001 package org.bukkit.util.noise;
002
003 import java.util.Random;
004 import org.bukkit.World;
005
006 /**
007 * Generates simplex-based noise.
008 * <p>
009 * This is a modified version of the freely published version in the paper by
010 * Stefan Gustavson at
011 * <a href="http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf">
012 * http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf</a>
013 */
014 public class SimplexNoiseGenerator extends PerlinNoiseGenerator {
015 protected static final double SQRT_3 = Math.sqrt(3);
016 protected static final double SQRT_5 = Math.sqrt(5);
017 protected static final double F2 = 0.5 * (SQRT_3 - 1);
018 protected static final double G2 = (3 - SQRT_3) / 6;
019 protected static final double G22 = G2 * 2.0 - 1;
020 protected static final double F3 = 1.0 / 3.0;
021 protected static final double G3 = 1.0 / 6.0;
022 protected static final double F4 = (SQRT_5 - 1.0) / 4.0;
023 protected static final double G4 = (5.0 - SQRT_5) / 20.0;
024 protected static final double G42 = G4 * 2.0;
025 protected static final double G43 = G4 * 3.0;
026 protected static final double G44 = G4 * 4.0 - 1.0;
027 protected static final int grad4[][] = {{0, 1, 1, 1}, {0, 1, 1, -1}, {0, 1, -1, 1}, {0, 1, -1, -1},
028 {0, -1, 1, 1}, {0, -1, 1, -1}, {0, -1, -1, 1}, {0, -1, -1, -1},
029 {1, 0, 1, 1}, {1, 0, 1, -1}, {1, 0, -1, 1}, {1, 0, -1, -1},
030 {-1, 0, 1, 1}, {-1, 0, 1, -1}, {-1, 0, -1, 1}, {-1, 0, -1, -1},
031 {1, 1, 0, 1}, {1, 1, 0, -1}, {1, -1, 0, 1}, {1, -1, 0, -1},
032 {-1, 1, 0, 1}, {-1, 1, 0, -1}, {-1, -1, 0, 1}, {-1, -1, 0, -1},
033 {1, 1, 1, 0}, {1, 1, -1, 0}, {1, -1, 1, 0}, {1, -1, -1, 0},
034 {-1, 1, 1, 0}, {-1, 1, -1, 0}, {-1, -1, 1, 0}, {-1, -1, -1, 0}};
035 protected static final int simplex[][] = {
036 {0, 1, 2, 3}, {0, 1, 3, 2}, {0, 0, 0, 0}, {0, 2, 3, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 2, 3, 0},
037 {0, 2, 1, 3}, {0, 0, 0, 0}, {0, 3, 1, 2}, {0, 3, 2, 1}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {1, 3, 2, 0},
038 {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
039 {1, 2, 0, 3}, {0, 0, 0, 0}, {1, 3, 0, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 3, 0, 1}, {2, 3, 1, 0},
040 {1, 0, 2, 3}, {1, 0, 3, 2}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {2, 0, 3, 1}, {0, 0, 0, 0}, {2, 1, 3, 0},
041 {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0},
042 {2, 0, 1, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {3, 0, 1, 2}, {3, 0, 2, 1}, {0, 0, 0, 0}, {3, 1, 2, 0},
043 {2, 1, 0, 3}, {0, 0, 0, 0}, {0, 0, 0, 0}, {0, 0, 0, 0}, {3, 1, 0, 2}, {0, 0, 0, 0}, {3, 2, 0, 1}, {3, 2, 1, 0}};
044 protected static double offsetW;
045 private static final SimplexNoiseGenerator instance = new SimplexNoiseGenerator();
046
047 protected SimplexNoiseGenerator() {
048 super();
049 }
050
051 /**
052 * Creates a seeded simplex noise generator for the given world
053 *
054 * @param world World to construct this generator for
055 */
056 public SimplexNoiseGenerator(World world) {
057 this(new Random(world.getSeed()));
058 }
059
060 /**
061 * Creates a seeded simplex noise generator for the given seed
062 *
063 * @param seed Seed to construct this generator for
064 */
065 public SimplexNoiseGenerator(long seed) {
066 this(new Random(seed));
067 }
068
069 /**
070 * Creates a seeded simplex noise generator with the given Random
071 *
072 * @param rand Random to construct with
073 */
074 public SimplexNoiseGenerator(Random rand) {
075 super(rand);
076 offsetW = rand.nextDouble() * 256;
077 }
078
079 protected static double dot(int g[], double x, double y) {
080 return g[0] * x + g[1] * y;
081 }
082
083 protected static double dot(int g[], double x, double y, double z) {
084 return g[0] * x + g[1] * y + g[2] * z;
085 }
086
087 protected static double dot(int g[], double x, double y, double z, double w) {
088 return g[0] * x + g[1] * y + g[2] * z + g[3] * w;
089 }
090
091 /**
092 * Computes and returns the 1D unseeded simplex noise for the given
093 * coordinates in 1D space
094 *
095 * @param xin X coordinate
096 * @return Noise at given location, from range -1 to 1
097 */
098 public static double getNoise(double xin) {
099 return instance.noise(xin);
100 }
101
102 /**
103 * Computes and returns the 2D unseeded simplex noise for the given
104 * coordinates in 2D space
105 *
106 * @param xin X coordinate
107 * @param yin Y coordinate
108 * @return Noise at given location, from range -1 to 1
109 */
110 public static double getNoise(double xin, double yin) {
111 return instance.noise(xin, yin);
112 }
113
114 /**
115 * Computes and returns the 3D unseeded simplex noise for the given
116 * coordinates in 3D space
117 *
118 * @param xin X coordinate
119 * @param yin Y coordinate
120 * @param zin Z coordinate
121 * @return Noise at given location, from range -1 to 1
122 */
123 public static double getNoise(double xin, double yin, double zin) {
124 return instance.noise(xin, yin, zin);
125 }
126
127 /**
128 * Computes and returns the 4D simplex noise for the given coordinates in
129 * 4D space
130 *
131 * @param x X coordinate
132 * @param y Y coordinate
133 * @param z Z coordinate
134 * @param w W coordinate
135 * @return Noise at given location, from range -1 to 1
136 */
137 public static double getNoise(double x, double y, double z, double w) {
138 return instance.noise(x, y, z, w);
139 }
140
141 @Override
142 public double noise(double xin, double yin, double zin) {
143 xin += offsetX;
144 yin += offsetY;
145 zin += offsetZ;
146
147 double n0, n1, n2, n3; // Noise contributions from the four corners
148
149 // Skew the input space to determine which simplex cell we're in
150 double s = (xin + yin + zin) * F3; // Very nice and simple skew factor for 3D
151 int i = floor(xin + s);
152 int j = floor(yin + s);
153 int k = floor(zin + s);
154 double t = (i + j + k) * G3;
155 double X0 = i - t; // Unskew the cell origin back to (x,y,z) space
156 double Y0 = j - t;
157 double Z0 = k - t;
158 double x0 = xin - X0; // The x,y,z distances from the cell origin
159 double y0 = yin - Y0;
160 double z0 = zin - Z0;
161
162 // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
163
164 // Determine which simplex we are in.
165 int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords
166 int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords
167 if (x0 >= y0) {
168 if (y0 >= z0) {
169 i1 = 1;
170 j1 = 0;
171 k1 = 0;
172 i2 = 1;
173 j2 = 1;
174 k2 = 0;
175 } // X Y Z order
176 else if (x0 >= z0) {
177 i1 = 1;
178 j1 = 0;
179 k1 = 0;
180 i2 = 1;
181 j2 = 0;
182 k2 = 1;
183 } // X Z Y order
184 else {
185 i1 = 0;
186 j1 = 0;
187 k1 = 1;
188 i2 = 1;
189 j2 = 0;
190 k2 = 1;
191 } // Z X Y order
192 } else { // x0<y0
193 if (y0 < z0) {
194 i1 = 0;
195 j1 = 0;
196 k1 = 1;
197 i2 = 0;
198 j2 = 1;
199 k2 = 1;
200 } // Z Y X order
201 else if (x0 < z0) {
202 i1 = 0;
203 j1 = 1;
204 k1 = 0;
205 i2 = 0;
206 j2 = 1;
207 k2 = 1;
208 } // Y Z X order
209 else {
210 i1 = 0;
211 j1 = 1;
212 k1 = 0;
213 i2 = 1;
214 j2 = 1;
215 k2 = 0;
216 } // Y X Z order
217 }
218
219 // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
220 // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
221 // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
222 // c = 1/6.
223 double x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
224 double y1 = y0 - j1 + G3;
225 double z1 = z0 - k1 + G3;
226 double x2 = x0 - i2 + 2.0 * G3; // Offsets for third corner in (x,y,z) coords
227 double y2 = y0 - j2 + 2.0 * G3;
228 double z2 = z0 - k2 + 2.0 * G3;
229 double x3 = x0 - 1.0 + 3.0 * G3; // Offsets for last corner in (x,y,z) coords
230 double y3 = y0 - 1.0 + 3.0 * G3;
231 double z3 = z0 - 1.0 + 3.0 * G3;
232
233 // Work out the hashed gradient indices of the four simplex corners
234 int ii = i & 255;
235 int jj = j & 255;
236 int kk = k & 255;
237 int gi0 = perm[ii + perm[jj + perm[kk]]] % 12;
238 int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1]]] % 12;
239 int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2]]] % 12;
240 int gi3 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1]]] % 12;
241
242 // Calculate the contribution from the four corners
243 double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0;
244 if (t0 < 0) {
245 n0 = 0.0;
246 } else {
247 t0 *= t0;
248 n0 = t0 * t0 * dot(grad3[gi0], x0, y0, z0);
249 }
250
251 double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1;
252 if (t1 < 0) {
253 n1 = 0.0;
254 } else {
255 t1 *= t1;
256 n1 = t1 * t1 * dot(grad3[gi1], x1, y1, z1);
257 }
258
259 double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2;
260 if (t2 < 0) {
261 n2 = 0.0;
262 } else {
263 t2 *= t2;
264 n2 = t2 * t2 * dot(grad3[gi2], x2, y2, z2);
265 }
266
267 double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3;
268 if (t3 < 0) {
269 n3 = 0.0;
270 } else {
271 t3 *= t3;
272 n3 = t3 * t3 * dot(grad3[gi3], x3, y3, z3);
273 }
274
275 // Add contributions from each corner to get the final noise value.
276 // The result is scaled to stay just inside [-1,1]
277 return 32.0 * (n0 + n1 + n2 + n3);
278 }
279
280 @Override
281 public double noise(double xin, double yin) {
282 xin += offsetX;
283 yin += offsetY;
284
285 double n0, n1, n2; // Noise contributions from the three corners
286
287 // Skew the input space to determine which simplex cell we're in
288 double s = (xin + yin) * F2; // Hairy factor for 2D
289 int i = floor(xin + s);
290 int j = floor(yin + s);
291 double t = (i + j) * G2;
292 double X0 = i - t; // Unskew the cell origin back to (x,y) space
293 double Y0 = j - t;
294 double x0 = xin - X0; // The x,y distances from the cell origin
295 double y0 = yin - Y0;
296
297 // For the 2D case, the simplex shape is an equilateral triangle.
298
299 // Determine which simplex we are in.
300 int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords
301 if (x0 > y0) {
302 i1 = 1;
303 j1 = 0;
304 } // lower triangle, XY order: (0,0)->(1,0)->(1,1)
305 else {
306 i1 = 0;
307 j1 = 1;
308 } // upper triangle, YX order: (0,0)->(0,1)->(1,1)
309
310 // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
311 // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
312 // c = (3-sqrt(3))/6
313
314 double x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords
315 double y1 = y0 - j1 + G2;
316 double x2 = x0 + G22; // Offsets for last corner in (x,y) unskewed coords
317 double y2 = y0 + G22;
318
319 // Work out the hashed gradient indices of the three simplex corners
320 int ii = i & 255;
321 int jj = j & 255;
322 int gi0 = perm[ii + perm[jj]] % 12;
323 int gi1 = perm[ii + i1 + perm[jj + j1]] % 12;
324 int gi2 = perm[ii + 1 + perm[jj + 1]] % 12;
325
326 // Calculate the contribution from the three corners
327 double t0 = 0.5 - x0 * x0 - y0 * y0;
328 if (t0 < 0) {
329 n0 = 0.0;
330 } else {
331 t0 *= t0;
332 n0 = t0 * t0 * dot(grad3[gi0], x0, y0); // (x,y) of grad3 used for 2D gradient
333 }
334
335 double t1 = 0.5 - x1 * x1 - y1 * y1;
336 if (t1 < 0) {
337 n1 = 0.0;
338 } else {
339 t1 *= t1;
340 n1 = t1 * t1 * dot(grad3[gi1], x1, y1);
341 }
342
343 double t2 = 0.5 - x2 * x2 - y2 * y2;
344 if (t2 < 0) {
345 n2 = 0.0;
346 } else {
347 t2 *= t2;
348 n2 = t2 * t2 * dot(grad3[gi2], x2, y2);
349 }
350
351 // Add contributions from each corner to get the final noise value.
352 // The result is scaled to return values in the interval [-1,1].
353 return 70.0 * (n0 + n1 + n2);
354 }
355
356 /**
357 * Computes and returns the 4D simplex noise for the given coordinates in
358 * 4D space
359 *
360 * @param x X coordinate
361 * @param y Y coordinate
362 * @param z Z coordinate
363 * @param w W coordinate
364 * @return Noise at given location, from range -1 to 1
365 */
366 public double noise(double x, double y, double z, double w) {
367 x += offsetX;
368 y += offsetY;
369 z += offsetZ;
370 w += offsetW;
371
372 double n0, n1, n2, n3, n4; // Noise contributions from the five corners
373
374 // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in
375 double s = (x + y + z + w) * F4; // Factor for 4D skewing
376 int i = floor(x + s);
377 int j = floor(y + s);
378 int k = floor(z + s);
379 int l = floor(w + s);
380
381 double t = (i + j + k + l) * G4; // Factor for 4D unskewing
382 double X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space
383 double Y0 = j - t;
384 double Z0 = k - t;
385 double W0 = l - t;
386 double x0 = x - X0; // The x,y,z,w distances from the cell origin
387 double y0 = y - Y0;
388 double z0 = z - Z0;
389 double w0 = w - W0;
390
391 // For the 4D case, the simplex is a 4D shape I won't even try to describe.
392 // To find out which of the 24 possible simplices we're in, we need to
393 // determine the magnitude ordering of x0, y0, z0 and w0.
394 // The method below is a good way of finding the ordering of x,y,z,w and
395 // then find the correct traversal order for the simplex we?re in.
396 // First, six pair-wise comparisons are performed between each possible pair
397 // of the four coordinates, and the results are used to add up binary bits
398 // for an integer index.
399 int c1 = (x0 > y0) ? 32 : 0;
400 int c2 = (x0 > z0) ? 16 : 0;
401 int c3 = (y0 > z0) ? 8 : 0;
402 int c4 = (x0 > w0) ? 4 : 0;
403 int c5 = (y0 > w0) ? 2 : 0;
404 int c6 = (z0 > w0) ? 1 : 0;
405 int c = c1 + c2 + c3 + c4 + c5 + c6;
406 int i1, j1, k1, l1; // The integer offsets for the second simplex corner
407 int i2, j2, k2, l2; // The integer offsets for the third simplex corner
408 int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner
409
410 // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order.
411 // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w
412 // impossible. Only the 24 indices which have non-zero entries make any sense.
413 // We use a thresholding to set the coordinates in turn from the largest magnitude.
414
415 // The number 3 in the "simplex" array is at the position of the largest coordinate.
416 i1 = simplex[c][0] >= 3 ? 1 : 0;
417 j1 = simplex[c][1] >= 3 ? 1 : 0;
418 k1 = simplex[c][2] >= 3 ? 1 : 0;
419 l1 = simplex[c][3] >= 3 ? 1 : 0;
420
421 // The number 2 in the "simplex" array is at the second largest coordinate.
422 i2 = simplex[c][0] >= 2 ? 1 : 0;
423 j2 = simplex[c][1] >= 2 ? 1 : 0;
424 k2 = simplex[c][2] >= 2 ? 1 : 0;
425 l2 = simplex[c][3] >= 2 ? 1 : 0;
426
427 // The number 1 in the "simplex" array is at the second smallest coordinate.
428 i3 = simplex[c][0] >= 1 ? 1 : 0;
429 j3 = simplex[c][1] >= 1 ? 1 : 0;
430 k3 = simplex[c][2] >= 1 ? 1 : 0;
431 l3 = simplex[c][3] >= 1 ? 1 : 0;
432
433 // The fifth corner has all coordinate offsets = 1, so no need to look that up.
434
435 double x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords
436 double y1 = y0 - j1 + G4;
437 double z1 = z0 - k1 + G4;
438 double w1 = w0 - l1 + G4;
439
440 double x2 = x0 - i2 + G42; // Offsets for third corner in (x,y,z,w) coords
441 double y2 = y0 - j2 + G42;
442 double z2 = z0 - k2 + G42;
443 double w2 = w0 - l2 + G42;
444
445 double x3 = x0 - i3 + G43; // Offsets for fourth corner in (x,y,z,w) coords
446 double y3 = y0 - j3 + G43;
447 double z3 = z0 - k3 + G43;
448 double w3 = w0 - l3 + G43;
449
450 double x4 = x0 + G44; // Offsets for last corner in (x,y,z,w) coords
451 double y4 = y0 + G44;
452 double z4 = z0 + G44;
453 double w4 = w0 + G44;
454
455 // Work out the hashed gradient indices of the five simplex corners
456 int ii = i & 255;
457 int jj = j & 255;
458 int kk = k & 255;
459 int ll = l & 255;
460
461 int gi0 = perm[ii + perm[jj + perm[kk + perm[ll]]]] % 32;
462 int gi1 = perm[ii + i1 + perm[jj + j1 + perm[kk + k1 + perm[ll + l1]]]] % 32;
463 int gi2 = perm[ii + i2 + perm[jj + j2 + perm[kk + k2 + perm[ll + l2]]]] % 32;
464 int gi3 = perm[ii + i3 + perm[jj + j3 + perm[kk + k3 + perm[ll + l3]]]] % 32;
465 int gi4 = perm[ii + 1 + perm[jj + 1 + perm[kk + 1 + perm[ll + 1]]]] % 32;
466
467 // Calculate the contribution from the five corners
468 double t0 = 0.6 - x0 * x0 - y0 * y0 - z0 * z0 - w0 * w0;
469 if (t0 < 0) {
470 n0 = 0.0;
471 } else {
472 t0 *= t0;
473 n0 = t0 * t0 * dot(grad4[gi0], x0, y0, z0, w0);
474 }
475
476 double t1 = 0.6 - x1 * x1 - y1 * y1 - z1 * z1 - w1 * w1;
477 if (t1 < 0) {
478 n1 = 0.0;
479 } else {
480 t1 *= t1;
481 n1 = t1 * t1 * dot(grad4[gi1], x1, y1, z1, w1);
482 }
483
484 double t2 = 0.6 - x2 * x2 - y2 * y2 - z2 * z2 - w2 * w2;
485 if (t2 < 0) {
486 n2 = 0.0;
487 } else {
488 t2 *= t2;
489 n2 = t2 * t2 * dot(grad4[gi2], x2, y2, z2, w2);
490 }
491
492 double t3 = 0.6 - x3 * x3 - y3 * y3 - z3 * z3 - w3 * w3;
493 if (t3 < 0) {
494 n3 = 0.0;
495 } else {
496 t3 *= t3;
497 n3 = t3 * t3 * dot(grad4[gi3], x3, y3, z3, w3);
498 }
499
500 double t4 = 0.6 - x4 * x4 - y4 * y4 - z4 * z4 - w4 * w4;
501 if (t4 < 0) {
502 n4 = 0.0;
503 } else {
504 t4 *= t4;
505 n4 = t4 * t4 * dot(grad4[gi4], x4, y4, z4, w4);
506 }
507
508 // Sum up and scale the result to cover the range [-1,1]
509 return 27.0 * (n0 + n1 + n2 + n3 + n4);
510 }
511
512 /**
513 * Gets the singleton unseeded instance of this generator
514 *
515 * @return Singleton
516 */
517 public static SimplexNoiseGenerator getInstance() {
518 return instance;
519 }
520 }