… | |
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22 | |
22 | |
23 | #include "noise.h" |
23 | #include "noise.h" |
24 | |
24 | |
25 | ///////////////////////////////////////////////////////////////////////////// |
25 | ///////////////////////////////////////////////////////////////////////////// |
26 | |
26 | |
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27 | // perl -e 'for(0..255) { $p = (atan2 1,0) / 64 * $_; printf " %10g, %10g,\n", sin $p, cos $p }' | sort -R |
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28 | static const float charges2[256][2] = { |
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29 | -.975702, -.219101, .893224, .449611, .870087, -.492898, .595699, -.803208, |
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30 | .14673, .989177, .995185, .0980171, .91421, -.405241, -.514103, .857729, |
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31 | -.985278, -.170962, -.689541, -.724247, -.427555, .903989, .83147, -.55557, |
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32 | .999699, -.0245412, .634393, .77301, -.514103, -.857729, -.0735646, -.99729, |
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33 | .514103, -.857729, -.595699, -.803208, -.290285, .95694, .595699, .803208, |
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34 | .266713, .963776, -.33689, .941544, .492898, -.870087, -.471397, -.881921, |
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35 | -.99729, -.0735646, .615232, -.788346, -.91421, -.405241, -.575808, .817585, |
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36 | .0980171, .995185, -.980785, .19509, -.122411, -.99248, .0735646, .99729, |
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37 | -.634393, .77301, -.91421, .405241, .99248, .122411, .903989, -.427555, |
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38 | -.24298, .970031, -.857729, .514103, -.359895, .932993, .382683, .92388, |
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39 | .740951, -.671559, -.893224, .449611, -.95694, -.290285, -.975702, .219101, |
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40 | -.970031, .24298, .999699, .0245412, -.405241, .91421, .985278, .170962, |
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41 | .382683, -.92388, .95694, -.290285, .707107, -.707107, -.817585, -.575808, |
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42 | -.989177, .14673, -.19509, -.980785, -.359895, -.932993, .313682, .949528, |
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43 | -.0980171, .995185, 1, 6.12323e-17, .963776, -.266713, .998795, -.0490677, |
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44 | -.998795, -.0490677, -.970031, -.24298, -.55557, .83147, -.14673, .989177, |
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45 | -.83147, -.55557, -.995185, -.0980171, .870087, .492898, .941544, -.33689, |
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46 | .575808, -.817585, .33689, .941544, .19509, -.980785, 0, 1, |
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47 | .219101, -.975702, -.83147, .55557, .757209, -.653173, -.95694, .290285, |
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48 | -.266713, .963776, -.0490677, .998795, .405241, .91421, -.405241, -.91421, |
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49 | -.689541, .724247, -.534998, -.844854, -.99248, -.122411, .724247, .689541, |
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50 | .492898, .870087, .817585, -.575808, .740951, .671559, -.33689, -.941544, |
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51 | .95694, .290285, .77301, -.634393, .0245412, -.999699, -.77301, -.634393, |
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52 | -.382683, .92388, -.24298, -.970031, -.893224, -.449611, .449611, .893224, |
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53 | .975702, -.219101, -.382683, -.92388, .844854, .534998, -.803208, -.595699, |
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54 | .941544, .33689, .963776, .266713, .932993, .359895, -.0735646, .99729, |
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55 | .634393, -.77301, .405241, -.91421, .33689, -.941544, .99729, .0735646, |
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56 | 1.22465e-16, -1, -.941544, -.33689, .0490677, -.998795, -.313682, .949528, |
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57 | .92388, .382683, -.999699, .0245412, .0245412, .999699, .653173, .757209, |
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58 | -.803208, .595699, .980785, -.19509, .817585, .575808, .975702, .219101, |
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59 | -.615232, -.788346, .99248, -.122411, .998795, .0490677, -.707107, .707107, |
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60 | .803208, -.595699, .671559, .740951, -.757209, -.653173, -.949528, .313682, |
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61 | -.989177, -.14673, -.817585, .575808, -.14673, -.989177, -1, -1.83697e-16, |
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62 | .290285, .95694, -.932993, -.359895, .24298, -.970031, .170962, .985278, |
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63 | -.671559, -.740951, .427555, .903989, .427555, -.903989, -.941544, .33689, |
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64 | -.492898, -.870087, -.266713, -.963776, .857729, -.514103, -.724247, .689541, |
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65 | .724247, -.689541, -.653173, .757209, .689541, -.724247, .949528, -.313682, |
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66 | -.19509, .980785, -.740951, .671559, -.999699, -.0245412, .689541, .724247, |
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67 | .803208, .595699, -.170962, .985278, .0735646, -.99729, .970031, -.24298, |
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68 | -.170962, -.985278, .471397, .881921, .91421, .405241, .893224, -.449611, |
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69 | .0490677, .998795, -.615232, .788346, -.998795, .0490677, -.427555, -.903989, |
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70 | -.0245412, .999699, -.534998, .844854, -.313682, -.949528, -.55557, -.83147, |
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71 | -.903989, -.427555, -.724247, -.689541, -.740951, -.671559, .985278, -.170962, |
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72 | -.857729, -.514103, -.99729, .0735646, .881921, -.471397, .534998, .844854, |
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73 | .359895, -.932993, .77301, .634393, .99729, -.0735646, .290285, -.95694, |
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74 | .575808, .817585, .757209, .653173, .903989, .427555, -.995185, .0980171, |
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75 | -.903989, .427555, -.844854, .534998, -.707107, -.707107, -.92388, .382683, |
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76 | -.653173, -.757209, -.881921, -.471397, -.219101, .975702, -.595699, .803208, |
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77 | .0980171, -.995185, -.788346, .615232, -.0980171, -.995185, -.985278, .170962, |
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78 | .122411, .99248, -.449611, -.893224, .170962, -.985278, .788346, .615232, |
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79 | -.492898, .870087, .671559, -.740951, .449611, -.893224, -.757209, .653173, |
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80 | .83147, .55557, -.290285, -.95694, -.932993, .359895, -.870087, -.492898, |
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81 | .266713, -.963776, -.881921, .471397, -.77301, .634393, -.471397, .881921, |
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82 | .844854, -.534998, .707107, .707107, .534998, -.844854, .514103, .857729, |
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83 | .14673, -.989177, .980785, .19509, -.122411, .99248, -.449611, .893224, |
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84 | .995185, -.0980171, -.634393, -.77301, .857729, .514103, .55557, .83147, |
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85 | -.92388, -.382683, -.844854, -.534998, -.963776, .266713, .989177, -.14673, |
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86 | .313682, -.949528, .359895, .932993, .24298, .970031, -.949528, -.313682, |
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87 | .932993, -.359895, .55557, -.83147, .615232, .788346, -.788346, -.615232, |
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88 | -.0245412, -.999699, -.219101, -.975702, .788346, -.615232, -.99248, .122411, |
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89 | -.671559, .740951, -.870087, .492898, .970031, .24298, .881921, .471397, |
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90 | .122411, -.99248, .471397, -.881921, .19509, .980785, -.963776, -.266713, |
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91 | .92388, -.382683, .989177, .14673, -.575808, -.817585, .219101, .975702, |
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92 | -.0490677, -.998795, -.980785, -.19509, .949528, .313682, .653173, -.757209, |
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93 | }; |
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94 | |
27 | // http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation |
95 | // http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation |
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96 | // used as gradient vectors for noise3d |
28 | static const float charges[256][3] = { |
97 | static const float charges3[256][3] = { |
29 | 6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01, |
98 | 6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01, |
30 | -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03, |
99 | -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03, |
31 | -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01, |
100 | -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01, |
32 | -6.44086082e-01, 3.21868600e-01, 6.93940720e-01, -4.42053435e-01, -1.94962529e-01, -8.75544615e-01, |
101 | -6.44086082e-01, 3.21868600e-01, 6.93940720e-01, -4.42053435e-01, -1.94962529e-01, -8.75544615e-01, |
33 | -6.86776297e-01, 5.34610386e-01, -4.92473403e-01, -8.45541961e-01, -2.41708225e-01, 4.76062943e-01, |
102 | -6.86776297e-01, 5.34610386e-01, -4.92473403e-01, -8.45541961e-01, -2.41708225e-01, 4.76062943e-01, |
… | |
… | |
154 | 4.98855035e-01, -3.98703643e-01, 7.69531714e-01, 2.55373649e-01, -7.56251592e-02, 9.63880249e-01, |
223 | 4.98855035e-01, -3.98703643e-01, 7.69531714e-01, 2.55373649e-01, -7.56251592e-02, 9.63880249e-01, |
155 | -1.51053916e-01, 3.85469253e-01, -9.10272580e-01, 6.78644990e-01, -7.26064181e-01, 1.10778074e-01, |
224 | -1.51053916e-01, 3.85469253e-01, -9.10272580e-01, 6.78644990e-01, -7.26064181e-01, 1.10778074e-01, |
156 | -3.07350590e-01, -9.14677987e-01, 2.62487703e-01, 5.60298616e-01, 1.74821302e-01, 8.09631381e-01, |
225 | -3.07350590e-01, -9.14677987e-01, 2.62487703e-01, 5.60298616e-01, 1.74821302e-01, 8.09631381e-01, |
157 | }; |
226 | }; |
158 | |
227 | |
159 | static vec2d |
228 | ///////////////////////////////////////////////////////////////////////////// |
160 | floor (vec2d v) |
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161 | { |
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162 | return vec2d (std::floor (v[0]), std::floor (v[1])); |
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163 | } |
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164 | |
229 | |
165 | static vec3d |
230 | template<int N, typename T> |
166 | floor (vec3d v) |
231 | void |
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232 | permutation<N,T>::seed (seedable_rand_gen &rng) |
167 | { |
233 | { |
168 | return vec3d (std::floor (v[0]), std::floor (v[1]), std::floor (v[2])); |
234 | for (int i = 0; i < N; ++i) |
169 | } |
235 | pmap[i] = i; |
170 | |
236 | |
171 | noise_gen<vec2d>::noise_gen (uint32_t seed) |
237 | // fisher-yates to randomly perturb |
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238 | for (int i = N; --i; ) |
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239 | ::swap (pmap[i], pmap[rng (i + 1)]); |
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240 | } |
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241 | |
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242 | template class permutation<256, uint8_t>; |
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243 | |
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244 | ///////////////////////////////////////////////////////////////////////////// |
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245 | |
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246 | template<class vec_t> |
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247 | void |
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248 | noise_gen_base<vec_t>::seed (seedable_rand_gen &rng) |
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249 | { |
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250 | for (int i = 0; i < array_length (rvmap); ++i) |
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251 | rvmap[i].seed (rng); |
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252 | } |
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253 | |
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254 | template<class vec_t> |
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255 | void |
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256 | noise_gen_base<vec_t>::seed (seed_t seed) |
172 | { |
257 | { |
173 | seedable_rand_gen rng (seed); |
258 | seedable_rand_gen rng (seed); |
174 | |
259 | |
175 | #if 1 |
260 | this->seed (rng); |
176 | for (int i = 0; i < 256; ++i) |
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177 | { |
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178 | vec2d rv (rng () - 0.5f, rng () - 0.5f); |
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179 | |
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180 | // normalise |
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181 | float mag = 1.f / sqrtf (dot (rv, rv)); |
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182 | |
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183 | rv[0] *= mag; |
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184 | rv[1] *= mag; |
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185 | |
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186 | rvec[i] = rv; |
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187 | } |
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188 | #endif |
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189 | |
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190 | #if 0 |
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191 | float offset = rng () * 3.14159265; |
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192 | |
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193 | for (int i = 0; i < 256; ++i) |
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194 | { |
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195 | float phi = i * (3.14159265 * 2 / 256) + offset; |
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196 | |
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197 | rvec[i][0] = sinf (phi); |
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198 | rvec[i][1] = -cosf (phi); |
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199 | } |
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200 | |
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201 | // fisher-yates to randomly perturb |
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202 | for (int i = 256; --i; ) |
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203 | ::swap (rvec [i], rvec [rng (i + 1)]); |
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204 | #endif |
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205 | |
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206 | rvmap[0].seed (rng); |
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207 | rvmap[1].seed (rng); |
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208 | } |
261 | } |
209 | |
262 | |
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263 | template<> |
210 | vec2d::T_numtype |
264 | vec2d::T_numtype |
211 | noise_gen<vec2d>::operator() (vec2d P) |
265 | noise_gen_base<vec2d>::operator() (vec2d P, uint32_t seed) |
212 | { |
266 | { |
213 | vec2d I = floor (P); |
267 | vec2d I = floor (P); |
214 | vec2d F = P - I; |
268 | vec2d F = P - I; |
215 | |
269 | |
216 | float v = 0; |
270 | value_t v = 0; |
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271 | |
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272 | seed *= 3039177861; |
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273 | uint8_t i1 = uint8_t (I[1]) + (seed >> 16); |
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274 | uint8_t i0 = uint8_t (I[0]) + (seed >> 8); |
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275 | |
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276 | uint8_t h2 = rvmap[2](seed); |
217 | |
277 | |
218 | for (int j = -1; j <= 2; ++j) |
278 | for (int j = -1; j <= 2; ++j) |
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279 | { |
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280 | uint8_t h1 = rvmap[1](i1 + j) ^ h2; |
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281 | |
219 | for (int i = -1; i <= 2; ++i) |
282 | for (int i = -1; i <= 2; ++i) |
220 | { |
283 | { |
221 | vec2d A = F - vec2d (i, j); |
284 | vec2d A = F - vec2d (i, j); |
222 | |
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223 | float d = dot (A, A); |
285 | value_t d = dot (A, A); |
224 | |
286 | |
225 | if (d < 4) |
287 | if (d < 4) |
226 | { |
288 | { |
227 | float t1 = 1 - d / 4; |
289 | value_t t1 = 1 - d / 4; |
228 | float t2 = t1 * t1; |
290 | value_t t2 = t1 * t1; |
229 | float t4 = t2 * t2; |
291 | value_t t4 = t2 * t2; |
230 | |
292 | |
231 | float p = (4 * t1 - 3) * t4; |
293 | value_t p = (4 * t1 - 3) * t4; |
232 | |
294 | |
233 | int h = rvmap [0](I[0] + i) ^ rvmap [1](I[1] + j); |
295 | uint8_t h = rvmap[0](i0 + i) ^ h1; |
234 | vec2d G = rvec [h & 0xff]; |
296 | vec2d G = charges2[h & 0xff]; |
235 | |
297 | |
236 | v += dot (A, G) * p; |
298 | v += dot (A, G) * p; |
237 | } |
299 | } |
238 | } |
300 | } |
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301 | } |
239 | |
302 | |
240 | return clamp (v, -.9999999f, .9999999f); |
303 | return v; |
241 | } |
304 | } |
242 | |
305 | |
243 | ///////////////////////////////////////////////////////////////////////////// |
306 | ///////////////////////////////////////////////////////////////////////////// |
244 | |
307 | |
245 | noise_gen<vec3d>::noise_gen (uint32_t seed) |
308 | template<> |
246 | { |
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247 | seedable_rand_gen rng (seed); |
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248 | |
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249 | rvmap [0].seed (rng); |
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250 | rvmap [1].seed (rng); |
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251 | rvmap [2].seed (rng); |
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252 | } |
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253 | |
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254 | vec3d::T_numtype |
309 | vec3d::T_numtype |
255 | noise_gen<vec3d>::operator() (vec3d P) |
310 | noise_gen_base<vec3d>::operator() (vec3d P, uint32_t seed) |
256 | { |
311 | { |
257 | vec3d I = floor (P); |
312 | vec3d I = floor (P); |
258 | vec3d F = P - I; |
313 | vec3d F = P - I; |
259 | |
314 | |
260 | float v = 0; |
315 | seed *= 3039177861; |
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316 | uint8_t i2 = uint8_t (I[2]) + (seed >> 24); |
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317 | uint8_t i1 = uint8_t (I[1]) + (seed >> 16); |
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318 | uint8_t i0 = uint8_t (I[0]) + (seed >> 8); |
261 | |
319 | |
262 | for (int j = -1; j <= 2; ++j) |
320 | uint8_t h3 = rvmap[3](seed); |
263 | for (int i = -1; i <= 2; ++i) |
321 | |
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322 | value_t v = 0; |
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323 | |
264 | for (int k = -1; k <= 2; ++k) |
324 | for (int k = -1; k <= 2; ++k) |
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325 | { |
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326 | uint8_t h2 = rvmap[2](i2 + k) ^ h3; |
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327 | |
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328 | for (int j = -1; j <= 2; ++j) |
265 | { |
329 | { |
266 | vec3d A = F - vec3d (i, j, k); |
330 | uint8_t h1 = rvmap[1](i1 + j) ^ h2; |
267 | float d = dot (A, A); |
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268 | |
331 | |
269 | if (d < 4) |
332 | for (int i = -1; i <= 2; ++i) |
270 | { |
333 | { |
271 | float t1 = 1 - d / 4; |
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272 | float t2 = t1 * t1; |
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273 | float t4 = t2 * t2; |
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274 | |
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275 | // (4t⁵ - 3t⁴) |
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276 | float p = (4 * t1 - 3) * t4; |
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277 | |
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278 | int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k); |
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279 | const float *G = charges[h & 0xff]; |
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280 | |
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281 | v += dot (A, vec3d (G[0], G[1], G[2])) * p; |
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282 | } |
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283 | } |
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284 | |
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285 | return clamp (v * 2, -.9999999f, .9999999f); |
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286 | } |
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287 | |
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288 | vec3d::T_numtype |
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289 | noise_gen<vec3d>::operator() (vec3d P, vec3d N) |
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290 | { |
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291 | vec3d I = floor (P); |
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292 | vec3d F = P - I; |
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293 | |
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294 | float v = 0; |
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295 | |
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296 | for (int j = -1; j <= 2; ++j) |
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297 | for (int i = -1; i <= 2; ++i) |
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298 | for (int k = -1; k <= 2; ++k) |
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299 | { |
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300 | vec3d D = F - vec3d (i, j, k); |
334 | vec3d A = F - vec3d (i, j, k); |
301 | float e = dot (D, N); |
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302 | float o = 1 - abs (e); |
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303 | |
|
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304 | if (o > 0) |
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305 | { |
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306 | vec3d A = D - e * N; |
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307 | float d = dot (A, A); |
335 | value_t d = dot (A, A); |
308 | |
336 | |
309 | if (d < 4) |
337 | if (d < 4) |
310 | { |
338 | { |
311 | float t1 = 1 - d / 4; |
339 | value_t t1 = 1 - d / 4; |
312 | float t2 = t1 * t1; |
340 | value_t t2 = t1 * t1; |
313 | float t4 = t2 * t2; |
341 | value_t t4 = t2 * t2; |
314 | |
342 | |
315 | float o2 = o * o; |
|
|
316 | |
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|
317 | // (4t⁵ - 3t⁴) * (3o³ - 2o²) |
343 | // (4t⁵ - 3t⁴) |
318 | // alternative? ((o * 6 - 15) * o + 10) * o³ |
344 | value_t p = (4 * t1 - 3) * t4; |
319 | float p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o); |
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320 | |
345 | |
321 | int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k); |
346 | uint8_t h = rvmap[0](i0 + i) ^ h1; |
322 | const float *G = charges[h & 0xff]; |
347 | const value_t *G = charges3[h & 0xff]; |
323 | |
348 | |
324 | v += dot (A, vec3d (G[0], G[1], G[2])) * p; |
349 | v += dot (A, vec3d (G[0], G[1], G[2])) * p; |
325 | } |
350 | } |
326 | } |
351 | } |
327 | } |
352 | } |
|
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353 | } |
328 | |
354 | |
329 | return clamp (v, -.9999999f, .9999999f); |
355 | return v * 2; |
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356 | } |
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357 | |
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358 | vec3d::T_numtype |
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359 | noise_gen<vec3d>::operator() (vec3d P, vec3d N, uint32_t seed) |
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360 | { |
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361 | vec3d I = floor (P); |
|
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362 | vec3d F = P - I; |
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363 | |
|
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364 | seed *= 3039177861; |
|
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365 | uint8_t i2 = uint8_t (I[2]) + (seed >> 24); |
|
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366 | uint8_t i1 = uint8_t (I[1]) + (seed >> 16); |
|
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367 | uint8_t i0 = uint8_t (I[0]) + (seed >> 8); |
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368 | |
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369 | uint8_t h3 = rvmap[3](seed); |
|
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370 | |
|
|
371 | value_t v = 0; |
|
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372 | |
|
|
373 | for (int k = -1; k <= 2; ++k) |
|
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374 | { |
|
|
375 | uint8_t h2 = rvmap[2](i2 + k) ^ h3; |
|
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376 | |
|
|
377 | for (int j = -1; j <= 2; ++j) |
|
|
378 | { |
|
|
379 | uint8_t h1 = rvmap[1](i1 + j) ^ h2; |
|
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380 | |
|
|
381 | for (int i = -1; i <= 2; ++i) |
|
|
382 | { |
|
|
383 | vec3d D = F - vec3d (i, j, k); |
|
|
384 | value_t e = dot (D, N); |
|
|
385 | value_t o = 1 - abs (e); |
|
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386 | |
|
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387 | if (o > 0) |
|
|
388 | { |
|
|
389 | vec3d A = D - e * N; |
|
|
390 | value_t d = dot (A, A); |
|
|
391 | |
|
|
392 | if (d < 4) |
|
|
393 | { |
|
|
394 | value_t t1 = 1 - d / 4; |
|
|
395 | value_t t2 = t1 * t1; |
|
|
396 | value_t t4 = t2 * t2; |
|
|
397 | |
|
|
398 | value_t o2 = o * o; |
|
|
399 | |
|
|
400 | // (4t⁵ - 3t⁴) * (3o³ - 2o²) |
|
|
401 | // alternative? ((o * 6 - 15) * o + 10) * o³ |
|
|
402 | value_t p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o); |
|
|
403 | |
|
|
404 | uint8_t h = rvmap[0](i0 + i) ^ h1; |
|
|
405 | const value_t *G = charges3[h & 0xff]; |
|
|
406 | |
|
|
407 | v += dot (A, vec3d (G[0], G[1], G[2])) * p; |
|
|
408 | } |
|
|
409 | } |
|
|
410 | } |
|
|
411 | } |
|
|
412 | } |
|
|
413 | |
|
|
414 | return v; |
330 | } |
415 | } |
331 | |
416 | |
332 | template class noise_gen<vec2d>; |
417 | template class noise_gen<vec2d>; |
333 | template class noise_gen<vec3d>; |
418 | template class noise_gen<vec3d>; |
334 | |
419 | |
335 | ///////////////////////////////////////////////////////////////////////////// |
420 | ///////////////////////////////////////////////////////////////////////////// |
336 | |
421 | |
337 | template<class vec_t> |
422 | template<class vec_t> |
338 | static vec_t |
423 | frac_gen<vec_t>::frac_gen (int octaves, value_t lacunarity, value_t hurst_expo, seed_t seed) |
339 | ith_octave (vec_t P, int i) |
424 | : octaves (octaves), lac (lacunarity), h (hurst_expo) |
340 | { |
425 | { |
341 | vec_t r = P; |
426 | this->seed (seed); |
342 | r[0] += i; |
|
|
343 | return r; |
|
|
344 | } |
|
|
345 | |
427 | |
346 | template<class vec_t> |
|
|
347 | frac_gen<vec_t>::frac_gen (value_t hurst_expo, value_t lacunarity) |
|
|
348 | : h (hurst_expo), lac (lacunarity), noise_gen<vec_t> (0) |
|
|
349 | { |
|
|
350 | value_t exsum = 0; |
428 | value_t exsum = 0; |
|
|
429 | value_t phi = noise (vec_t (value_t (0))) * 0.5 + 1; |
351 | |
430 | |
352 | for (int i = 0; i < MAX_OCTAVES; ++i) |
431 | for (int i = 0; i < octaves; ++i) |
353 | { |
432 | { |
354 | ex [i] = powf (lac, -h * i); |
433 | ex [i] = pow (lac, -h * i); |
355 | exsum += ex [i]; |
434 | exsum += ex [i]; |
356 | fbm_mul [i] = 0.5f / (exsum * 0.75f); // .75f is a heuristic |
435 | fbm_mul [i] = 0.5 / (exsum * 0.75); // .75 is a heuristic |
357 | rot [i].set (0.4488f * i); |
436 | rot [i].set (phi * i + 1); |
358 | } |
437 | } |
359 | } |
438 | } |
360 | |
439 | |
361 | template<class vec_t> |
440 | template<class vec_t> |
362 | typename frac_gen<vec_t>::value_t |
441 | typename frac_gen<vec_t>::value_t |
363 | frac_gen<vec_t>::fBm (vec_t P, int octaves) |
442 | frac_gen<vec_t>::fBm (vec_t P) |
364 | { |
443 | { |
365 | value_t v = 0.f; |
444 | value_t v = 0; |
366 | |
445 | |
367 | for (int i = 0; i < octaves; ++i) |
446 | for (int i = 0; i < octaves; ++i) |
368 | { |
447 | { |
369 | rot [i](P); |
448 | rot [i](P); |
370 | v += noise (ith_octave (P, i)) * ex [i]; |
449 | v += noise (P, i) * ex [i]; |
371 | P *= lac; |
450 | P *= lac; |
372 | } |
451 | } |
373 | |
452 | |
374 | return clamp (v * fbm_mul [octaves - 1] + 0.5f, 0.f, .9999999f); |
453 | return v * fbm_mul [octaves - 1]; |
375 | } |
454 | } |
376 | |
455 | |
377 | template<class vec_t> |
456 | template<class vec_t> |
378 | typename frac_gen<vec_t>::value_t |
457 | typename frac_gen<vec_t>::value_t |
379 | frac_gen<vec_t>::turbulence (vec_t P, int octaves) |
458 | frac_gen<vec_t>::turbulence (vec_t P) |
380 | { |
459 | { |
381 | value_t v = 0.f; |
460 | value_t v = 0; |
382 | |
461 | |
383 | for (int i = 0; i < octaves; ++i) |
462 | for (int i = 0; i < octaves; ++i) |
384 | { |
463 | { |
385 | rot [i](P); |
464 | rot [i](P); |
386 | v += abs (noise (ith_octave (P, i))) * ex [i]; |
465 | v += abs (noise (P, i)) * ex [i]; |
387 | P *= lac; |
466 | P *= lac; |
388 | } |
467 | } |
389 | |
468 | |
390 | return clamp (v * fbm_mul [octaves - 1] * 2.f, 0.f, .9999999f); |
469 | return v * fbm_mul [octaves - 1] * (0.5 / noise_gen<vec_t>::abs_avg ()); |
391 | } |
470 | } |
392 | |
471 | |
393 | template<class vec_t> |
472 | template<class vec_t> |
394 | typename frac_gen<vec_t>::value_t |
473 | typename frac_gen<vec_t>::value_t |
395 | frac_gen<vec_t>::multifractal (vec_t P, int octaves, value_t offset) |
474 | frac_gen<vec_t>::multifractal (vec_t P, value_t offset) |
396 | { |
475 | { |
397 | value_t v = 1.f; |
476 | value_t v = 1; |
398 | |
477 | |
399 | for (int i = 0; i < octaves; ++i) |
478 | for (int i = 0; i < octaves; ++i) |
400 | { |
479 | { |
401 | rot [i](P); |
480 | rot [i](P); |
402 | v *= noise (P) * ex [i] + offset; |
481 | v *= noise (P) * ex [i] + offset; |
403 | P *= lac; |
482 | P *= lac; |
404 | } |
483 | } |
405 | |
484 | |
406 | return clamp (v * 0.5f, 0.f, .9999999f); |
485 | return v * value_t (0.5); |
407 | } |
486 | } |
408 | |
487 | |
409 | template<class vec_t> |
488 | template<class vec_t> |
410 | typename frac_gen<vec_t>::value_t |
489 | typename frac_gen<vec_t>::value_t |
411 | frac_gen<vec_t>::heterofractal (vec_t P, int octaves, value_t offset) |
490 | frac_gen<vec_t>::heterofractal (vec_t P, value_t offset) |
412 | { |
491 | { |
413 | value_t v = noise (P) + offset; |
492 | value_t v = noise (P) + offset; |
414 | int i; |
|
|
415 | |
493 | |
416 | for (i = 1; i < octaves; ++i) |
494 | for (int i = 1; i < octaves; ++i) |
417 | { |
495 | { |
418 | rot [i](P); |
496 | rot [i](P); |
419 | P *= lac; |
497 | P *= lac; |
420 | v += v * (noise (P) * ex [i] + offset); |
498 | v += v * (noise (P) * ex [i] + offset); |
421 | } |
499 | } |
422 | |
500 | |
423 | return v / powf (2., octaves); |
501 | return v / (1 << octaves); |
424 | } |
502 | } |
425 | |
503 | |
426 | template<class vec_t> |
504 | template<class vec_t> |
427 | typename frac_gen<vec_t>::value_t |
505 | typename frac_gen<vec_t>::value_t |
428 | frac_gen<vec_t>::hybridfractal (vec_t P, int octaves, value_t offset, value_t gain) |
506 | frac_gen<vec_t>::hybridfractal (vec_t P, value_t offset, value_t gain) |
429 | { |
507 | { |
430 | value_t v = (noise (P) + offset) * ex [0]; |
508 | value_t v = (noise (P) + offset) * ex [0]; |
431 | value_t weight = v; |
509 | value_t weight = v; |
432 | int i; |
|
|
433 | |
510 | |
434 | for (i = 1; i < octaves; ++i) |
511 | for (int i = 1; i < octaves; ++i) |
435 | { |
512 | { |
436 | rot [i](P); |
513 | rot [i](P); |
437 | P *= lac; |
514 | P *= lac; |
438 | |
515 | |
439 | min_it (weight, 1.f); |
516 | min_it (weight, 1); |
440 | |
517 | |
441 | value_t sig = (noise (P) + offset) * ex [i]; |
518 | value_t sig = (noise (P) + offset) * ex [i]; |
442 | v += weight * sig; |
519 | v += weight * sig; |
443 | weight *= gain * sig; |
520 | weight *= gain * sig; |
444 | } |
521 | } |
445 | |
522 | |
446 | return clamp (v * 0.5f + 0.5f, 0.f, .9999999f); |
523 | return v * value_t (0.5) + value_t (0.5); |
447 | } |
524 | } |
448 | |
525 | |
449 | template<class vec_t> |
526 | template<class vec_t> |
450 | typename frac_gen<vec_t>::value_t |
527 | typename frac_gen<vec_t>::value_t |
451 | frac_gen<vec_t>::ridgedmultifractal (vec_t P, int octaves, value_t offset, value_t gain) |
528 | frac_gen<vec_t>::ridgedmultifractal (vec_t P, value_t offset, value_t gain) |
452 | { |
529 | { |
453 | value_t sig = offset - abs (noise (P)); |
530 | value_t sig = offset - abs (noise (P)); |
454 | sig *= sig; |
531 | sig *= sig; |
455 | value_t v = sig; |
532 | value_t v = sig; |
456 | |
533 | |
457 | for (int i = 1; i < octaves; ++i) |
534 | for (int i = 1; i < octaves; ++i) |
458 | { |
535 | { |
459 | rot [i](P); |
536 | rot [i](P); |
460 | P *= lac; |
537 | P *= lac; |
461 | |
538 | |
|
|
539 | // weight higher octaves by previous signal |
462 | value_t w = clamp (sig * gain, 0.f, 1.f); |
540 | value_t w = clamp (sig * gain, 0, 1); |
463 | |
541 | |
464 | sig = offset - abs (noise (P)); |
542 | sig = offset - abs (noise (P)); |
465 | sig *= sig; |
543 | sig *= sig; |
466 | sig *= w; |
544 | sig *= w; |
467 | |
545 | |
468 | v += sig * ex [i]; |
546 | v += sig * ex [i]; |
469 | } |
547 | } |
470 | |
548 | |
471 | return clamp (v * 0.25f, 0.f, .9999999f); |
549 | return v * value_t (0.25); |
|
|
550 | } |
|
|
551 | |
|
|
552 | template<class vec_t> |
|
|
553 | typename frac_gen<vec_t>::value_t |
|
|
554 | frac_gen<vec_t>::billowfractal (vec_t P, value_t offset, value_t gain) |
|
|
555 | { |
|
|
556 | value_t v = 0; |
|
|
557 | |
|
|
558 | offset += 2 * noise_gen<vec_t>::abs_avg () - 1; |
|
|
559 | |
|
|
560 | for (int i = 0; i < octaves; ++i) |
|
|
561 | { |
|
|
562 | rot [i](P); |
|
|
563 | v += (abs (noise (P, i)) * gain - offset) * ex [i]; |
|
|
564 | P *= lac; |
|
|
565 | } |
|
|
566 | |
|
|
567 | return v; |
472 | } |
568 | } |
473 | |
569 | |
474 | // http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2 |
570 | // http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2 |
475 | template<class vec_t> |
571 | template<class vec_t> |
476 | typename frac_gen<vec_t>::value_t |
572 | typename frac_gen<vec_t>::value_t |
477 | frac_gen<vec_t>::terrain (vec_t P, int octaves) |
573 | frac_gen<vec_t>::terrain (vec_t P) |
478 | { |
574 | { |
479 | value_t v = 0.f; |
575 | value_t v = 0; |
480 | |
576 | |
481 | for (int i = 0; i < octaves; ++i) |
577 | for (int i = 0; i < octaves; ++i) |
482 | { |
578 | { |
483 | rot [i](P); |
579 | rot [i](P); |
484 | v += noise (P) * ex [i]; |
580 | v += noise (P) * ex [i]; |
485 | P *= lac; |
581 | P *= lac; |
486 | } |
582 | } |
487 | |
583 | |
488 | v *= fbm_mul [octaves - 1]; |
584 | v *= fbm_mul [octaves - 1]; |
489 | |
585 | |
490 | return v <= 0.f ? - powf (-v, 0.7f) : powf (v, 1. + noise (P) * v); |
586 | return v <= 0 ? - pow (-v, 0.7) : pow (v, 1 + noise (P) * v); |
491 | } |
587 | } |
492 | |
588 | |
493 | template<class vec_t> |
589 | template<class vec_t> |
494 | typename frac_gen<vec_t>::value_t |
590 | typename frac_gen<vec_t>::value_t |
495 | frac_gen<vec_t>::terrain2 (vec_t P, int octaves) |
591 | frac_gen<vec_t>::terrain2 (vec_t P) |
496 | { |
592 | { |
497 | value_t a = fBm (P, octaves); |
593 | value_t a = fBm (P); |
498 | value_t b = ridgedmultifractal (P, octaves, 1, 8); |
594 | value_t b = ridgedmultifractal (P, 1, 8); |
499 | value_t fade = fBm (P + vec_t(10.3), octaves); |
595 | value_t fade = fBm (P + vec_t(10.3)); |
500 | |
596 | |
501 | const value_t width = 0.05f; |
597 | const value_t width = 0.05; |
502 | |
598 | |
503 | if (fade > 0.5f + width) |
599 | if (fade > 0.5 + width) |
504 | return a; |
600 | return a; |
505 | else if (fade < 0.5f - width) |
601 | else if (fade < 0.5 - width) |
506 | return b; |
602 | return b; |
507 | |
603 | |
508 | fade = (fade - 0.5f + width) / (width * 2); |
604 | fade = (fade - 0.5 + width) / (width * 2); |
509 | |
605 | |
510 | // sigmoidal curve |
606 | // sigmoidal curve |
511 | fade = fade * fade * 2 * (1.5f - fade); |
607 | fade = fade * fade * 2 * (1.5 - fade); |
512 | |
608 | |
513 | return a * fade + b * (1 - fade); |
609 | return a * fade + b * (1 - fade); |
514 | } |
610 | } |
515 | |
611 | |
516 | template class frac_gen<vec2d>; |
612 | template class frac_gen<vec2d>; |
517 | template class frac_gen<vec3d>; |
613 | template class frac_gen<vec3d>; |
518 | |
614 | |
519 | ///////////////////////////////////////////////////////////////////////////// |
615 | ///////////////////////////////////////////////////////////////////////////// |
520 | |
616 | |
|
|
617 | template<typename T, typename U> |
|
|
618 | T |
|
|
619 | inline border_blend (T a, T b, vec2d P, U N, U W) |
|
|
620 | { |
|
|
621 | U border = W; // within n places of the border |
|
|
622 | |
|
|
623 | min_it (border, P [0]); |
|
|
624 | min_it (border, N - P [0]); |
|
|
625 | min_it (border, P [1]); |
|
|
626 | min_it (border, N - P [1]); |
|
|
627 | |
|
|
628 | return blend (a, b,border, U(0), W); |
|
|
629 | } |
|
|
630 | |
|
|
631 | static void |
|
|
632 | gen_height (int x, int y) |
|
|
633 | { |
|
|
634 | vec2d P = vec2d (x, y); |
|
|
635 | |
|
|
636 | static frac2d gen(13); |
|
|
637 | |
|
|
638 | static frac2d vec_gen1 (6, 2, 0.5, 1); |
|
|
639 | static frac2d vec_gen2 (6, 2, 0.5, 2); |
|
|
640 | |
|
|
641 | const float continent_scale = 0.00008; |
|
|
642 | |
|
|
643 | vec2d perturb_pos = pow (P, 1.4) * 1e-5; |
|
|
644 | |
|
|
645 | vec2d perturb ( |
|
|
646 | vec_gen1.fBm (perturb_pos), |
|
|
647 | vec_gen2.fBm (perturb_pos) |
|
|
648 | ); |
|
|
649 | |
|
|
650 | float perturb_perturb = 1 - (P[1] - P[0]) * (1. / 25000 / 2); |
|
|
651 | perturb_perturb = perturb_perturb * perturb_perturb * 0.4; |
|
|
652 | perturb *= perturb_perturb; |
|
|
653 | |
|
|
654 | vec2d P_continent = P * continent_scale + perturb; |
|
|
655 | |
|
|
656 | static frac2d continent_gen (13, 2.13, 0.5); |
|
|
657 | float continent = continent_gen.fBm (P_continent) + 0.05f; |
|
|
658 | |
|
|
659 | float land_gradient = sigmoid1 (P[0] * (1. / 25000)); |
|
|
660 | |
|
|
661 | const float W = 1000 * continent_scale; |
|
|
662 | const float N = (25000 - 1) * continent_scale; |
|
|
663 | |
|
|
664 | continent = border_blend (-1.f, continent, P_continent , N, 400 * continent_scale); |
|
|
665 | continent = border_blend (-1.f, continent, P * continent_scale + perturb * 0.1, N, 100 * continent_scale); |
|
|
666 | |
|
|
667 | vec3d c; |
|
|
668 | float v; |
|
|
669 | |
|
|
670 | if (continent < 0) |
|
|
671 | { |
|
|
672 | // ocean |
|
|
673 | |
|
|
674 | v = min (continent * 10, -0.2f); |
|
|
675 | c = vec3d (0, 0, 1); |
|
|
676 | } |
|
|
677 | else |
|
|
678 | { |
|
|
679 | // continent |
|
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680 | |
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681 | // big rivers |
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682 | static frac2d river_gen (1); |
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683 | float river1 = abs (river_gen.fBm (P * 0.001 + perturb * 4)); |
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684 | float river2 = river_gen.ridgedmultifractal (P * 0.04 + vec2d (3, 5), 0.8, 10) - (P[1] / 25000) * 0.1; |
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685 | |
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686 | if (river1 < 0.03f) |
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687 | { |
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688 | v = min (-0.1f, -river1); |
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689 | c = vec3d (0.2, 0.2, 1); |
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690 | } |
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691 | else if (river1 < 0.2f && river2 > 0.1f) |
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692 | { |
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693 | v = -0.05f; |
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694 | c = vec3d (0.4, 0.4, 1); |
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695 | } |
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696 | else |
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697 | { |
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698 | //c = river1 > 0 ? vec3d (0.8, 0.8, 0) : vec3d (0.8, 0, 0); |
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699 | c = blend0 (vec3d (0.8, 0, 0), vec3d (0.8, 0.8, 0), 0.01f, river1); |
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700 | |
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701 | static frac2d mountain_gen (8, 2.14, 0.5); |
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702 | float mountain = mountain_gen.ridgedmultifractal (P * 0.004); |
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703 | v = blend0 (mountain * 3 - 1, continent, 0.05f, river1); |
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704 | } |
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705 | } |
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706 | |
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707 | c *= v * 0.5 + 0.5; |
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708 | |
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709 | putc (clamp<int> (255 * c[0], 0, 255), stdout); |
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710 | putc (clamp<int> (255 * c[1], 0, 255), stdout); |
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711 | putc (clamp<int> (255 * c[2], 0, 255), stdout); |
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712 | } |
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713 | |
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714 | void noise_test (); |
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715 | void noise_test () |
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716 | { |
521 | #if 0 |
717 | #if 1 |
522 | void hack(); void hack() |
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523 | { |
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524 | frac_gen<vec2d> gen (0.5, 2); |
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525 | frac_gen<vec3d> gen3; |
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526 | |
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527 | #if 0 |
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528 | int N = 1024; |
718 | int Nw = 700; |
529 | |
719 | |
530 | printf ("P5 %d %d 255\n", N, N); |
720 | printf ("P6 %d %d 255\n", Nw * 3, Nw * 2); |
531 | // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm |
721 | // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm |
532 | for (int y = 0; y < N; ++y) |
722 | for (int y = 0; y < Nw; ++y) |
533 | { |
723 | { |
534 | if (!(y&63))fprintf (stderr, "y %d\n", y);//D |
724 | if (!(y&63))fprintf (stderr, "y %d\n", y * 50 / Nw);//D |
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725 | |
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726 | for (int x = 0; x < Nw; ++x) gen_height (x * 25000 / Nw, y * 25000 / Nw); |
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727 | |
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728 | for (int x = 0; x < Nw; ++x) gen_height (x, y); |
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729 | for (int x = 0; x < Nw; ++x) gen_height (x + 22000, y + 2000); |
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730 | } |
535 | for (int x = 0; x < N; ++x) |
731 | for (int y = 0; y < Nw; ++y) |
536 | { |
732 | { |
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733 | if (!(y&63))fprintf (stderr, "y %d\n", y * 50 / Nw+50);//D |
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734 | |
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735 | for (int x = 0; x < Nw; ++x) gen_height (x + 1000, y + 22000); |
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736 | for (int x = 0; x < Nw; ++x) gen_height (x + 12000, y + 12000); |
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737 | for (int x = 0; x < Nw; ++x) gen_height (x + 22000, y + 22000); |
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738 | } |
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739 | |
537 | //putc (127 * n.noise (x * 0.1, y * 0.1, 0, 0,0,1) + 128, stdout); |
740 | //putc (127 * gen.noise (vec2d (x * 0.01, y * 0.01)) + 128, stdout); |
538 | //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout); |
741 | //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout); |
539 | //putc (256 * gen.fBm (x * 0.01, y * 0.01, 3), stdout); |
742 | //putc (256 * gen.fBm (vec2d(x * 0.01, y * 0.01), 16), stdout); |
540 | //putc (256 * gen.turbulence (x * 0.004 - 1, y * 0.004 - 1, 8), stdout); |
743 | //putc (256 * gen.turbulence (vec2d (x * 0.004 - 1, y * 0.004 - 1), 10), stdout); |
541 | //putc (256 * gen.heterofractal (x * 0.008, y * 0.008, 8, 0.9), stdout); |
744 | //putc (256 * gen.heterofractal (vec2d (x * 0.008, y * 0.008), 8, 0.9), stdout); |
542 | |
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543 | // mountais or somesuch(?) |
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544 | //putc (256 * gen.hybridfractal (x * 0.01, y * 0.01, 8, -.4, -4), stdout); |
745 | //putc (256 * gen.hybridfractal (vec2d (x * 0.01, y * 0.01), 8, -.4, -4), stdout); |
545 | |
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546 | // temperature |
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547 | //putc (256 * gen.fBm (x * 0.002, y * 0.002, 2), stdout); |
746 | //putc (256 * gen.fBm (vec2d (x * 0.002, y * 0.002), 2), stdout); |
548 | // rain |
747 | //putc (127.49 * gen.billowfractal (vec2d (x * 0.01, y * 0.01), 9) + 128, stdout); |
549 | //putc (256 * gen.ridgedmultifractal (x * 0.01, y * 0.01, 3, 1.03, 2), stdout); |
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550 | } |
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551 | } |
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552 | #else |
748 | #else |
553 | int N = 512; |
749 | int N = 128; |
554 | |
750 | |
555 | //printf ("P6 %d %d 255\n", N, N); |
751 | //printf ("P6 %d %d 255\n", N, N); |
556 | // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm |
752 | // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm |
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753 | frac3d gen3 (3);; |
557 | for (int z = 0; z < N; ++z) |
754 | for (int z = 0; z < N; ++z) |
558 | { |
755 | { |
559 | if (!(z&7))fprintf (stderr, "z %d\n", z);//D |
756 | if (!(z&7))fprintf (stderr, "z %d\n", z);//D |
560 | for (int y = 0; y < N; ++y) |
757 | for (int y = 0; y < N; ++y) |
561 | for (int x = 0; x < N; ++x) |
758 | for (int x = 0; x < N; ++x) |
562 | { |
759 | { |
563 | float v = gen3.ridgedmultifractal (vec3d (x * 0.01 + 0.2, y * 0.01 + 0.2, z * 0.01 + 0.2), 3, 1.03, 2) * 2; |
760 | float v = gen3.ridgedmultifractal (vec3d (x * 0.001 + 0.2, y * 0.001 + 0.2, z * 0.01 + 0.2), 1.03, 2) * 2; |
564 | |
761 | |
565 | #if 0 |
762 | #if 0 |
566 | if (z < 64) |
763 | if (z < 64) |
567 | v = v * (z * z) / (64 * 64); |
764 | v = v * (z * z) / (64 * 64); |
568 | #endif |
765 | #endif |
569 | |
766 | |
570 | if (v <= 0.9999) |
767 | if (v <= 0.9) |
571 | continue; |
768 | continue; |
572 | |
769 | |
573 | float r[4]; |
770 | float r[4]; |
574 | int i[4]; |
771 | int i[4]; |
575 | |
772 | |
… | |
… | |
590 | } |
787 | } |
591 | #endif |
788 | #endif |
592 | |
789 | |
593 | exit (0); |
790 | exit (0); |
594 | } |
791 | } |
595 | #endif |
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