simplexnoise.cc (20253B)
1 /* SimplexNoise1234, Simplex noise with true analytic derivative in 1D to 4D. 2 * 3 * Author: Stefan Gustavson, 2003-2005 4 * Contact: stegu@itn.liu.se 5 * 6 * This code was GPL licensed until February 2011. As the original 7 * author of this code, I hereby release it irrevocably into the public 8 * domain. Please feel free to use it for whatever you want. Credit 9 * is appreciated where appropriate, and I also appreciate being told 10 * where this code finds any use, but you may do as you like. 11 * Alternatively, if you want to have a familiar OSI-approved license, 12 * you may use This code under the terms of the MIT license: 13 * 14 * Copyright (C) 2003-2005 by Stefan Gustavson. All rights reserved. 15 * This code is licensed to you under the terms of the MIT license: 16 * 17 * Permission is hereby granted, free of charge, to any person obtaining 18 * a copy of this software and associated documentation files (the 19 * "Software"), to deal in the Software without restriction, including 20 * without limitation the rights to use, copy, modify, merge, publish, 21 * distribute, sublicense, and/or sell copies of the Software, and to 22 * permit persons to whom the Software is furnished to do so, subject 23 * to the following conditions: 24 * 25 * The above copyright notice and this permission notice shall be 26 * included in all copies or substantial portions of the Software. 27 * 28 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, 29 * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF 30 * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. 31 * IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY 32 * CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, 33 * TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE 34 * SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. 35 * 36 */ 37 38 /* 39 * This implementation is "Simplex Noise" as presented by 40 * Ken Perlin at a relatively obscure and not often cited course 41 * session "Real-Time Shading" at Siggraph 2001 (before real 42 * time shading actually took on), under the title "hardware noise". 43 * The 3D function is numerically equivalent to his Java reference 44 * code available in the PDF course notes, although I re-implemented 45 * it from scratch to get more readable code. The 1D, 2D and 4D cases 46 * were implemented from scratch by me from Ken Perlin's text. 47 * 48 * This file has no dependencies on any other file, not even its own 49 * header file. The header file is made for use by external code only. 50 */ 51 52 #define FASTFLOOR(x) ( ((x)>0) ? ((int)x) : (((int)x)-1) ) 53 54 //--------------------------------------------------------------------- 55 // Static data 56 57 /* 58 * Permutation table. This is just a random jumble of all numbers 0-255, 59 * repeated twice to avoid wrapping the index at 255 for each lookup. 60 * This needs to be exactly the same for all instances on all platforms, 61 * so it's easiest to just keep it as static explicit data. 62 * This also removes the need for any initialisation of this class. 63 * 64 * Note that making this an int[] instead of a char[] might make the 65 * code run faster on platforms with a high penalty for unaligned single 66 * byte addressing. Intel x86 is generally single-byte-friendly, but 67 * some other CPUs are faster with 4-aligned reads. 68 * However, a char[] is smaller, which avoids cache trashing, and that 69 * is probably the most important aspect on most architectures. 70 * This array is accessed a *lot* by the noise functions. 71 * A vector-valued noise over 3D accesses it 96 times, and a 72 * float-valued 4D noise 64 times. We want this to fit in the cache! 73 */ 74 static unsigned char perm[512] = {151,160,137,91,90,15, 75 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, 76 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, 77 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, 78 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, 79 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, 80 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, 81 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, 82 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, 83 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, 84 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, 85 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, 86 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180, 87 151,160,137,91,90,15, 88 131,13,201,95,96,53,194,233,7,225,140,36,103,30,69,142,8,99,37,240,21,10,23, 89 190, 6,148,247,120,234,75,0,26,197,62,94,252,219,203,117,35,11,32,57,177,33, 90 88,237,149,56,87,174,20,125,136,171,168, 68,175,74,165,71,134,139,48,27,166, 91 77,146,158,231,83,111,229,122,60,211,133,230,220,105,92,41,55,46,245,40,244, 92 102,143,54, 65,25,63,161, 1,216,80,73,209,76,132,187,208, 89,18,169,200,196, 93 135,130,116,188,159,86,164,100,109,198,173,186, 3,64,52,217,226,250,124,123, 94 5,202,38,147,118,126,255,82,85,212,207,206,59,227,47,16,58,17,182,189,28,42, 95 223,183,170,213,119,248,152, 2,44,154,163, 70,221,153,101,155,167, 43,172,9, 96 129,22,39,253, 19,98,108,110,79,113,224,232,178,185, 112,104,218,246,97,228, 97 251,34,242,193,238,210,144,12,191,179,162,241, 81,51,145,235,249,14,239,107, 98 49,192,214, 31,181,199,106,157,184, 84,204,176,115,121,50,45,127, 4,150,254, 99 138,236,205,93,222,114,67,29,24,72,243,141,128,195,78,66,215,61,156,180 100 }; 101 102 //--------------------------------------------------------------------- 103 104 /* 105 * Helper functions to compute gradients-dot-residualvectors (1D to 4D) 106 * Note that these generate gradients of more than unit length. To make 107 * a close match with the value range of classic Perlin noise, the final 108 * noise values need to be rescaled to fit nicely within [-1,1]. 109 * (The simplex noise functions as such also have different scaling.) 110 * Note also that these noise functions are the most practical and useful 111 * signed version of Perlin noise. To return values according to the 112 * RenderMan specification from the SL noise() and pnoise() functions, 113 * the noise values need to be scaled and offset to [0,1], like this: 114 * float SLnoise = (noise(x,y,z) + 1.0) * 0.5; 115 */ 116 117 static float grad1( int hash, float x ) { 118 int h = hash & 15; 119 float grad = 1.0f + (h & 7); // Gradient value 1.0, 2.0, ..., 8.0 120 if (h&8) grad = -grad; // Set a random sign for the gradient 121 return ( grad * x ); // Multiply the gradient with the distance 122 } 123 124 static float grad2( int hash, float x, float y ) { 125 int h = hash & 7; // Convert low 3 bits of hash code 126 float u = h<4 ? x : y; // into 8 simple gradient directions, 127 float v = h<4 ? y : x; // and compute the dot product with (x,y). 128 return ((h&1)? -u : u) + ((h&2)? -2.0f*v : 2.0f*v); 129 } 130 131 static float grad3( int hash, float x, float y , float z ) { 132 int h = hash & 15; // Convert low 4 bits of hash code into 12 simple 133 float u = h<8 ? x : y; // gradient directions, and compute dot product. 134 float v = h<4 ? y : h==12||h==14 ? x : z; // Fix repeats at h = 12 to 15 135 return ((h&1)? -u : u) + ((h&2)? -v : v); 136 } 137 138 static float grad4( int hash, float x, float y, float z, float t ) { 139 int h = hash & 31; // Convert low 5 bits of hash code into 32 simple 140 float u = h<24 ? x : y; // gradient directions, and compute dot product. 141 float v = h<16 ? y : z; 142 float w = h<8 ? z : t; 143 return ((h&1)? -u : u) + ((h&2)? -v : v) + ((h&4)? -w : w); 144 } 145 146 // A lookup table to traverse the simplex around a given point in 4D. 147 // Details can be found where this table is used, in the 4D noise method. 148 /* TODO: This should not be required, backport it from Bill's GLSL code! */ 149 static unsigned char simplex[64][4] = { 150 {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}, 151 {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}, 152 {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}, 153 {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}, 154 {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}, 155 {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}, 156 {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}, 157 {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}}; 158 159 // 1D simplex noise 160 float snoise(float x) { 161 162 int i0 = FASTFLOOR(x); 163 int i1 = i0 + 1; 164 float x0 = x - i0; 165 float x1 = x0 - 1.0f; 166 167 float n0, n1; 168 169 float t0 = 1.0f - x0*x0; 170 // if(t0 < 0.0f) t0 = 0.0f; // this never happens for the 1D case 171 t0 *= t0; 172 n0 = t0 * t0 * grad1(perm[i0 & 0xff], x0); 173 174 float t1 = 1.0f - x1*x1; 175 // if(t1 < 0.0f) t1 = 0.0f; // this never happens for the 1D case 176 t1 *= t1; 177 n1 = t1 * t1 * grad1(perm[i1 & 0xff], x1); 178 // The maximum value of this noise is 8*(3/4)^4 = 2.53125 179 // A factor of 0.395 would scale to fit exactly within [-1,1], but 180 // we want to match PRMan's 1D noise, so we scale it down some more. 181 return 0.25f * (n0 + n1); 182 183 } 184 185 // 2D simplex noise 186 float snoise(float x, float y) { 187 188 #define F2 0.366025403 // F2 = 0.5*(sqrt(3.0)-1.0) 189 #define G2 0.211324865 // G2 = (3.0-Math.sqrt(3.0))/6.0 190 191 float n0, n1, n2; // Noise contributions from the three corners 192 193 // Skew the input space to determine which simplex cell we're in 194 float s = (x+y)*F2; // Hairy factor for 2D 195 float xs = x + s; 196 float ys = y + s; 197 int i = FASTFLOOR(xs); 198 int j = FASTFLOOR(ys); 199 200 float t = (float)(i+j)*G2; 201 float X0 = i-t; // Unskew the cell origin back to (x,y) space 202 float Y0 = j-t; 203 float x0 = x-X0; // The x,y distances from the cell origin 204 float y0 = y-Y0; 205 206 // For the 2D case, the simplex shape is an equilateral triangle. 207 // Determine which simplex we are in. 208 int i1, j1; // Offsets for second (middle) corner of simplex in (i,j) coords 209 if(x0>y0) {i1=1; j1=0;} // lower triangle, XY order: (0,0)->(1,0)->(1,1) 210 else {i1=0; j1=1;} // upper triangle, YX order: (0,0)->(0,1)->(1,1) 211 212 // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and 213 // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where 214 // c = (3-sqrt(3))/6 215 216 float x1 = x0 - i1 + G2; // Offsets for middle corner in (x,y) unskewed coords 217 float y1 = y0 - j1 + G2; 218 float x2 = x0 - 1.0f + 2.0f * G2; // Offsets for last corner in (x,y) unskewed coords 219 float y2 = y0 - 1.0f + 2.0f * G2; 220 221 // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds 222 int ii = i & 0xff; 223 int jj = j & 0xff; 224 225 // Calculate the contribution from the three corners 226 float t0 = 0.5f - x0*x0-y0*y0; 227 if(t0 < 0.0f) n0 = 0.0f; 228 else { 229 t0 *= t0; 230 n0 = t0 * t0 * grad2(perm[ii+perm[jj]], x0, y0); 231 } 232 233 float t1 = 0.5f - x1*x1-y1*y1; 234 if(t1 < 0.0f) n1 = 0.0f; 235 else { 236 t1 *= t1; 237 n1 = t1 * t1 * grad2(perm[ii+i1+perm[jj+j1]], x1, y1); 238 } 239 240 float t2 = 0.5f - x2*x2-y2*y2; 241 if(t2 < 0.0f) n2 = 0.0f; 242 else { 243 t2 *= t2; 244 n2 = t2 * t2 * grad2(perm[ii+1+perm[jj+1]], x2, y2); 245 } 246 247 // Add contributions from each corner to get the final noise value. 248 // The result is scaled to return values in the interval [-1,1]. 249 return 40.0f * (n0 + n1 + n2); // TODO: The scale factor is preliminary! 250 } 251 252 // 3D simplex noise 253 float snoise(float x, float y, float z) { 254 255 // Simple skewing factors for the 3D case 256 #define F3 0.333333333 257 #define G3 0.166666667 258 259 float n0, n1, n2, n3; // Noise contributions from the four corners 260 261 // Skew the input space to determine which simplex cell we're in 262 float s = (x+y+z)*F3; // Very nice and simple skew factor for 3D 263 float xs = x+s; 264 float ys = y+s; 265 float zs = z+s; 266 int i = FASTFLOOR(xs); 267 int j = FASTFLOOR(ys); 268 int k = FASTFLOOR(zs); 269 270 float t = (float)(i+j+k)*G3; 271 float X0 = i-t; // Unskew the cell origin back to (x,y,z) space 272 float Y0 = j-t; 273 float Z0 = k-t; 274 float x0 = x-X0; // The x,y,z distances from the cell origin 275 float y0 = y-Y0; 276 float z0 = z-Z0; 277 278 // For the 3D case, the simplex shape is a slightly irregular tetrahedron. 279 // Determine which simplex we are in. 280 int i1, j1, k1; // Offsets for second corner of simplex in (i,j,k) coords 281 int i2, j2, k2; // Offsets for third corner of simplex in (i,j,k) coords 282 283 /* This code would benefit from a backport from the GLSL version! */ 284 if(x0>=y0) { 285 if(y0>=z0) 286 { i1=1; j1=0; k1=0; i2=1; j2=1; k2=0; } // X Y Z order 287 else if(x0>=z0) { i1=1; j1=0; k1=0; i2=1; j2=0; k2=1; } // X Z Y order 288 else { i1=0; j1=0; k1=1; i2=1; j2=0; k2=1; } // Z X Y order 289 } 290 else { // x0<y0 291 if(y0<z0) { i1=0; j1=0; k1=1; i2=0; j2=1; k2=1; } // Z Y X order 292 else if(x0<z0) { i1=0; j1=1; k1=0; i2=0; j2=1; k2=1; } // Y Z X order 293 else { i1=0; j1=1; k1=0; i2=1; j2=1; k2=0; } // Y X Z order 294 } 295 296 // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z), 297 // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and 298 // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where 299 // c = 1/6. 300 301 float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords 302 float y1 = y0 - j1 + G3; 303 float z1 = z0 - k1 + G3; 304 float x2 = x0 - i2 + 2.0f*G3; // Offsets for third corner in (x,y,z) coords 305 float y2 = y0 - j2 + 2.0f*G3; 306 float z2 = z0 - k2 + 2.0f*G3; 307 float x3 = x0 - 1.0f + 3.0f*G3; // Offsets for last corner in (x,y,z) coords 308 float y3 = y0 - 1.0f + 3.0f*G3; 309 float z3 = z0 - 1.0f + 3.0f*G3; 310 311 // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds 312 int ii = i & 0xff; 313 int jj = j & 0xff; 314 int kk = k & 0xff; 315 316 // Calculate the contribution from the four corners 317 float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0; 318 if(t0 < 0.0f) n0 = 0.0f; 319 else { 320 t0 *= t0; 321 n0 = t0 * t0 * grad3(perm[ii+perm[jj+perm[kk]]], x0, y0, z0); 322 } 323 324 float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1; 325 if(t1 < 0.0f) n1 = 0.0f; 326 else { 327 t1 *= t1; 328 n1 = t1 * t1 * grad3(perm[ii+i1+perm[jj+j1+perm[kk+k1]]], x1, y1, z1); 329 } 330 331 float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2; 332 if(t2 < 0.0f) n2 = 0.0f; 333 else { 334 t2 *= t2; 335 n2 = t2 * t2 * grad3(perm[ii+i2+perm[jj+j2+perm[kk+k2]]], x2, y2, z2); 336 } 337 338 float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3; 339 if(t3<0.0f) n3 = 0.0f; 340 else { 341 t3 *= t3; 342 n3 = t3 * t3 * grad3(perm[ii+1+perm[jj+1+perm[kk+1]]], x3, y3, z3); 343 } 344 345 // Add contributions from each corner to get the final noise value. 346 // The result is scaled to stay just inside [-1,1] 347 return 32.0f * (n0 + n1 + n2 + n3); // TODO: The scale factor is preliminary! 348 } 349 350 351 // 4D simplex noise 352 float snoise(float x, float y, float z, float w) { 353 354 // The skewing and unskewing factors are hairy again for the 4D case 355 #define F4 0.309016994 // F4 = (Math.sqrt(5.0)-1.0)/4.0 356 #define G4 0.138196601 // G4 = (5.0-Math.sqrt(5.0))/20.0 357 358 float n0, n1, n2, n3, n4; // Noise contributions from the five corners 359 360 // Skew the (x,y,z,w) space to determine which cell of 24 simplices we're in 361 float s = (x + y + z + w) * F4; // Factor for 4D skewing 362 float xs = x + s; 363 float ys = y + s; 364 float zs = z + s; 365 float ws = w + s; 366 int i = FASTFLOOR(xs); 367 int j = FASTFLOOR(ys); 368 int k = FASTFLOOR(zs); 369 int l = FASTFLOOR(ws); 370 371 float t = (i + j + k + l) * G4; // Factor for 4D unskewing 372 float X0 = i - t; // Unskew the cell origin back to (x,y,z,w) space 373 float Y0 = j - t; 374 float Z0 = k - t; 375 float W0 = l - t; 376 377 float x0 = x - X0; // The x,y,z,w distances from the cell origin 378 float y0 = y - Y0; 379 float z0 = z - Z0; 380 float w0 = w - W0; 381 382 // For the 4D case, the simplex is a 4D shape I won't even try to describe. 383 // To find out which of the 24 possible simplices we're in, we need to 384 // determine the magnitude ordering of x0, y0, z0 and w0. 385 // The method below is a good way of finding the ordering of x,y,z,w and 386 // then find the correct traversal order for the simplex we’re in. 387 // First, six pair-wise comparisons are performed between each possible pair 388 // of the four coordinates, and the results are used to add up binary bits 389 // for an integer index. 390 int c1 = (x0 > y0) ? 32 : 0; 391 int c2 = (x0 > z0) ? 16 : 0; 392 int c3 = (y0 > z0) ? 8 : 0; 393 int c4 = (x0 > w0) ? 4 : 0; 394 int c5 = (y0 > w0) ? 2 : 0; 395 int c6 = (z0 > w0) ? 1 : 0; 396 int c = c1 + c2 + c3 + c4 + c5 + c6; 397 398 int i1, j1, k1, l1; // The integer offsets for the second simplex corner 399 int i2, j2, k2, l2; // The integer offsets for the third simplex corner 400 int i3, j3, k3, l3; // The integer offsets for the fourth simplex corner 401 402 // simplex[c] is a 4-vector with the numbers 0, 1, 2 and 3 in some order. 403 // Many values of c will never occur, since e.g. x>y>z>w makes x<z, y<w and x<w 404 // impossible. Only the 24 indices which have non-zero entries make any sense. 405 // We use a thresholding to set the coordinates in turn from the largest magnitude. 406 // The number 3 in the "simplex" array is at the position of the largest coordinate. 407 i1 = simplex[c][0]>=3 ? 1 : 0; 408 j1 = simplex[c][1]>=3 ? 1 : 0; 409 k1 = simplex[c][2]>=3 ? 1 : 0; 410 l1 = simplex[c][3]>=3 ? 1 : 0; 411 // The number 2 in the "simplex" array is at the second largest coordinate. 412 i2 = simplex[c][0]>=2 ? 1 : 0; 413 j2 = simplex[c][1]>=2 ? 1 : 0; 414 k2 = simplex[c][2]>=2 ? 1 : 0; 415 l2 = simplex[c][3]>=2 ? 1 : 0; 416 // The number 1 in the "simplex" array is at the second smallest coordinate. 417 i3 = simplex[c][0]>=1 ? 1 : 0; 418 j3 = simplex[c][1]>=1 ? 1 : 0; 419 k3 = simplex[c][2]>=1 ? 1 : 0; 420 l3 = simplex[c][3]>=1 ? 1 : 0; 421 // The fifth corner has all coordinate offsets = 1, so no need to look that up. 422 423 float x1 = x0 - i1 + G4; // Offsets for second corner in (x,y,z,w) coords 424 float y1 = y0 - j1 + G4; 425 float z1 = z0 - k1 + G4; 426 float w1 = w0 - l1 + G4; 427 float x2 = x0 - i2 + 2.0f*G4; // Offsets for third corner in (x,y,z,w) coords 428 float y2 = y0 - j2 + 2.0f*G4; 429 float z2 = z0 - k2 + 2.0f*G4; 430 float w2 = w0 - l2 + 2.0f*G4; 431 float x3 = x0 - i3 + 3.0f*G4; // Offsets for fourth corner in (x,y,z,w) coords 432 float y3 = y0 - j3 + 3.0f*G4; 433 float z3 = z0 - k3 + 3.0f*G4; 434 float w3 = w0 - l3 + 3.0f*G4; 435 float x4 = x0 - 1.0f + 4.0f*G4; // Offsets for last corner in (x,y,z,w) coords 436 float y4 = y0 - 1.0f + 4.0f*G4; 437 float z4 = z0 - 1.0f + 4.0f*G4; 438 float w4 = w0 - 1.0f + 4.0f*G4; 439 440 // Wrap the integer indices at 256, to avoid indexing perm[] out of bounds 441 int ii = i & 0xff; 442 int jj = j & 0xff; 443 int kk = k & 0xff; 444 int ll = l & 0xff; 445 446 // Calculate the contribution from the five corners 447 float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0 - w0*w0; 448 if(t0 < 0.0f) n0 = 0.0f; 449 else { 450 t0 *= t0; 451 n0 = t0 * t0 * grad4(perm[ii+perm[jj+perm[kk+perm[ll]]]], x0, y0, z0, w0); 452 } 453 454 float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1 - w1*w1; 455 if(t1 < 0.0f) n1 = 0.0f; 456 else { 457 t1 *= t1; 458 n1 = t1 * t1 * grad4(perm[ii+i1+perm[jj+j1+perm[kk+k1+perm[ll+l1]]]], x1, y1, z1, w1); 459 } 460 461 float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2 - w2*w2; 462 if(t2 < 0.0f) n2 = 0.0f; 463 else { 464 t2 *= t2; 465 n2 = t2 * t2 * grad4(perm[ii+i2+perm[jj+j2+perm[kk+k2+perm[ll+l2]]]], x2, y2, z2, w2); 466 } 467 468 float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3 - w3*w3; 469 if(t3 < 0.0f) n3 = 0.0f; 470 else { 471 t3 *= t3; 472 n3 = t3 * t3 * grad4(perm[ii+i3+perm[jj+j3+perm[kk+k3+perm[ll+l3]]]], x3, y3, z3, w3); 473 } 474 475 float t4 = 0.6f - x4*x4 - y4*y4 - z4*z4 - w4*w4; 476 if(t4 < 0.0f) n4 = 0.0f; 477 else { 478 t4 *= t4; 479 n4 = t4 * t4 * grad4(perm[ii+1+perm[jj+1+perm[kk+1+perm[ll+1]]]], x4, y4, z4, w4); 480 } 481 482 // Sum up and scale the result to cover the range [-1,1] 483 return 27.0f * (n0 + n1 + n2 + n3 + n4); // TODO: The scale factor is preliminary! 484 }