.74754355, 0.13665502 }, { 0.83566743, 0.53294928, -0.13275921 }, { 0.90454761, -0.35449497, -0.23691126 }, { -0.64270969, 0.21532175, 0.73522839 },
{ -0.39693478, -0.17553935, -0.90090439 }, { 0.45073049, 0.65155528, 0.61017845 }, { 0.69618384, -0.07989842, 0.71340333 }, { 0.09059934, 0.85274641, -0.51440773 },
{ -0.00560267, 0.69197466, 0.72190005 }, { 0.23586856, -0.95830502, 0.16129945 }, { 0.20354340, -0.96925430, -0.13826128 }, { -0.45516395, 0.63885905, 0.62022970 },
{ 0.80792021, 0.47917579, 0.34300946 }, { 0.40886670, -0.32579857, -0.85245722 }, { -0.83819701, -0.30910810, 0.44930831 }, { -0.57602641, -0.75801200, 0.30595978 },
{ -0.16591524, -0.96579983, -0.19925569 }, { 0.27174061, 0.93638167, -0.22214053 }, { -0.45758922, 0.73185326, -0.50497812 }, { -0.18029934, -0.78067110, -0.59836843 },
{ 0.14087163, -0.39189764, -0.90915974 }, { -0.03534787, -0.02750024, 0.99899663 }, { 0.91016878, 0.06772570, 0.40866370 }, { 0.70142578, 0.70903193, 0.07263332 },
{ -0.49486157, -0.54111502, -0.67993129 }, { -0.26972486, -0.84418773, -0.46324462 }, { 0.91931005, 0.03121901, 0.39229378 }, { -0.15332070, -0.87495538, 0.45928842 },
{ -0.59010107, -0.66883868, 0.45214549 }, { 0.51964273, -0.78565398, -0.33573688 }, { -0.25845001, 0.87348329, -0.41259003 }, { -0.64741807, -0.59846669, 0.47189773 },
{ -0.79348688, -0.32782128, -0.51274923 }, { -0.86280237, -0.14342378, -0.48476972 }, { 0.19469709, -0.76349966, 0.61576076 }, { 0.39371236, -0.70742193, -0.58697938 },
{ 0.62103834, -0.50000004, -0.60358209 }, { -0.19652824, -0.51508695, 0.83430335 }, { -0.96016549, -0.26826630, -0.07820118 }, { 0.52655683, 0.84118729, 0.12305219 },
{ 0.56222101, 0.70557745, -0.43135599 }, { 0.06395307, 0.99025162, -0.12374061 }, { -0.65379289, 0.52521996, 0.54470070 }, { 0.81206590, -0.38643765, 0.43728128 },
{ -0.69449067, -0.71926243, -0.01855435 }, { 0.33968533, 0.75504287, 0.56082452 }, { -0.52402654, -0.70537870, -0.47732282 }, { -0.65379327, -0.46369816, 0.59794512 },
{ -0.08582021, -0.01217948, 0.99623619 }, { -0.66287577, 0.49604924, 0.56083051 }, { 0.70911302, 0.68748287, -0.15660789 }, { -0.58662137, -0.46475685, 0.66323181 },
{ -0.76681755, 0.63310950, -0.10565607 }, { 0.68601816, -0.59353001, 0.42083395 }, { 0.64792478, -0.72668696, 0.22829704 }, { 0.68756542, -0.69062543, 0.22425499 },
{ -0.46901797, -0.72307343, -0.50713604 }, { -0.71418521, -0.11738817, 0.69004312 }, { 0.50880449, -0.80611081, 0.30216445 }, { 0.27793962, -0.58372922, -0.76289565 },
{ -0.39417207, 0.91575060, -0.07764800 }, { -0.84724113, -0.47860304, 0.23048124 }, { 0.67628991, 0.54362408, -0.49709638 }, { 0.65073821, -0.09420630, 0.75343544 },
{ 0.66910202, 0.73566783, -0.10533437 }, { 0.72191995, -0.00305613, 0.69196983 }, { -0.00313125, 0.06634333, 0.99779194 }, { -0.06908811, 0.28990653, -0.95455803 },
{ 0.17507626, 0.73870621, 0.65089280 }, { -0.57470594, 0.75735703, 0.31003777 }, { -0.91870733, 0.08883536, 0.38481830 }, { -0.27399536, 0.39846316, 0.87530203 },
{ 0.99772699, -0.05473919, 0.03929993 }, { 0.22663907, 0.97393801, -0.00891541 }, { 0.62338001, 0.59656797, -0.50547405 }, { 0.59177247, 0.49473684, -0.63642816 },
{ -0.24457664, -0.31345545, 0.91756632 }, { -0.44691491, -0.89198404, -0.06805539 }, { -0.83115967, -0.44685014, 0.33090566 }, { -0.39940345, 0.67719937, -0.61796270 },
{ 0.55460272, -0.63265953, -0.54051619 }, { 0.82284412, 0.14794174, -0.54867185 }, { -0.39887172, -0.82890906, -0.39218761 }, { 0.28591109, 0.71270085, 0.64055628 },
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{ -0.39046281, -0.70398950, 0.59324327 }, { 0.70990020, 0.62433400, -0.32595821 }, { -0.99157404, 0.01300690, 0.12888658 }, { -0.55765988, -0.46179257, 0.68975581 },
{ -0.53736280, -0.34635255, -0.76894807 }, { 0.25083685, 0.44726649, -0.85850659 }, { 0.45758528, 0.86982087, -0.18446507 }, { -0.18615519, 0.23441065, -0.95414773 },
{ 0.56359579, -0.41325118, -0.71525048 }, { -0.48542469, 0.59678985, -0.63890903 }, { -0.72243931, -0.40815930, 0.55811059 }, { -0.23748605, 0.68466361, -0.68908354 },
{ -0.69257361, 0.27959985, -0.66495543 }, { -0.10352601, -0.17369566, -0.97934273 }, { 0.00192480, -0.09194122, 0.99576258 }, { 0.36297645, 0.86362173, 0.34986513 },
{ -0.71118388, -0.10242990, 0.69550385 }, { 0.45146824, 0.43080300, 0.78139952 }, { -0.13265094, -0.68773403, -0.71374059 }, { 0.56016516, -0.56270148, -0.60793259 },
{ -0.95871022, -0.27465634, -0.07374694 }, { -0.84169709, 0.06533746, -0.53598230 }, { 0.69711911, -0.61618111, -0.36653212 }, { -0.01620384, 0.59778204, -0.80149490 },
{ -0.34911215, 0.65899531, -0.66621760 }, { -0.19279427, -0.50540811, -0.84106659 }, { -0.60506152, 0.72292944, 0.33357695 }, { 0.79789244, -0.59553505, 0.09330415 },
{ -0.48173680, -0.74189415, 0.46639331 }, { 0.84140763, 0.31839867, 0.43664115 }, { 0.79614481, 0.60391839, -0.03789486 }, { 0.19384456, 0.57096572, 0.79776089 },
{ 0.83441754, -0.25078854, -0.49076723 }, { -0.62605441, 0.72550166, 0.28583776 }, { 0.55337866, -0.75558589, 0.35051679 }, { 0.80543476, -0.01571309, 0.59247611 },
{ -0.00851542, 0.98991715, 0.14139139 }, { -0.94076275, -0.29730096, -0.16302633 }, { -0.75465549, -0.41353736, -0.50939371 }, { 0.37739255, -0.63080384, 0.67798332 },
{ 0.47325376, -0.73145333, -0.49092453 }, { 0.12930721, -0.49066326, -0.86170135 }, { 0.71173142, -0.11663112, 0.69270165 }, { 0.41952295, -0.63051086, -0.65303641 },
{ 0.85916103, 0.42641569, 0.28286390 }, { 0.54792224, -0.66418740, 0.50856299 }, { 0.28479416, 0.43856869, 0.85237890 }, { -0.59050384, -0.68486024, -0.42693285 },
{ 0.54884141, 0.60847988, 0.57317130 }, { 0.87567478, 0.25649070, -0.40915304 }, { 0.02961573, 0.33496172, 0.94176619 }, { 0.67428181, 0.70665199, 0.21444580 },
{ 0.23609059, -0.51982231, 0.82100305 }, { 0.93726653, 0.00671493, 0.34854893 }, { -0.39891590, -0.91536143, -0.05458531 }, { 0.93359117, -0.35793085, 0.01711843 },
{ 0.53572079, -0.56879583, 0.62407896 }, { -0.61516933, -0.36856434, -0.69694119 }, { 0.74630703, -0.65946218, -0.09019675 }, { 0.50607373, -0.59204544, -0.62719342 },
{ -0.89793356, 0.43675114, 0.05444050 }, { -0.91682171, 0.07126199, 0.39288634 }, { -0.61178292, -0.15203616, -0.77627744 }, { -0.14028895, 0.63023583, 0.76362413 },
{ 0.71475895, -0.54060748, 0.44369268 }, { -0.31764961, 0.92630790, -0.20261391 }, { 0.59833443, -0.58864018, -0.54359788 }, { -0.81450219, 0.22699691, -0.53390879 },
{ 0.00452737, -0.06652318, 0.99777461 }, { 0.59311614, 0.19797584, -0.78039657 }, { -0.71375488, -0.02586188, 0.69991795 }, { -0.75600145, -0.26384588, -0.59903853 },
{ 0.25716644, 0.77480857, -0.57752671 }, { 0.71712423, 0.61984999, -0.31862018 }, { -0.28194922, -0.55108799, 0.78537040 }, { 0.57068285, -0.67066160, 0.47385030 },
{ 0.48969101, -0.22604767, -0.84208382 }, { -0.93763991, -0.34062289, 0.06933579 }, { -0.67376035, 0.15110895, -0.72333469 }, { -0.72414406, -0.65877431, -0.20403872 },
{ -0.71204285, 0.41163046, -0.56881926 }, { 0.23641604, -0.86280490, 0.44685026 }, { 0.84208951, 0.19949878, -0.50108432 }, { -0.67481860, 0.67904385, -0.28899707 },
{ 0.52167146, 0.66360202, 0.53618211 }, { -0.49330390, -0.48590434, 0.72149029 }, { -0.18240720, 0.04137646, -0.98235208 }, { 0.30714395, 0.55170433, 0.77542564 },
{ -0.14577549, 0.95376355, -0.26283949 }, { -0.54373260, -0.69781662, -0.46626905 }, { 0.01799205, -0.81833182, 0.57446437 }, { 0.51019037, -0.56615200, -0.64743934 },
{ 0.48463473, 0.59436639, 0.64176146 }, { 0.09115853, -0.52830175, -0.84414891 }, { -0.62962436, -0.38408030, -0.67531880 }, { 0.50864721, -0.48401592, -0.71204396 },
{ -0.69669235, -0.63427804, -0.33512853 }, { 0.60735178, -0.18339351, 0.77297518 }, { 0.74102699, 0.67064566, 0.03336744 }, { -0.47352242, -0.76145583, -0.44267543 },
{ 0.47751531, -0.79737827, -0.36900816 }, { 0.74175025, -0.64892413, 0.16942269 }, { 0.65484829, -0.70924167, -0.26105549 }, { 0.60455058, -0.64392987, -0.46890608 },
{ -0.61878613, -0.77223405, 0.14407742 }, { -0.72376655, -0.65562529, 0.21521492 }, { 0.24420910, -0.52118606, -0.81775731 }, { 0.61291622, 0.39870471, -0.68217906 },
{ 0.67751893, 0.65970488, 0.32520389 }, { -0.04366879, -0.96113671, 0.27259726 }, { 0.36541094, 0.62808212, 0.68701361 }, { -0.92572867, 0.10611717, -0.36299528 },
{ 0.80766374, -0.02031352, -0.58929335 }, { -0.82117076, 0.53034081, 0.21075390 }, { -0.62778197, -0.51872129, 0.58036025 }, { 0.37696186, 0.57743439, -0.72420251 },
{ -0.56818895, -0.47089866, -0.67484500 }, { -0.61126182, -0.69853192, 0.37203783 }, { 0.57901952, 0.81284241, -0.06343191 }, { -0.53287943, 0.70445351, 0.46881208 },
{ 0.22300157, -0.93258969, 0.28380764 }, { -0.63832115, -0.40157013, -0.65672486 }, { -0.22074780, 0.50999380, 0.83137040 }, { -0.59081050, -0.13684815, -0.79511982 },
{ -0.79824305, 0.52060475, -0.30295004 }, { -0.56871170, 0.76435226, 0.30386284 }, { 0.12786983, -0.64236825, -0.75565358 }, { -0.17631562, -0.76167939, -0.62350405 },
{ 0.34713709, 0.61125835, -0.71123770 }, { -0.39238887, -0.52886732, 0.75254922 }, { 0.38116332, 0.71358998, -0.58779577 }, { -0.72949527, -0.67040404, 0.13562844 },
{ -0.62057913, 0.45165344, -0.64100757 }, { -0.10668918, -0.98309252, -0.14881706 }, { 0.59490400, -0.46196716, -0.65778079 }, { 0.22433782, 0.49054463, 0.84204424 },
{ 0.77498791, -0.57220981, 0.26827165 }, { 0.26474565, 0.93986866, -0.21576987 }, { -0.01328623, 0.99975439, 0.01773780 }, { 0.53097408, 0.47771884, 0.69989373 },
{ 0.24635212, -0.37499947, -0.89369236 }, { 0.31300988, -0.54171955, 0.78010560 }, { 0.77494650, -0.52634980, 0.34987684 }, { 0.65518408, 0.51410661, -0.55355958 },
{ 0.78000762, -0.61855443, -0.09475515 }, { 0.58176976, 0.62638121, 0.51883574 }, { -0.62371886, -0.59433046, 0.50768699 }, { 0.85206333, 0.17478222, -0.49339564 },
{ 0.69974170, -0.42963013, 0.57077098 }, { -0.44953934, 0.62956163, -0.63369277 }, { 0.63562255, 0.51965998, -0.57090935 }, { -0.02766532, -0.52812789, -0.84871406 },
{ 0.78698609, 0.04742916, -0.61514500 }, { 0.37827449, 0.78614098, 0.48876454 }, { 0.90534508, -0.25600916, -0.33883565 }, { -0.37701605, 0.47347359, -0.79604124 },
{ -0.43802429, 0.40756165, -0.80126664 }, { -0.87945568, -0.47372426, -0.04629300 }, { -0.22787901, -0.82242670, 0.52123457 }, { 0.48721529, 0.74652617, -0.45312243 },
{ -0.68473990, -0.68222429, 0.25632263 }, { -0.33289944, 0.62102263, -0.70958358 }, { -0.07838790, -0.85438083, -0.51370101 }, { 0.18575601, 0.96209034, 0.19969195 },
{ 0.09048656, -0.68256793, -0.72519874 }, { 0.29506068, -0.68306389, -0.66810397 }, { -0.94937153, -0.17748927, 0.25921277 }, { -0.38725072, 0.16372291, 0.90732116 },
{ -0.02691563, 0.81898594, 0.57318198 }, { -0.65244629, -0.52276924, -0.54865851 }, { 0.15270967, -0.00097578, 0.98827061 }, { 0.39108739, 0.55471383, -0.73439990 },
{ 0.85379797, -0.05140234, 0.51806064 }, { 0.31443713, 0.14998906, -0.93735403 }, { -0.44277186, -0.56474741, -0.69642907 }, { -0.31521736, 0.37268196, 0.87278071 },
{ 0.97997903, -0.16829529, 0.10638514 }, { -0.25174419, -0.84939324, 0.46384910 }, { 0.03867740, -0.72044135, 0.69243651 }, { -0.80207202, 0.48047131, 0.35472214 },
{ 0.48200634, -0.48413492, 0.73026246 }, { -0.41800015, 0.44068588, -0.79440029 }, { 0.58661859, -0.43233611, 0.68480955 }, { 0.40830998, -0.53710845, 0.73810397 },
{ 0.61242611, -0.72220206, -0.32149407 }, { -0.34159283, -0.62199145, -0.70458567 }, { -0.29885191, 0.58492128, -0.75402562 }, { -0.62924060, 0.77130626, -0.09561862 },
{ 0.91118189, 0.27762192, 0.30442344 }, { 0.08064464, -0.99213777, -0.09570315 }, { 0.93083382, -0.34928416, -0.10746612 }, { 0.66101659, -0.67569323, 0.32633681 },
{ 0.07148482, -0.97619739, -0.20476469 }, { 0.30440743, -0.78193565, -0.54397863 }, { -0.35656518, -0.19962907, 0.91269355 }, { 0.82151650, -0.31061678, 0.47815045 },
{ -0.69709423, -0.71173375, -0.08657198 }, { -0.46044170, -0.78565215, -0.41321197 }, { -0.70275364, -0.21121895, 0.67935548 }, { 0.38087769, 0.63933041, 0.66797366 } };
//Simplex noise is evaluated on a tetrahedral grid, as opposed to a regular
//cube-based one. The two "skew factors" are used to convert between views
//of the grid so that calculations of which gridpoints to use are simpler.
//These numbers are straightforward for 3D, but the geometry is not so kind in
//2D or 4D
private static final double skewF3 = 1.0 / 3.0;
private static final double skewG3 = 1.0 / 6.0;
//simplexNoise3D - given a vector in (x,y,z) returns the noise value for the
//location
public static final double simplexNoise3D(double V[]) {
double C[][] = new double[4][3]; // Co-ordinates of four simplex shape corners in (x,y,z)
double n = 0.0; // Noise total value
int gi[] = new int[4]; // Hashed grid index for each corner, used to determine gradient
double U[]; // Pointer to current gradient vector . . .
int corner; // Iterator for which corner is being processed
double t; // Temp double
// Convert input co-ordinates ( x, y, z ) to
// integer-based simplex grid ( i, j, k )
double skewIn = (V[_x_] + V[_y_] + V[_z_]) * skewF3;
int i = (int) floor(V[_x_] + skewIn);
int j = (int) floor(V[_y_] + skewIn);
int k = (int) floor(V[_z_] + skewIn);
t = (double) (i + j + k) * skewG3;
// Cell origin co-ordinates in input space (x,y,z)
double X0 = i - t;
double Y0 = j - t;
double Z0 = k - t;
// This value of t finished with, not used later . . .
// Point offset within cell, in input space (x,y,z)
C[0][_x_] = V[_x_] - X0;
C[0][_y_] = V[_y_] - Y0;
C[0][_z_] = V[_z_] - Z0;
// For the 3D case, the simplex shape is a slightly irregular tetrahedron.
// The nested logic determines which simplex we are in, and therefore in which
// order to get gradients for the four corners
int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
// The fourth corner is always i3 = 1, j3 = 1, k3 = 1, so no need to
// calculate values
if (C[0][_x_] >= C[0][_y_]) {
if (C[0][_y_] >= C[0][_z_]) {
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
}
else { // y0<z0
if (C[0][_x_] >= C[0][_z_]) {
i1 = 1;
j1 = 0;
k1 = 0;
i2 = 1;
j2 = 0;
k2 = 1;
}
else {
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 1;
j2 = 0;
k2 = 1;
}
}
}
else { // x0<y0
if (C[0][_y_] < C[0][_z_]) {
i1 = 0;
j1 = 0;
k1 = 1;
i2 = 0;
j2 = 1;
k2 = 1;
}
else {
if (C[0][_x_] < C[0][_z_]) {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 0;
j2 = 1;
k2 = 1;
}
else {
i1 = 0;
j1 = 1;
k1 = 0;
i2 = 1;
j2 = 1;
k2 = 0;
} // Y X Z order
}
}
// A step of 1i in (i,j,k) is a step of (1-skewG3, -skewG3, -skewG3) in (x,y,z),
// and this is similar for j and k . . .
// Offsets for second corner in (x,y,z) coords
C[1][_x_] = C[0][_x_] - i1 + skewG3;
C[1][_y_] = C[0][_y_] - j1 + skewG3;
C[1][_z_] = C[0][_z_] - k1 + skewG3;
// Offsets for third corner in (x,y,z) coords
C[2][_x_] = C[0][_x_] - i2 + 2.0 * skewG3;
C[2][_y_] = C[0][_y_] - j2 + 2.0 * skewG3;
C[2][_z_] = C[0][_z_] - k2 + 2.0 * skewG3;
// Offsets for last corner in (x,y,z) coords
C[3][_x_] = C[0][_x_] - 1.0 + 3.0 * skewG3;
C[3][_y_] = C[0][_y_] - 1.0 + 3.0 * skewG3;
C[3][_z_] = C[0][_z_] - 1.0 + 3.0 * skewG3;
// Work out the hashed gradient indices of the four simplex corners
int ii = i & 0x3ff;
int jj = j & 0x3ff;
int kk = k & 0x3ff;
gi[0] = p[ii + p[jj + p[kk]]];
gi[1] = p[ii + i1 + p[jj + j1 + p[kk + k1]]];
gi[2] = p[ii + i2 + p[jj + j2 + p[kk + k2]]];
gi[3] = p[ii + 1 + p[jj + 1 + p[kk + 1]]];
// Calculate the contribution from the four corners, and add to total
for (corner = 0; corner < 4; corner++) {
t = 0.6 - C[corner][_x_] * C[corner][_x_] - C[corner][_y_] * C[corner][_y_] - C[corner][_z_] * C[corner][_z_];
if (t > 0.0) {
U = grad3[gi[corner]];
t *= t;
n += t * t * (U[_x_] * C[corner][_x_] + U[_y_] * C[corner][_y_] + U[_z_] * C[corner][_z_]);
}
}
// The result is scaled be fit -1.0 to 1.0
return 32.0 * n;
}
//The Perlin noise function is based on summing coherent noise in "octaves"
public final static double perlinNoise3D(double V[], double aScale, double fScale, int octaves) {
int i; // Iterator
double n = 0.0; // Sum of noise values
double U[] = new double[3];
double a = 1.0;
U[_x_] = V[_x_];
U[_y_] = V[_y_];
U[_z_] = V[_z_];
for (i = 0; i < octaves; i++) {
n += simplexNoise3D(U) / a;
// None of the below required for last octave . . .
a *= aScale;
U[_x_] *= fScale;
U[_y_] *= fScale;
U[_z_] *= fScale;
}
return n;
}
}