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/cvs/deliantra/server/common/noise.C
Revision: 1.12
Committed: Tue Apr 26 14:41:35 2011 UTC (13 years, 1 month ago) by root
Content type: text/plain
Branch: MAIN
Changes since 1.11: +121 -32 lines
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File Contents

# User Rev Content
1 root 1.1 /*
2     * This file is part of Deliantra, the Roguelike Realtime MMORPG.
3     *
4 root 1.5 * Copyright (©) 2010,2011 Marc Alexander Lehmann / Robin Redeker / the Deliantra team
5 root 1.1 *
6     * Deliantra is free software: you can redistribute it and/or modify it under
7     * the terms of the Affero GNU General Public License as published by the
8     * Free Software Foundation, either version 3 of the License, or (at your
9     * option) any later version.
10     *
11     * This program is distributed in the hope that it will be useful,
12     * but WITHOUT ANY WARRANTY; without even the implied warranty of
13     * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14     * GNU General Public License for more details.
15     *
16     * You should have received a copy of the Affero GNU General Public License
17     * and the GNU General Public License along with this program. If not, see
18     * <http://www.gnu.org/licenses/>.
19     *
20     * The authors can be reached via e-mail to <support@deliantra.net>
21     */
22    
23     #include "noise.h"
24    
25 root 1.2 /////////////////////////////////////////////////////////////////////////////
26    
27 root 1.8 // perl -e 'for(0..255) { $p = (atan2 1,0) / 64 * $_; printf " %10g, %10g,\n", sin $p, cos $p }' | sort -R
28     static const float charges2[256][2] = {
29     -.975702, -.219101, .893224, .449611, .870087, -.492898, .595699, -.803208,
30     .14673, .989177, .995185, .0980171, .91421, -.405241, -.514103, .857729,
31     -.985278, -.170962, -.689541, -.724247, -.427555, .903989, .83147, -.55557,
32     .999699, -.0245412, .634393, .77301, -.514103, -.857729, -.0735646, -.99729,
33     .514103, -.857729, -.595699, -.803208, -.290285, .95694, .595699, .803208,
34     .266713, .963776, -.33689, .941544, .492898, -.870087, -.471397, -.881921,
35     -.99729, -.0735646, .615232, -.788346, -.91421, -.405241, -.575808, .817585,
36     .0980171, .995185, -.980785, .19509, -.122411, -.99248, .0735646, .99729,
37     -.634393, .77301, -.91421, .405241, .99248, .122411, .903989, -.427555,
38     -.24298, .970031, -.857729, .514103, -.359895, .932993, .382683, .92388,
39     .740951, -.671559, -.893224, .449611, -.95694, -.290285, -.975702, .219101,
40     -.970031, .24298, .999699, .0245412, -.405241, .91421, .985278, .170962,
41     .382683, -.92388, .95694, -.290285, .707107, -.707107, -.817585, -.575808,
42     -.989177, .14673, -.19509, -.980785, -.359895, -.932993, .313682, .949528,
43     -.0980171, .995185, 1, 6.12323e-17, .963776, -.266713, .998795, -.0490677,
44     -.998795, -.0490677, -.970031, -.24298, -.55557, .83147, -.14673, .989177,
45     -.83147, -.55557, -.995185, -.0980171, .870087, .492898, .941544, -.33689,
46     .575808, -.817585, .33689, .941544, .19509, -.980785, 0, 1,
47     .219101, -.975702, -.83147, .55557, .757209, -.653173, -.95694, .290285,
48     -.266713, .963776, -.0490677, .998795, .405241, .91421, -.405241, -.91421,
49     -.689541, .724247, -.534998, -.844854, -.99248, -.122411, .724247, .689541,
50     .492898, .870087, .817585, -.575808, .740951, .671559, -.33689, -.941544,
51     .95694, .290285, .77301, -.634393, .0245412, -.999699, -.77301, -.634393,
52     -.382683, .92388, -.24298, -.970031, -.893224, -.449611, .449611, .893224,
53     .975702, -.219101, -.382683, -.92388, .844854, .534998, -.803208, -.595699,
54     .941544, .33689, .963776, .266713, .932993, .359895, -.0735646, .99729,
55     .634393, -.77301, .405241, -.91421, .33689, -.941544, .99729, .0735646,
56     1.22465e-16, -1, -.941544, -.33689, .0490677, -.998795, -.313682, .949528,
57     .92388, .382683, -.999699, .0245412, .0245412, .999699, .653173, .757209,
58     -.803208, .595699, .980785, -.19509, .817585, .575808, .975702, .219101,
59     -.615232, -.788346, .99248, -.122411, .998795, .0490677, -.707107, .707107,
60     .803208, -.595699, .671559, .740951, -.757209, -.653173, -.949528, .313682,
61     -.989177, -.14673, -.817585, .575808, -.14673, -.989177, -1, -1.83697e-16,
62     .290285, .95694, -.932993, -.359895, .24298, -.970031, .170962, .985278,
63     -.671559, -.740951, .427555, .903989, .427555, -.903989, -.941544, .33689,
64     -.492898, -.870087, -.266713, -.963776, .857729, -.514103, -.724247, .689541,
65     .724247, -.689541, -.653173, .757209, .689541, -.724247, .949528, -.313682,
66     -.19509, .980785, -.740951, .671559, -.999699, -.0245412, .689541, .724247,
67     .803208, .595699, -.170962, .985278, .0735646, -.99729, .970031, -.24298,
68     -.170962, -.985278, .471397, .881921, .91421, .405241, .893224, -.449611,
69     .0490677, .998795, -.615232, .788346, -.998795, .0490677, -.427555, -.903989,
70     -.0245412, .999699, -.534998, .844854, -.313682, -.949528, -.55557, -.83147,
71     -.903989, -.427555, -.724247, -.689541, -.740951, -.671559, .985278, -.170962,
72     -.857729, -.514103, -.99729, .0735646, .881921, -.471397, .534998, .844854,
73     .359895, -.932993, .77301, .634393, .99729, -.0735646, .290285, -.95694,
74     .575808, .817585, .757209, .653173, .903989, .427555, -.995185, .0980171,
75     -.903989, .427555, -.844854, .534998, -.707107, -.707107, -.92388, .382683,
76     -.653173, -.757209, -.881921, -.471397, -.219101, .975702, -.595699, .803208,
77     .0980171, -.995185, -.788346, .615232, -.0980171, -.995185, -.985278, .170962,
78     .122411, .99248, -.449611, -.893224, .170962, -.985278, .788346, .615232,
79     -.492898, .870087, .671559, -.740951, .449611, -.893224, -.757209, .653173,
80     .83147, .55557, -.290285, -.95694, -.932993, .359895, -.870087, -.492898,
81     .266713, -.963776, -.881921, .471397, -.77301, .634393, -.471397, .881921,
82     .844854, -.534998, .707107, .707107, .534998, -.844854, .514103, .857729,
83     .14673, -.989177, .980785, .19509, -.122411, .99248, -.449611, .893224,
84     .995185, -.0980171, -.634393, -.77301, .857729, .514103, .55557, .83147,
85     -.92388, -.382683, -.844854, -.534998, -.963776, .266713, .989177, -.14673,
86     .313682, -.949528, .359895, .932993, .24298, .970031, -.949528, -.313682,
87     .932993, -.359895, .55557, -.83147, .615232, .788346, -.788346, -.615232,
88     -.0245412, -.999699, -.219101, -.975702, .788346, -.615232, -.99248, .122411,
89     -.671559, .740951, -.870087, .492898, .970031, .24298, .881921, .471397,
90     .122411, -.99248, .471397, -.881921, .19509, .980785, -.963776, -.266713,
91     .92388, -.382683, .989177, .14673, -.575808, -.817585, .219101, .975702,
92     -.0490677, -.998795, -.980785, -.19509, .949528, .313682, .653173, -.757209,
93     };
94    
95 root 1.4 // http://www-wales.ch.cam.ac.uk/~wales/CCD/Thomson/table.html, random permutation
96 root 1.6 // used as gradient vectors for noise3d
97 root 1.8 static const float charges3[256][3] = {
98 root 1.4 6.32096444e-01, -6.11406706e-01, 4.76062943e-01, 5.19172442e-01, 8.08229585e-01, -2.77893708e-01,
99     -8.81072422e-01, -4.68301230e-01, 6.63727731e-02, -1.92122323e-01, 9.81341519e-01, -7.60505942e-03,
100     -2.57478265e-01, 9.34157733e-01, -2.47091628e-01, 8.75501090e-01, -1.48087600e-01, -4.59965112e-01,
101     -6.44086082e-01, 3.21868600e-01, 6.93940720e-01, -4.42053435e-01, -1.94962529e-01, -8.75544615e-01,
102     -6.86776297e-01, 5.34610386e-01, -4.92473403e-01, -8.45541961e-01, -2.41708225e-01, 4.76062943e-01,
103     1.87301993e-01, 3.04913657e-01, 9.33780287e-01, -8.21274139e-01, 4.76841979e-01, -3.13257905e-01,
104     1.82393582e-01, 9.78673695e-01, -9.45006918e-02, -5.13996405e-01, 5.64894294e-01, -6.45524695e-01,
105     -2.85987088e-01, -5.27238900e-01, -8.00144067e-01, 3.72992508e-01, 8.73495087e-01, 3.12862464e-01,
106     3.07149790e-02, -1.36108589e-01, 9.90217674e-01, -9.42965190e-01, -1.13726556e-01, 3.12862464e-01,
107     -7.63495246e-01, -8.89713729e-02, -6.39655457e-01, -4.93181655e-01, 3.84537051e-01, -7.80322441e-01,
108     9.59053138e-01, -6.07981062e-03, -2.83160934e-01, 8.47504655e-02, 6.82510620e-01, -7.25945323e-01,
109     2.72233465e-01, 7.06503091e-01, 6.53255175e-01, -6.69781595e-01, 6.75521448e-01, -3.08323512e-01,
110     -9.83646297e-01, 1.64266522e-01, -7.38679386e-02, -1.33230986e-01, 4.14543427e-02, 9.90217674e-01,
111     -9.68112521e-01, -2.24691711e-01, 1.10778074e-01, 2.60286884e-01, 5.44444585e-01, -7.97390012e-01,
112     -9.59533574e-01, 4.55017306e-02, -2.77893708e-01, 6.34082129e-01, 7.69729420e-01, -7.38679387e-02,
113     8.71590956e-01, -4.57032412e-01, -1.77343115e-01, -5.65998169e-01, -6.84162385e-01, -4.59965112e-01,
114     1.31348131e-01, -9.34573215e-01, 3.30636620e-01, 9.37743461e-01, -2.44096148e-01, -2.47091628e-01,
115     -2.32019785e-03, -9.49665258e-01, -3.13257905e-01, 5.58257270e-01, -6.92564967e-01, -4.56839782e-01,
116     5.79609682e-01, 2.34839316e-01, -7.80322441e-01, 5.21842141e-02, 4.80310769e-01, -8.75544615e-01,
117     5.48696303e-01, -4.14651366e-01, -7.25945323e-01, -5.13713359e-02, -3.67059868e-01, 9.28777712e-01,
118     -8.31597157e-01, -5.26303703e-01, -1.77343115e-01, 7.60006362e-01, -6.75440951e-02, -6.46396260e-01,
119     -6.35840799e-01, -7.53287574e-01, 1.68119925e-01, 6.00789426e-01, 3.96860609e-01, 6.93940720e-01,
120     -3.99937982e-02, 9.83336115e-01, -1.77343115e-01, -4.74261299e-01, 8.33604286e-01, -2.83160934e-01,
121     8.74744319e-01, 8.54351386e-02, -4.76993934e-01, 2.64896284e-01, -6.69736874e-01, 6.93745254e-01,
122     -2.24976555e-01, -1.01696579e-01, -9.69042494e-01, 6.08580404e-01, -2.06649545e-01, 7.66110865e-01,
123     -2.32214607e-01, -7.27581091e-01, -6.45524695e-01, -1.14732673e-01, 7.81826288e-01, -6.12849141e-01,
124     -5.46171508e-01, 5.27060305e-01, 6.51079195e-01, 1.70411976e-01, -3.14665113e-01, 9.33780287e-01,
125     -1.14827108e-01, 9.66494440e-01, 2.29571847e-01, 6.62214703e-01, -4.23664923e-01, 6.18045079e-01,
126     3.43568839e-01, 1.39041052e-01, 9.28777712e-01, 2.65015805e-01, 5.00565290e-01, 8.24136526e-01,
127     -4.26259648e-01, -7.20031380e-01, 5.47592480e-01, 7.57191364e-01, -5.91945814e-01, 2.76154652e-01,
128     9.94315593e-01, 4.60290452e-02, 9.60095232e-02, 9.70286575e-01, -1.74010497e-01, 1.68119925e-01,
129     1.34044431e-01, 9.51719864e-01, 2.76154652e-01, -3.21508279e-01, 6.91956864e-01, -6.46396261e-01,
130     -9.15927355e-01, 3.90047734e-01, -9.45507570e-02, -3.57713970e-01, 9.75145600e-03, 9.33780287e-01,
131     4.58799092e-01, -6.16720593e-01, -6.39655457e-01, -4.06287592e-01, 9.10837959e-01, -7.28327195e-02,
132     7.69084079e-01, -2.21547533e-01, 5.99521785e-01, 4.32966564e-02, -7.18729210e-01, 6.93940720e-01,
133     7.91803580e-01, -4.28020920e-01, 4.35712270e-01, 3.04696154e-01, 7.05691965e-01, -6.39655457e-01,
134     6.46420856e-01, 4.00281039e-01, -6.49549973e-01, 8.31864266e-01, -3.69542234e-01, -4.14053595e-01,
135     8.23594337e-01, 4.72823279e-01, -3.13257905e-01, -5.85665015e-01, -8.07274355e-01, -7.28327193e-02,
136     -5.65385161e-02, -4.32158277e-01, -9.00023678e-01, 2.06686552e-01, -8.22754465e-01, 5.29486316e-01,
137     8.65928642e-01, 3.96271834e-01, 3.05182275e-01, 1.87431189e-02, 4.56064322e-01, 8.89749419e-01,
138     -5.94715001e-01, -2.32669312e-01, 7.69531714e-01, 5.99595825e-01, 1.59473663e-02, -8.00144067e-01,
139     9.58599657e-02, 6.31372955e-01, 7.69531714e-01, 3.20650220e-01, 8.29747462e-01, -4.56839782e-01,
140     -3.13608737e-01, 5.11291534e-01, -8.00144067e-01, -8.67906788e-01, 4.85339988e-01, 1.05749252e-01,
141     3.22455909e-01, 9.12507983e-01, -2.51696976e-01, 5.15563696e-01, 7.07202113e-01, -4.83796700e-01,
142     7.50491607e-01, -5.66571271e-01, -3.40234247e-01, -2.58299208e-01, -3.23551155e-01, -9.10272580e-01,
143     3.49564167e-01, -9.33995942e-01, -7.38679386e-02, 4.02529304e-01, 1.67115347e-01, -9.00023678e-01,
144     9.45927846e-01, -3.24287947e-01, -7.60505937e-03, -4.04334848e-01, -2.11800144e-01, 8.89749419e-01,
145     3.41359400e-01, -4.97637347e-01, -7.97390012e-01, 7.43690080e-01, 5.81037425e-01, 3.30636620e-01,
146     -8.15869544e-01, 2.32381428e-01, 5.29486316e-01, -2.73993936e-01, -4.03941386e-01, 8.72787878e-01,
147     -1.14485896e-01, -9.85759380e-01, -1.23172337e-01, -6.69863977e-01, 3.59676363e-01, -6.49549972e-01,
148     -7.96449717e-01, 5.92027384e-01, -1.23172337e-01, -6.19715090e-01, -4.90274553e-01, -6.12849141e-01,
149     -8.65910917e-01, -3.66659161e-01, -3.40234247e-01, 8.46096973e-01, -5.28880485e-01, 6.63727731e-02,
150     -8.91235794e-01, -3.59774050e-01, 2.76154652e-01, 4.20417732e-01, 3.46935142e-01, 8.38382334e-01,
151     -6.38459078e-01, 7.23512413e-01, 2.62487703e-01, -7.53805524e-01, -6.57053571e-01, -7.60505938e-03,
152     4.47561005e-01, 5.64275348e-01, 6.93745254e-01, 3.49754488e-02, 9.97181715e-01, 6.63727730e-02,
153     -1.28749619e-01, -5.72643486e-01, 8.09631381e-01, -6.36032129e-01, -6.58092804e-01, 4.02960285e-01,
154     -5.37020119e-01, 8.38088040e-01, 9.60095232e-02, -8.78907490e-01, -1.37182495e-01, -4.56839782e-01,
155     -9.33228374e-01, 1.34065997e-01, 3.33333333e-01, 6.80411181e-01, 5.47277055e-01, -4.87368906e-01,
156     -7.12457289e-01, 1.05461526e-01, 6.93745254e-01, 2.30586085e-01, 3.30051738e-01, -9.15366543e-01,
157     2.34431211e-02, -7.59957402e-01, -6.49549973e-01, -6.98011937e-01, -3.61662294e-01, 6.18045079e-01,
158     8.59171516e-01, 2.05105173e-01, 4.68781584e-01, 7.11862181e-01, 6.90797320e-01, 1.26693714e-01,
159     -2.12826534e-01, 4.39256402e-01, 8.72787878e-01, -3.62298594e-01, -9.25543476e-01, -1.10040912e-01,
160     -3.63383159e-01, -8.00268371e-01, -4.76993934e-01, -7.76145796e-01, 5.51780285e-01, 3.05182275e-01,
161     -1.92676248e-01, 7.76820116e-01, 5.99521785e-01, -9.19690664e-01, 2.65359911e-01, -2.89401453e-01,
162     -2.52247996e-02, 8.99732475e-01, 4.35712270e-01, 7.52676085e-01, 4.12472645e-01, 5.13171539e-01,
163     -1.19598027e-01, -8.62070913e-01, -4.92473403e-01, 9.40191063e-01, -1.58443230e-02, 3.40278890e-01,
164     -9.89903836e-01, 3.37653035e-02, 1.37660085e-01, 3.00994355e-01, -4.79793064e-01, 8.24136526e-01,
165     4.35219899e-01, 8.98427220e-01, -5.84137724e-02, -9.54179119e-01, 2.71092073e-01, 1.26693714e-01,
166     9.02457799e-02, -5.37560007e-01, 8.38382334e-01, -9.58991702e-02, 9.05186704e-01, -4.14053596e-01,
167     -8.97828463e-02, -9.48052118e-01, 3.05182275e-01, -7.79595183e-01, -5.82690413e-01, 2.29571847e-01,
168     -6.01646284e-01, -4.68072388e-02, -7.97390012e-01, -6.80265196e-01, -6.90061585e-01, -2.47091628e-01,
169     6.89653756e-01, 6.63795523e-01, -2.89401453e-01, -7.35965096e-01, -5.35644470e-01, -4.14053595e-01,
170     -4.83817118e-01, -8.06307183e-01, 3.40278890e-01, -2.51959468e-01, -8.46616946e-01, 4.68781584e-01,
171     2.89467531e-01, 9.50755892e-01, 1.10778074e-01, -4.31548997e-01, 3.97822184e-01, 8.09631381e-01,
172     1.03460411e-01, 8.29768433e-01, -5.48434400e-01, -7.70330748e-01, -3.25284873e-01, -5.48434400e-01,
173     4.75732892e-01, -5.89012642e-01, 6.53255175e-01, -4.56373945e-01, 8.22151506e-01, 3.40278890e-01,
174     -7.47966357e-01, -1.17490449e-01, 6.53255175e-01, -4.84791839e-01, -8.27524476e-01, -2.83160934e-01,
175     -8.75038211e-01, 3.53535790e-01, 3.30636620e-01, 4.09353123e-01, -6.19180984e-02, -9.10272580e-01,
176     -9.95670746e-01, -7.23021212e-02, -5.84137724e-02, -4.57295474e-01, -8.84117086e-01, 9.60095233e-02,
177     -8.64280276e-02, -6.19376367e-01, -7.80322441e-01, 2.44164564e-02, 2.45683701e-01, -9.69042494e-01,
178     8.94422292e-01, -3.83804027e-01, 2.29571847e-01, -8.62566691e-01, 4.52816156e-03, 5.05923116e-01,
179     9.19909533e-01, 2.42287152e-01, -3.08323512e-01, -4.01126232e-01, 3.46675383e-02, -9.15366543e-01,
180     9.51367455e-01, 2.99880902e-01, 7.05082324e-02, -5.61852646e-01, 1.73058019e-01, -8.08932956e-01,
181     5.60450847e-01, -8.26125099e-01, -5.84137724e-02, -4.83253958e-01, -4.23721318e-01, 7.66110865e-01,
182     -1.91262533e-02, -8.58072933e-01, 5.13171539e-01, 4.27361843e-01, -7.49268748e-01, 5.05923116e-01,
183     8.06374324e-01, 3.27460527e-01, -4.92473403e-01, -3.49075205e-01, -5.94876216e-01, 7.24064077e-01,
184     1.70540147e-01, -3.64719277e-01, -9.15366543e-01, -9.51483049e-01, -1.76998983e-01, -2.51696976e-01,
185     -3.34445776e-01, 9.27298072e-01, 1.68119925e-01, -2.58769450e-02, -2.24111854e-01, -9.74219821e-01,
186     3.50509628e-01, -8.75232478e-01, 3.33333333e-01, -5.11361160e-01, 7.14833233e-01, -4.76993934e-01,
187     2.13445517e-01, 8.53114931e-01, 4.76062943e-01, -7.35388206e-01, 6.73967933e-01, 7.05082324e-02,
188     -5.10663512e-01, 1.90624866e-01, 8.38382334e-01, 2.07025032e-01, 8.96458354e-02, -9.74219821e-01,
189     2.30036908e-01, -9.29155434e-01, -2.89401453e-01, -4.38498083e-01, -6.24412769e-01, -6.46396260e-01,
190     7.56359490e-01, -6.47294323e-01, -9.45006918e-02, -7.33549832e-01, 4.45600288e-01, 5.13171539e-01,
191     5.69972682e-01, -7.59768531e-01, 3.12862464e-01, 1.36366351e-02, -9.94299320e-01, 1.05749252e-01,
192     -1.20108971e-01, 6.12129242e-01, -7.81582770e-01, -6.20394866e-01, 7.76531524e-01, -1.10040912e-01,
193     3.85591729e-01, -2.44264178e-01, 8.89749420e-01, -8.14161423e-01, 3.15614840e-01, -4.87368906e-01,
194     1.15419311e-01, 9.33230432e-01, -3.40234248e-01, 5.90173960e-01, -2.02047201e-01, -7.81582770e-01,
195     8.54270153e-01, 5.08959332e-01, 1.05749252e-01, 7.95754924e-01, 5.98192490e-01, -9.45507571e-02,
196     3.54673147e-01, -8.00092315e-01, -4.83796700e-01, 9.91952607e-01, -1.03563604e-01, -7.28327194e-02,
197     -6.21935152e-02, 2.58972647e-01, 9.63880249e-01, -3.09502921e-01, 8.32249985e-01, -4.59965112e-01,
198     4.65710308e-01, -8.74164521e-01, 1.37660085e-01, 1.33750242e-01, -8.62891895e-01, -4.87368906e-01,
199     -2.51909022e-01, 8.79866384e-01, 4.02960285e-01, -6.67371446e-11, -8.00239945e-11, -1.00000000e+00,
200     -5.76407831e-01, -5.55272584e-01, 5.99521785e-01, -4.70064989e-01, -4.10082041e-01, -7.81582770e-01,
201     8.36695291e-01, -9.13599363e-03, 5.47592480e-01, 5.24193529e-01, 8.40399218e-01, 1.37660085e-01,
202     2.48438744e-01, -7.05895175e-01, -6.63317565e-01, 1.20172431e-01, -9.88240224e-01, -9.45507569e-02,
203     4.30798964e-01, 4.00049655e-01, -8.08932956e-01, -2.50127938e-01, -9.17808600e-01, -3.08323512e-01,
204     6.09182992e-01, 5.90373037e-01, 5.29486316e-01, -3.40640313e-01, 5.99746104e-01, 7.24064077e-01,
205     4.40361132e-01, -8.53731316e-01, -2.77893708e-01, -1.83361859e-01, -7.36528553e-01, 6.51079195e-01,
206     9.82693460e-01, 1.49011952e-01, -1.10040912e-01, 6.29027140e-01, -7.35509000e-01, -2.51696976e-01,
207     -8.70236843e-01, 9.28902018e-02, -4.83796700e-01, 9.45809668e-01, 1.91165575e-01, 2.62487703e-01,
208     2.00560098e-01, -1.43987122e-01, -9.69042494e-01, 1.02516007e-01, 9.46542469e-02, 9.90217674e-01,
209     -6.07212048e-01, 6.41511773e-01, 4.68781584e-01, 2.42316938e-01, -9.61889393e-01, 1.26693714e-01,
210     4.87103783e-01, 5.68101851e-01, -6.63317565e-01, -9.38753073e-01, -3.31379371e-01, -9.45006918e-02,
211     3.89869221e-01, -2.85348240e-01, -8.75544615e-01, -6.33446768e-01, -2.67859254e-01, -7.25945323e-01,
212     5.82718746e-01, 7.41166481e-01, 3.33333333e-01, 6.66870337e-01, -5.04483561e-01, -5.48434400e-01,
213     7.34447763e-01, -2.91551734e-01, -6.12849141e-01, 9.10935613e-01, 3.93731996e-01, -1.23172337e-01,
214     3.57972341e-02, 7.85327217e-01, 6.18045079e-01, -2.92197503e-01, 2.28018816e-01, 9.28777712e-01
215     -1.93180133e-01, -1.83347487e-01, 9.63880249e-01, -2.15979248e-01, -9.73848835e-01, 7.05082325e-02,
216     8.87941151e-01, -2.21773580e-01, 4.02960285e-01, 6.89715518e-01, -4.86988739e-03, 7.24064077e-01,
217     -4.10435643e-01, 7.29167374e-01, 5.47592480e-01, 7.46211012e-01, 1.62686797e-01, -6.45524695e-01,
218     -1.81148087e-01, 1.34466019e-01, -9.74219821e-01, -7.66578780e-01, -4.71711555e-01, 4.35712270e-01,
219     -5.66010160e-01, -2.07722258e-02, 8.24136526e-01, 7.29533368e-01, 2.09468249e-01, 6.51079195e-01,
220     -3.45990788e-01, 2.65042929e-01, -9.00023678e-01, -7.35542526e-01, 1.37793324e-01, -6.63317565e-01,
221     -1.25326447e-01, 6.30370863e-01, 7.66110865e-01, 1.31053682e-01, -5.73107674e-01, -8.08932955e-01,
222     4.86820470e-01, -3.53150162e-02, 8.72787878e-01, 4.35204849e-01, 7.44740586e-01, 5.05923116e-01,
223     4.98855035e-01, -3.98703643e-01, 7.69531714e-01, 2.55373649e-01, -7.56251592e-02, 9.63880249e-01,
224     -1.51053916e-01, 3.85469253e-01, -9.10272580e-01, 6.78644990e-01, -7.26064181e-01, 1.10778074e-01,
225     -3.07350590e-01, -9.14677987e-01, 2.62487703e-01, 5.60298616e-01, 1.74821302e-01, 8.09631381e-01,
226     };
227    
228 root 1.6 /////////////////////////////////////////////////////////////////////////////
229    
230     template<int N, typename T>
231     void
232 root 1.12 permutation<N,T>::seed (seedable_rand_gen &rng)
233 root 1.6 {
234     for (int i = 0; i < N; ++i)
235     pmap[i] = i;
236    
237     // fisher-yates to randomly perturb
238     for (int i = N; --i; )
239     ::swap (pmap[i], pmap[rng (i + 1)]);
240     }
241    
242     template class permutation<256, uint8_t>;
243    
244     /////////////////////////////////////////////////////////////////////////////
245    
246 root 1.12 // various s-shaped curves, smooth to, first, or second derivative
247     // used for smooth interpolation from 0..1
248    
249     // linear
250     template<typename T>
251     inline T
252     sigmoid0 (T x)
253     {
254     return x;
255     }
256    
257     // 3x²-2x³
258     template<typename T>
259     inline T
260     sigmoid1 (T x)
261     {
262     return (3 - 2 * x) * x * x;
263     }
264    
265     // 6x⁵ - 15x⁴ + 10x³
266     template<typename T>
267     inline T
268     sigmoid2 (T x)
269     {
270     #ifdef MORE_PARALLELITY
271     float x2 = x * x;
272     float x4 = x2 * x2;
273    
274     return (6 * x4 + 10 * x2) * x - 15 * x4;
275     #endif
276    
277     // simple horner
278     return ((6 * x - 15) * x + 10) * x * x * x;
279     }
280    
281     // blend between a and b
282     // c is the control function - if lower than ca
283     // then return a, if higher than cb, return b
284     template<typename T, typename U>
285     inline T
286     blend (T a, T b, U c, U ca, U cb, T weight (U) = sigmoid1)
287     {
288     if (c <= ca) return a;
289     if (c >= cb) return b;
290    
291     T w = weight (lerp (c, ca, cb, T(0), T(1)));
292     return (T(1) - w) * a + w * b;
293     }
294    
295     // blend between a and b
296     // c is the control function - if lower than -c_w
297     // then return a, if higher than +c_w then b.
298     template<typename T, typename U>
299     inline T
300     blend0 (T a, T b, U c, U c_w, T weight (U) = sigmoid1)
301     {
302     return blend<T,U> (a, b, c, -c_w, c_w, weight);
303     }
304    
305     /////////////////////////////////////////////////////////////////////////////
306    
307 root 1.4 static vec2d
308     floor (vec2d v)
309     {
310 root 1.12 return vec2d (fastfloor (v[0]), fastfloor (v[1]));
311 root 1.4 }
312    
313     static vec3d
314     floor (vec3d v)
315     {
316 root 1.12 return vec3d (fastfloor (v[0]), fastfloor (v[1]), fastfloor (v[2]));
317 root 1.4 }
318    
319 root 1.12 template<class vec_t>
320     void
321     noise_gen_base<vec_t>::seed (seedable_rand_gen &rng)
322     {
323     for (int i = 0; i < array_length (rvmap); ++i)
324     rvmap[i].seed (rng);
325     }
326    
327     template<class vec_t>
328     void
329     noise_gen_base<vec_t>::seed (seed_t seed)
330 root 1.1 {
331     seedable_rand_gen rng (seed);
332    
333 root 1.12 this->seed (rng);
334 root 1.1 }
335    
336 root 1.12 template<>
337 root 1.4 vec2d::T_numtype
338 root 1.12 noise_gen_base<vec2d>::operator() (vec2d P)
339 root 1.1 {
340 root 1.4 vec2d I = floor (P);
341     vec2d F = P - I;
342 root 1.1
343     float v = 0;
344    
345     for (int j = -1; j <= 2; ++j)
346     for (int i = -1; i <= 2; ++i)
347     {
348 root 1.4 vec2d A = F - vec2d (i, j);
349 root 1.1
350 root 1.4 float d = dot (A, A);
351    
352 root 1.1 if (d < 4)
353     {
354     float t1 = 1 - d / 4;
355     float t2 = t1 * t1;
356     float t4 = t2 * t2;
357    
358     float p = (4 * t1 - 3) * t4;
359 root 1.3
360 root 1.8 int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j);
361     vec2d G = charges2[h & 0xff];
362 root 1.2
363 root 1.4 v += dot (A, G) * p;
364 root 1.2 }
365     }
366 root 1.4
367 root 1.12 return v;
368 root 1.2 }
369    
370     /////////////////////////////////////////////////////////////////////////////
371    
372 root 1.12 template<>
373 root 1.4 vec3d::T_numtype
374 root 1.12 noise_gen_base<vec3d>::operator() (vec3d P)
375 root 1.2 {
376 root 1.4 vec3d I = floor (P);
377     vec3d F = P - I;
378 root 1.2
379     float v = 0;
380    
381     for (int j = -1; j <= 2; ++j)
382     for (int i = -1; i <= 2; ++i)
383     for (int k = -1; k <= 2; ++k)
384     {
385 root 1.4 vec3d A = F - vec3d (i, j, k);
386     float d = dot (A, A);
387 root 1.2
388     if (d < 4)
389     {
390     float t1 = 1 - d / 4;
391     float t2 = t1 * t1;
392     float t4 = t2 * t2;
393    
394     // (4t⁵ - 3t⁴)
395     float p = (4 * t1 - 3) * t4;
396 root 1.4
397     int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k);
398 root 1.8 const float *G = charges3[h & 0xff];
399 root 1.4
400     v += dot (A, vec3d (G[0], G[1], G[2])) * p;
401 root 1.2 }
402     }
403    
404 root 1.12 return v * 2;
405 root 1.2 }
406    
407 root 1.4 vec3d::T_numtype
408     noise_gen<vec3d>::operator() (vec3d P, vec3d N)
409 root 1.2 {
410 root 1.4 vec3d I = floor (P);
411     vec3d F = P - I;
412 root 1.2
413     float v = 0;
414    
415     for (int j = -1; j <= 2; ++j)
416     for (int i = -1; i <= 2; ++i)
417     for (int k = -1; k <= 2; ++k)
418     {
419 root 1.4 vec3d D = F - vec3d (i, j, k);
420     float e = dot (D, N);
421 root 1.2 float o = 1 - abs (e);
422    
423     if (o > 0)
424     {
425 root 1.4 vec3d A = D - e * N;
426     float d = dot (A, A);
427 root 1.2
428     if (d < 4)
429     {
430     float t1 = 1 - d / 4;
431     float t2 = t1 * t1;
432     float t4 = t2 * t2;
433    
434     float o2 = o * o;
435    
436     // (4t⁵ - 3t⁴) * (3o³ - 2o²)
437 root 1.4 // alternative? ((o * 6 - 15) * o + 10) * o³
438 root 1.2 float p = (4 * t1 - 3) * t4 * (3 * o2 - 2 * o2 * o);
439 root 1.4
440     int h = rvmap[0](I[0] + i) ^ rvmap[1](I[1] + j) ^ rvmap[2](I[2] + k);
441 root 1.8 const float *G = charges3[h & 0xff];
442 root 1.4
443     v += dot (A, vec3d (G[0], G[1], G[2])) * p;
444 root 1.2 }
445     }
446     }
447    
448 root 1.12 return v;
449 root 1.4 }
450    
451     template class noise_gen<vec2d>;
452     template class noise_gen<vec3d>;
453    
454     /////////////////////////////////////////////////////////////////////////////
455    
456 root 1.8 // find some uncorrelated spot - we assume that noise 2 units away
457     // is completely uncorrelated - this is not true for other coordinates,
458     // but generally works well.
459 root 1.4 template<class vec_t>
460     static vec_t
461     ith_octave (vec_t P, int i)
462     {
463     vec_t r = P;
464     r[0] += i;
465 root 1.8 r[1] += i * 2;
466 root 1.4 return r;
467 root 1.2 }
468    
469 root 1.4 template<class vec_t>
470 root 1.12 frac_gen<vec_t>::frac_gen (value_t hurst_expo, value_t lacunarity, seed_t seed)
471     : h (hurst_expo), lac (lacunarity)
472 root 1.1 {
473 root 1.12 this->seed (seed);
474    
475 root 1.4 value_t exsum = 0;
476 root 1.8 value_t phi = noise (vec_t (value_t (0))) * 0.5 + 1;
477 root 1.1
478     for (int i = 0; i < MAX_OCTAVES; ++i)
479     {
480 root 1.8 ex [i] = pow (lac, -h * i);
481 root 1.1 exsum += ex [i];
482 root 1.8 fbm_mul [i] = 0.5 / (exsum * 0.75); // .75 is a heuristic
483     rot [i].set (phi * i + 1);
484 root 1.1 }
485     }
486    
487 root 1.4 template<class vec_t>
488     typename frac_gen<vec_t>::value_t
489     frac_gen<vec_t>::fBm (vec_t P, int octaves)
490 root 1.1 {
491 root 1.8 value_t v = 0;
492 root 1.1
493     for (int i = 0; i < octaves; ++i)
494     {
495 root 1.4 rot [i](P);
496     v += noise (ith_octave (P, i)) * ex [i];
497     P *= lac;
498 root 1.1 }
499    
500 root 1.12 return v * fbm_mul [octaves - 1];
501 root 1.1 }
502    
503 root 1.4 template<class vec_t>
504     typename frac_gen<vec_t>::value_t
505     frac_gen<vec_t>::turbulence (vec_t P, int octaves)
506 root 1.1 {
507 root 1.8 value_t v = 0;
508 root 1.1
509     for (int i = 0; i < octaves; ++i)
510     {
511 root 1.4 rot [i](P);
512     v += abs (noise (ith_octave (P, i))) * ex [i];
513     P *= lac;
514 root 1.1 }
515    
516 root 1.12 return v * fbm_mul [octaves - 1] * (0.5 / noise_gen<vec_t>::abs_avg ());
517 root 1.1 }
518    
519 root 1.4 template<class vec_t>
520     typename frac_gen<vec_t>::value_t
521     frac_gen<vec_t>::multifractal (vec_t P, int octaves, value_t offset)
522 root 1.1 {
523 root 1.8 value_t v = 1;
524 root 1.1
525     for (int i = 0; i < octaves; ++i)
526     {
527 root 1.4 rot [i](P);
528     v *= noise (P) * ex [i] + offset;
529     P *= lac;
530 root 1.1 }
531    
532 root 1.12 return v * value_t (0.5);
533 root 1.1 }
534    
535 root 1.4 template<class vec_t>
536     typename frac_gen<vec_t>::value_t
537     frac_gen<vec_t>::heterofractal (vec_t P, int octaves, value_t offset)
538 root 1.1 {
539 root 1.4 value_t v = noise (P) + offset;
540 root 1.1
541 root 1.8 for (int i = 1; i < octaves; ++i)
542 root 1.1 {
543 root 1.4 rot [i](P);
544     P *= lac;
545     v += v * (noise (P) * ex [i] + offset);
546 root 1.1 }
547    
548 root 1.8 return v / (1 << octaves);
549 root 1.1 }
550    
551 root 1.4 template<class vec_t>
552     typename frac_gen<vec_t>::value_t
553     frac_gen<vec_t>::hybridfractal (vec_t P, int octaves, value_t offset, value_t gain)
554 root 1.1 {
555 root 1.4 value_t v = (noise (P) + offset) * ex [0];
556     value_t weight = v;
557 root 1.1
558 root 1.8 for (int i = 1; i < octaves; ++i)
559 root 1.1 {
560 root 1.4 rot [i](P);
561     P *= lac;
562 root 1.1
563 root 1.8 min_it (weight, 1);
564 root 1.1
565 root 1.4 value_t sig = (noise (P) + offset) * ex [i];
566 root 1.1 v += weight * sig;
567     weight *= gain * sig;
568     }
569    
570 root 1.12 return v * value_t (0.5) + value_t (0.5);
571 root 1.1 }
572    
573 root 1.4 template<class vec_t>
574     typename frac_gen<vec_t>::value_t
575     frac_gen<vec_t>::ridgedmultifractal (vec_t P, int octaves, value_t offset, value_t gain)
576     {
577     value_t sig = offset - abs (noise (P));
578     sig *= sig;
579     value_t v = sig;
580    
581     for (int i = 1; i < octaves; ++i)
582     {
583     rot [i](P);
584     P *= lac;
585    
586 root 1.8 value_t w = clamp (sig * gain, 0, 1);
587 root 1.4
588     sig = offset - abs (noise (P));
589     sig *= sig;
590     sig *= w;
591    
592     v += sig * ex [i];
593     }
594    
595 root 1.12 return v * value_t (0.25);
596 root 1.8 }
597    
598     template<class vec_t>
599     typename frac_gen<vec_t>::value_t
600     frac_gen<vec_t>::billowfractal (vec_t P, int octaves, value_t offset, value_t gain)
601     {
602     value_t v = 0;
603    
604     offset += 2 * noise_gen<vec_t>::abs_avg () - 1;
605    
606     for (int i = 0; i < octaves; ++i)
607     {
608     rot [i](P);
609     v += (abs (noise (ith_octave (P, i))) * gain - offset) * ex [i];
610     P *= lac;
611     }
612    
613 root 1.12 return v;
614 root 1.4 }
615    
616 root 1.1 // http://www.gamasutra.com/view/feature/3098/a_realtime_procedural_universe_.php?page=2
617 root 1.4 template<class vec_t>
618     typename frac_gen<vec_t>::value_t
619     frac_gen<vec_t>::terrain (vec_t P, int octaves)
620 root 1.1 {
621 root 1.8 value_t v = 0;
622 root 1.1
623     for (int i = 0; i < octaves; ++i)
624     {
625 root 1.4 rot [i](P);
626     v += noise (P) * ex [i];
627     P *= lac;
628 root 1.1 }
629    
630     v *= fbm_mul [octaves - 1];
631    
632 root 1.8 return v <= 0 ? - pow (-v, 0.7) : pow (v, 1 + noise (P) * v);
633 root 1.1 }
634    
635 root 1.4 template<class vec_t>
636     typename frac_gen<vec_t>::value_t
637     frac_gen<vec_t>::terrain2 (vec_t P, int octaves)
638 root 1.1 {
639 root 1.4 value_t a = fBm (P, octaves);
640     value_t b = ridgedmultifractal (P, octaves, 1, 8);
641     value_t fade = fBm (P + vec_t(10.3), octaves);
642 root 1.1
643 root 1.8 const value_t width = 0.05;
644 root 1.1
645 root 1.8 if (fade > 0.5 + width)
646 root 1.1 return a;
647 root 1.8 else if (fade < 0.5 - width)
648 root 1.1 return b;
649    
650 root 1.8 fade = (fade - 0.5 + width) / (width * 2);
651 root 1.1
652     // sigmoidal curve
653 root 1.8 fade = fade * fade * 2 * (1.5 - fade);
654 root 1.1
655     return a * fade + b * (1 - fade);
656     }
657    
658 root 1.4 template class frac_gen<vec2d>;
659     template class frac_gen<vec3d>;
660 root 1.1
661 root 1.4 /////////////////////////////////////////////////////////////////////////////
662 root 1.1
663 root 1.7 void noise_test ();
664     void noise_test ()
665 root 1.1 {
666 root 1.12 frac_gen<vec2d> gen;
667 root 1.4 frac_gen<vec3d> gen3;
668 root 1.1
669 root 1.7 #if 1
670 root 1.1 int N = 1024;
671    
672 root 1.3 printf ("P5 %d %d 255\n", N, N);
673 root 1.1 // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm
674     for (int y = 0; y < N; ++y)
675     {
676     if (!(y&63))fprintf (stderr, "y %d\n", y);//D
677     for (int x = 0; x < N; ++x)
678     {
679 root 1.12 vec2d P = vec2d (x, y) * (5000.f / N);
680    
681 root 1.8 //putc (127 * gen.noise (vec2d (x * 0.01, y * 0.01)) + 128, stdout);
682 root 1.2 //putc (256 * gen.terrain2 (x * 0.004, y * 0.004, 8), stdout);
683 root 1.8 //putc (256 * gen.fBm (vec2d(x * 0.01, y * 0.01), 16), stdout);
684 root 1.12 //putc (256 * gen.turbulence (vec2d (x * 0.004 - 1, y * 0.004 - 1), 10), stdout);
685 root 1.8 //putc (256 * gen.heterofractal (vec2d (x * 0.008, y * 0.008), 8, 0.9), stdout);
686 root 1.4
687     // mountais or somesuch(?)
688 root 1.8 //putc (256 * gen.hybridfractal (vec2d (x * 0.01, y * 0.01), 8, -.4, -4), stdout);
689 root 1.4
690     // temperature
691 root 1.8 //putc (256 * gen.fBm (vec2d (x * 0.002, y * 0.002), 2), stdout);
692 root 1.4 // rain
693 root 1.7
694 root 1.12 float continent = gen.fBm (P * 0.0004, 12) + 0.1f;
695     float mountain = gen.ridgedmultifractal (P * 0.004, 8, 0.8, 10) * 2;
696     float river = gen.ridgedmultifractal (P * 0.004, 3, 0.8, 10);
697     float sel1 = gen.noise (P * 0.001 + vec2d (5,0));
698    
699     {
700     const float W = 100;
701     const float N = 5000 - 1;
702    
703     float border = W; // within n places of the border
704    
705     min_it (border, P [0]);
706     min_it (border, N - P [0]);
707     min_it (border, P [1]);
708     min_it (border, N - P [1]);
709    
710     continent = blend (-1.f, continent, border, 0.f, W);
711     }
712    
713     //float v = blend (mountain, 0.f, river + sel1 * 0.2f, 0.25f, 0.1f);
714     float v = blend0 (0.f, 1.f, continent, 0.05f);
715    
716    
717     putc (255 * clamp (v, 0.f, 1.f), stdout);
718 root 1.9
719 root 1.7 //cells
720 root 1.8 //putc (127.49 * gen.billowfractal (vec2d (x * 0.01, y * 0.01), 9) + 128, stdout);
721 root 1.1 }
722     }
723 root 1.2 #else
724 root 1.4 int N = 512;
725 root 1.2
726     //printf ("P6 %d %d 255\n", N, N);
727     // pmake&&server/deliantra-server >x&&convert -depth 8 -size 512xx512 gray:x x.ppm&& cv x.ppm
728     for (int z = 0; z < N; ++z)
729     {
730 root 1.4 if (!(z&7))fprintf (stderr, "z %d\n", z);//D
731 root 1.2 for (int y = 0; y < N; ++y)
732     for (int x = 0; x < N; ++x)
733     {
734 root 1.4 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;
735 root 1.2
736 root 1.4 #if 0
737 root 1.2 if (z < 64)
738     v = v * (z * z) / (64 * 64);
739 root 1.4 #endif
740 root 1.2
741 root 1.4 if (v <= 0.9999)
742 root 1.2 continue;
743    
744     float r[4];
745     int i[4];
746    
747     r[0] = x;
748     r[1] = y;
749     r[2] = z;
750     r[3] = v;
751    
752     memcpy (i, r, 16);
753    
754     i[0] = htonl (i[0]);
755     i[1] = htonl (i[1]);
756     i[2] = htonl (i[2]);
757     i[3] = htonl (i[3]);
758    
759     fwrite (i, 4*4, 1, stdout);
760     }
761     }
762     #endif
763 root 1.1
764     exit (0);
765     }