SimplexNoise.cpp 17 KB
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
/**
 * @file    SimplexNoise.cpp
 * @brief   A Perlin Simplex Noise C++ Implementation (1D, 2D, 3D).
 *
 * Copyright (c) 2014-2018 Sebastien Rombauts (sebastien.rombauts@gmail.com)
 *
 * This C++ implementation is based on the speed-improved Java version 2012-03-09
 * by Stefan Gustavson (original Java source code in the public domain).
 * http://webstaff.itn.liu.se/~stegu/simplexnoise/SimplexNoise.java:
 * - Based on example code by Stefan Gustavson (stegu@itn.liu.se).
 * - Optimisations by Peter Eastman (peastman@drizzle.stanford.edu).
 * - Better rank ordering method by Stefan Gustavson in 2012.
 *
 * This implementation is "Simplex Noise" as presented by
 * Ken Perlin at a relatively obscure and not often cited course
 * session "Real-Time Shading" at Siggraph 2001 (before real
 * time shading actually took on), under the title "hardware noise".
 * The 3D function is numerically equivalent to his Java reference
 * code available in the PDF course notes, although I re-implemented
 * it from scratch to get more readable code. The 1D, 2D and 4D cases
 * were implemented from scratch by me from Ken Perlin's text.
 *
 * Distributed under the MIT License (MIT) (See accompanying file LICENSE.txt
 * or copy at http://opensource.org/licenses/MIT)
 */

#include "SimplexNoise.h"

#include <cstdint>  // int32_t/uint8_t

/**
 * Computes the largest integer value not greater than the float one
 *
 * This method is faster than using (int32_t)std::floor(fp).
 *
 * I measured it to be approximately twice as fast:
 *  float:  ~18.4ns instead of ~39.6ns on an AMD APU),
 *  double: ~20.6ns instead of ~36.6ns on an AMD APU),
 * Reference: http://www.codeproject.com/Tips/700780/Fast-floor-ceiling-functions
 *
 * @param[in] fp    float input value
 *
 * @return largest integer value not greater than fp
 */
static inline int32_t fastfloor(float fp) {
    int32_t i = static_cast<int32_t>(fp);
    return (fp < i) ? (i - 1) : (i);
}

/**
 * Permutation table. This is just a random jumble of all numbers 0-255.
 *
 * This produce a repeatable pattern of 256, but Ken Perlin stated
 * that it is not a problem for graphic texture as the noise features disappear
 * at a distance far enough to be able to see a repeatable pattern of 256.
 *
 * This needs to be exactly the same for all instances on all platforms,
 * so it's easiest to just keep it as static explicit data.
 * This also removes the need for any initialisation of this class.
 *
 * Note that making this an uint32_t[] instead of a uint8_t[] might make the
 * code run faster on platforms with a high penalty for unaligned single
 * byte addressing. Intel x86 is generally single-byte-friendly, but
 * some other CPUs are faster with 4-aligned reads.
 * However, a char[] is smaller, which avoids cache trashing, and that
 * is probably the most important aspect on most architectures.
 * This array is accessed a *lot* by the noise functions.
 * A vector-valued noise over 3D accesses it 96 times, and a
 * float-valued 4D noise 64 times. We want this to fit in the cache!
 */
static const uint8_t perm[256] = {
    151, 160, 137, 91, 90, 15,
    131, 13, 201, 95, 96, 53, 194, 233, 7, 225, 140, 36, 103, 30, 69, 142, 8, 99, 37, 240, 21, 10, 23,
    190, 6, 148, 247, 120, 234, 75, 0, 26, 197, 62, 94, 252, 219, 203, 117, 35, 11, 32, 57, 177, 33,
    88, 237, 149, 56, 87, 174, 20, 125, 136, 171, 168, 68, 175, 74, 165, 71, 134, 139, 48, 27, 166,
    77, 146, 158, 231, 83, 111, 229, 122, 60, 211, 133, 230, 220, 105, 92, 41, 55, 46, 245, 40, 244,
    102, 143, 54, 65, 25, 63, 161, 1, 216, 80, 73, 209, 76, 132, 187, 208, 89, 18, 169, 200, 196,
    135, 130, 116, 188, 159, 86, 164, 100, 109, 198, 173, 186, 3, 64, 52, 217, 226, 250, 124, 123,
    5, 202, 38, 147, 118, 126, 255, 82, 85, 212, 207, 206, 59, 227, 47, 16, 58, 17, 182, 189, 28, 42,
    223, 183, 170, 213, 119, 248, 152, 2, 44, 154, 163, 70, 221, 153, 101, 155, 167, 43, 172, 9,
    129, 22, 39, 253, 19, 98, 108, 110, 79, 113, 224, 232, 178, 185, 112, 104, 218, 246, 97, 228,
    251, 34, 242, 193, 238, 210, 144, 12, 191, 179, 162, 241, 81, 51, 145, 235, 249, 14, 239, 107,
    49, 192, 214, 31, 181, 199, 106, 157, 184, 84, 204, 176, 115, 121, 50, 45, 127, 4, 150, 254,
    138, 236, 205, 93, 222, 114, 67, 29, 24, 72, 243, 141, 128, 195, 78, 66, 215, 61, 156, 180
};

/**
 * Helper function to hash an integer using the above permutation table
 *
 *  This inline function costs around 1ns, and is called N+1 times for a noise of N dimension.
 *
 *  Using a real hash function would be better to improve the "repeatability of 256" of the above permutation table,
 * but fast integer Hash functions uses more time and have bad random properties.
 *
 * @param[in] i Integer value to hash
 *
 * @return 8-bits hashed value
 */
static inline uint8_t hash(int32_t i) {
    return perm[static_cast<uint8_t>(i)];
}

/* NOTE Gradient table to test if lookup-table are more efficient than calculs
static const float gradients1D[16] = {
        -8.f, -7.f, -6.f, -5.f, -4.f, -3.f, -2.f, -1.f,
         1.f,  2.f,  3.f,  4.f,  5.f,  6.f,  7.f,  8.f
};
*/

/**
 * Helper function to compute gradients-dot-residual vectors (1D)
 *
 * @note that these generate gradients of more than unit length. To make
 * a close match with the value range of classic Perlin noise, the final
 * noise values need to be rescaled to fit nicely within [-1,1].
 * (The simplex noise functions as such also have different scaling.)
 * Note also that these noise functions are the most practical and useful
 * signed version of Perlin noise.
 *
 * @param[in] hash  hash value
 * @param[in] x     distance to the corner
 *
 * @return gradient value
 */
static float grad(int32_t hash, float x) {
    const int32_t h = hash & 0x0F;  // Convert low 4 bits of hash code
    float grad = 1.0f + (h & 7);    // Gradient value 1.0, 2.0, ..., 8.0
    if ((h & 8) != 0) grad = -grad; // Set a random sign for the gradient
//  float grad = gradients1D[h];    // NOTE : Test of Gradient look-up table instead of the above
    return (grad * x);              // Multiply the gradient with the distance
}

/**
 * Helper functions to compute gradients-dot-residual vectors (2D)
 *
 * @param[in] hash  hash value
 * @param[in] x     x coord of the distance to the corner
 * @param[in] y     y coord of the distance to the corner
 *
 * @return gradient value
 */
static float grad(int32_t hash, float x, float y) {
    const int32_t h = hash & 0x3F;  // Convert low 3 bits of hash code
    const float u = h < 4 ? x : y;  // into 8 simple gradient directions,
    const float v = h < 4 ? y : x;
    return ((h & 1) ? -u : u) + ((h & 2) ? -2.0f * v : 2.0f * v); // and compute the dot product with (x,y).
}

/**
 * Helper functions to compute gradients-dot-residual vectors (3D)
 *
 * @param[in] hash  hash value
 * @param[in] x     x coord of the distance to the corner
 * @param[in] y     y coord of the distance to the corner
 * @param[in] z     z coord of the distance to the corner
 *
 * @return gradient value
 */
static float grad(int32_t hash, float x, float y, float z) {
    int h = hash & 15;     // Convert low 4 bits of hash code into 12 simple
    float u = h < 8 ? x : y; // gradient directions, and compute dot product.
    float v = h < 4 ? y : h == 12 || h == 14 ? x : z; // Fix repeats at h = 12 to 15
    return ((h & 1) ? -u : u) + ((h & 2) ? -v : v);
}

/**
 * 1D Perlin simplex noise
 *
 *  Takes around 74ns on an AMD APU.
 *
 * @param[in] x float coordinate
 *
 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
 */
float SimplexNoise::noise(float x) {
    float n0, n1;   // Noise contributions from the two "corners"

    // No need to skew the input space in 1D

    // Corners coordinates (nearest integer values):
    int32_t i0 = fastfloor(x);
    int32_t i1 = i0 + 1;
    // Distances to corners (between 0 and 1):
    float x0 = x - i0;
    float x1 = x0 - 1.0f;

    // Calculate the contribution from the first corner
    float t0 = 1.0f - x0*x0;
//  if(t0 < 0.0f) t0 = 0.0f; // not possible
    t0 *= t0;
    n0 = t0 * t0 * grad(hash(i0), x0);

    // Calculate the contribution from the second corner
    float t1 = 1.0f - x1*x1;
//  if(t1 < 0.0f) t1 = 0.0f; // not possible
    t1 *= t1;
    n1 = t1 * t1 * grad(hash(i1), x1);

    // The maximum value of this noise is 8*(3/4)^4 = 2.53125
    // A factor of 0.395 scales to fit exactly within [-1,1]
    return 0.395f * (n0 + n1);
}

/**
 * 2D Perlin simplex noise
 *
 *  Takes around 150ns on an AMD APU.
 *
 * @param[in] x float coordinate
 * @param[in] y float coordinate
 *
 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
 */
float SimplexNoise::noise(float x, float y) {
    float n0, n1, n2;   // Noise contributions from the three corners

    // Skewing/Unskewing factors for 2D
    static const float F2 = 0.366025403f;  // F2 = (sqrt(3) - 1) / 2
    static const float G2 = 0.211324865f;  // G2 = (3 - sqrt(3)) / 6   = F2 / (1 + 2 * K)

    // Skew the input space to determine which simplex cell we're in
    const float s = (x + y) * F2;  // Hairy factor for 2D
    const float xs = x + s;
    const float ys = y + s;
    const int32_t i = fastfloor(xs);
    const int32_t j = fastfloor(ys);

    // Unskew the cell origin back to (x,y) space
    const float t = static_cast<float>(i + j) * G2;
    const float X0 = i - t;
    const float Y0 = j - t;
    const float x0 = x - X0;  // The x,y distances from the cell origin
    const float y0 = y - Y0;

    // For the 2D case, the simplex shape is an equilateral triangle.
    // Determine which simplex we are in.
    int32_t i1, j1;  // Offsets for second (middle) corner of simplex in (i,j) coords
    if (x0 > y0) {   // lower triangle, XY order: (0,0)->(1,0)->(1,1)
        i1 = 1;
        j1 = 0;
    } else {   // upper triangle, YX order: (0,0)->(0,1)->(1,1)
        i1 = 0;
        j1 = 1;
    }

    // A step of (1,0) in (i,j) means a step of (1-c,-c) in (x,y), and
    // a step of (0,1) in (i,j) means a step of (-c,1-c) in (x,y), where
    // c = (3-sqrt(3))/6

    const float x1 = x0 - i1 + G2;            // Offsets for middle corner in (x,y) unskewed coords
    const float y1 = y0 - j1 + G2;
    const float x2 = x0 - 1.0f + 2.0f * G2;   // Offsets for last corner in (x,y) unskewed coords
    const float y2 = y0 - 1.0f + 2.0f * G2;

    // Work out the hashed gradient indices of the three simplex corners
    const int gi0 = hash(i + hash(j));
    const int gi1 = hash(i + i1 + hash(j + j1));
    const int gi2 = hash(i + 1 + hash(j + 1));

    // Calculate the contribution from the first corner
    float t0 = 0.5f - x0*x0 - y0*y0;
    if (t0 < 0.0f) {
        n0 = 0.0f;
    } else {
        t0 *= t0;
        n0 = t0 * t0 * grad(gi0, x0, y0);
    }

    // Calculate the contribution from the second corner
    float t1 = 0.5f - x1*x1 - y1*y1;
    if (t1 < 0.0f) {
        n1 = 0.0f;
    } else {
        t1 *= t1;
        n1 = t1 * t1 * grad(gi1, x1, y1);
    }

    // Calculate the contribution from the third corner
    float t2 = 0.5f - x2*x2 - y2*y2;
    if (t2 < 0.0f) {
        n2 = 0.0f;
    } else {
        t2 *= t2;
        n2 = t2 * t2 * grad(gi2, x2, y2);
    }

    // Add contributions from each corner to get the final noise value.
    // The result is scaled to return values in the interval [-1,1].
    return 45.23065f * (n0 + n1 + n2);
}


/**
 * 3D Perlin simplex noise
 *
 * @param[in] x float coordinate
 * @param[in] y float coordinate
 * @param[in] z float coordinate
 *
 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
 */
float SimplexNoise::noise(float x, float y, float z) {
    float n0, n1, n2, n3; // Noise contributions from the four corners

    // Skewing/Unskewing factors for 3D
    static const float F3 = 1.0f / 3.0f;
    static const float G3 = 1.0f / 6.0f;

    // Skew the input space to determine which simplex cell we're in
    float s = (x + y + z) * F3; // Very nice and simple skew factor for 3D
    int i = fastfloor(x + s);
    int j = fastfloor(y + s);
    int k = fastfloor(z + s);
    float t = (i + j + k) * G3;
    float X0 = i - t; // Unskew the cell origin back to (x,y,z) space
    float Y0 = j - t;
    float Z0 = k - t;
    float x0 = x - X0; // The x,y,z distances from the cell origin
    float y0 = y - Y0;
    float z0 = z - Z0;

    // For the 3D case, the simplex shape is a slightly irregular tetrahedron.
    // Determine which simplex we are in.
    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
    if (x0 >= y0) {
        if (y0 >= z0) {
            i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 1; k2 = 0; // X Y Z order
        } else if (x0 >= z0) {
            i1 = 1; j1 = 0; k1 = 0; i2 = 1; j2 = 0; k2 = 1; // X Z Y order
        } else {
            i1 = 0; j1 = 0; k1 = 1; i2 = 1; j2 = 0; k2 = 1; // Z X Y order
        }
    } else { // x0<y0
        if (y0 < z0) {
            i1 = 0; j1 = 0; k1 = 1; i2 = 0; j2 = 1; k2 = 1; // Z Y X order
        } else if (x0 < z0) {
            i1 = 0; j1 = 1; k1 = 0; i2 = 0; j2 = 1; k2 = 1; // Y Z X order
        } else {
            i1 = 0; j1 = 1; k1 = 0; i2 = 1; j2 = 1; k2 = 0; // Y X Z order
        }
    }

    // A step of (1,0,0) in (i,j,k) means a step of (1-c,-c,-c) in (x,y,z),
    // a step of (0,1,0) in (i,j,k) means a step of (-c,1-c,-c) in (x,y,z), and
    // a step of (0,0,1) in (i,j,k) means a step of (-c,-c,1-c) in (x,y,z), where
    // c = 1/6.
    float x1 = x0 - i1 + G3; // Offsets for second corner in (x,y,z) coords
    float y1 = y0 - j1 + G3;
    float z1 = z0 - k1 + G3;
    float x2 = x0 - i2 + 2.0f * G3; // Offsets for third corner in (x,y,z) coords
    float y2 = y0 - j2 + 2.0f * G3;
    float z2 = z0 - k2 + 2.0f * G3;
    float x3 = x0 - 1.0f + 3.0f * G3; // Offsets for last corner in (x,y,z) coords
    float y3 = y0 - 1.0f + 3.0f * G3;
    float z3 = z0 - 1.0f + 3.0f * G3;

    // Work out the hashed gradient indices of the four simplex corners
    int gi0 = hash(i + hash(j + hash(k)));
    int gi1 = hash(i + i1 + hash(j + j1 + hash(k + k1)));
    int gi2 = hash(i + i2 + hash(j + j2 + hash(k + k2)));
    int gi3 = hash(i + 1 + hash(j + 1 + hash(k + 1)));

    // Calculate the contribution from the four corners
    float t0 = 0.6f - x0*x0 - y0*y0 - z0*z0;
    if (t0 < 0) {
        n0 = 0.0;
    } else {
        t0 *= t0;
        n0 = t0 * t0 * grad(gi0, x0, y0, z0);
    }
    float t1 = 0.6f - x1*x1 - y1*y1 - z1*z1;
    if (t1 < 0) {
        n1 = 0.0;
    } else {
        t1 *= t1;
        n1 = t1 * t1 * grad(gi1, x1, y1, z1);
    }
    float t2 = 0.6f - x2*x2 - y2*y2 - z2*z2;
    if (t2 < 0) {
        n2 = 0.0;
    } else {
        t2 *= t2;
        n2 = t2 * t2 * grad(gi2, x2, y2, z2);
    }
    float t3 = 0.6f - x3*x3 - y3*y3 - z3*z3;
    if (t3 < 0) {
        n3 = 0.0;
    } else {
        t3 *= t3;
        n3 = t3 * t3 * grad(gi3, x3, y3, z3);
    }
    // Add contributions from each corner to get the final noise value.
    // The result is scaled to stay just inside [-1,1]
    return 32.0f*(n0 + n1 + n2 + n3);
}


/**
 * Fractal/Fractional Brownian Motion (fBm) summation of 1D Perlin Simplex noise
 *
 * @param[in] octaves   number of fraction of noise to sum
 * @param[in] x         float coordinate
 *
 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
 */
float SimplexNoise::fractal(size_t octaves, float x) const {
    float output    = 0.f;
    float denom     = 0.f;
    float frequency = mFrequency;
    float amplitude = mAmplitude;

    for (size_t i = 0; i < octaves; i++) {
        output += (amplitude * noise(x * frequency));
        denom += amplitude;

        frequency *= mLacunarity;
        amplitude *= mPersistence;
    }

    return (output / denom);
}

/**
 * Fractal/Fractional Brownian Motion (fBm) summation of 2D Perlin Simplex noise
 *
 * @param[in] octaves   number of fraction of noise to sum
 * @param[in] x         x float coordinate
 * @param[in] y         y float coordinate
 *
 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
 */
float SimplexNoise::fractal(size_t octaves, float x, float y) const {
    float output = 0.f;
    float denom  = 0.f;
    float frequency = mFrequency;
    float amplitude = mAmplitude;

    for (size_t i = 0; i < octaves; i++) {
        output += (amplitude * noise(x * frequency, y * frequency));
        denom += amplitude;

        frequency *= mLacunarity;
        amplitude *= mPersistence;
    }

    return (output / denom);
}

/**
 * Fractal/Fractional Brownian Motion (fBm) summation of 3D Perlin Simplex noise
 *
 * @param[in] octaves   number of fraction of noise to sum
 * @param[in] x         x float coordinate
 * @param[in] y         y float coordinate
 * @param[in] z         z float coordinate
 *
 * @return Noise value in the range[-1; 1], value of 0 on all integer coordinates.
 */
float SimplexNoise::fractal(size_t octaves, float x, float y, float z) const {
    float output = 0.f;
    float denom  = 0.f;
    float frequency = mFrequency;
    float amplitude = mAmplitude;

    for (size_t i = 0; i < octaves; i++) {
        output += (amplitude * noise(x * frequency, y * frequency, z * frequency));
        denom += amplitude;

        frequency *= mLacunarity;
        amplitude *= mPersistence;
    }

    return (output / denom);
}