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* 関数体操 [#g78bec5f] &ref(https://pbs.twimg.com/media/DWXPRDdVAAAU38j.jpg:large); * Links [#v1d57db0] - [[行列計算:http://matrixmultiplication.xyz/]] - [[Microsoft Mathematics:https://www.microsoft.com/ja-jp/download/details.aspx?id=15702]] * WolframAlpha [#r19b781e] http://www.wolframalpha.com/ * 関数グラフアート全国コンテスト [#m0e3c4d4] http://www.ge.fukui-nct.ac.jp/~math/graph_art/ * 読めば必ずわかる分散分析の基礎 [#b353c903] http://elsur.jpn.org/resource/anova.pdf * パーリンノイズ [#r40568ee] http://mrl.nyu.edu/~perlin/noise/ // JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN. public final class ImprovedNoise { static public double noise(double x, double y, double z) { int X = (int)Math.floor(x) & 255, // FIND UNIT CUBE THAT Y = (int)Math.floor(y) & 255, // CONTAINS POINT. Z = (int)Math.floor(z) & 255; x -= Math.floor(x); // FIND RELATIVE X,Y,Z y -= Math.floor(y); // OF POINT IN CUBE. z -= Math.floor(z); double u = fade(x), // COMPUTE FADE CURVES v = fade(y), // FOR EACH OF X,Y,Z. w = fade(z); int A = p[X ]+Y, AA = p[A]+Z, AB = p[A+1]+Z, // HASH COORDINATES OF B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z; // THE 8 CUBE CORNERS, return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), // AND ADD grad(p[BA ], x-1, y , z )), // BLENDED lerp(u, grad(p[AB ], x , y-1, z ), // RESULTS grad(p[BB ], x-1, y-1, z ))),// FROM 8 lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), // CORNERS grad(p[BA+1], x-1, y , z-1 )), // OF CUBE lerp(u, grad(p[AB+1], x , y-1, z-1 ), grad(p[BB+1], x-1, y-1, z-1 )))); } static double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); } static double lerp(double t, double a, double b) { return a + t * (b - a); } static double grad(int hash, double x, double y, double z) { int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS. v = h<4 ? y : h==12||h==14 ? x : z; return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v); } static final int p[] = new int[512], permutation[] = { 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 }; static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; } } * マンデルブロ集合 [#w81c919f] Z(n+1) = Z(n) * Z(n) + c ただし c = a + ib * ゲルストナー波 [#h9ca4d1d] http://www.fun.ac.jp/~sisp/old_report/2008/08/document08_A.pdf * Verlet(ベルレ)積分 [#bb0112b6] ある瞬間の位置をr0、次の瞬間の位置をr1として、さらに次の瞬間の位置をr2し、r1からr2へ移動する間の加速度の和をatとすると、 r2 = 2 * r1 - r0 + at * フィボナッチ数列 [#f53bb701] 1 1 2 3 5 8 13 21 34 55 89 144 233 377
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* 関数体操 [#g78bec5f] &ref(https://pbs.twimg.com/media/DWXPRDdVAAAU38j.jpg:large); * Links [#v1d57db0] - [[行列計算:http://matrixmultiplication.xyz/]] - [[Microsoft Mathematics:https://www.microsoft.com/ja-jp/download/details.aspx?id=15702]] * WolframAlpha [#r19b781e] http://www.wolframalpha.com/ * 関数グラフアート全国コンテスト [#m0e3c4d4] http://www.ge.fukui-nct.ac.jp/~math/graph_art/ * 読めば必ずわかる分散分析の基礎 [#b353c903] http://elsur.jpn.org/resource/anova.pdf * パーリンノイズ [#r40568ee] http://mrl.nyu.edu/~perlin/noise/ // JAVA REFERENCE IMPLEMENTATION OF IMPROVED NOISE - COPYRIGHT 2002 KEN PERLIN. public final class ImprovedNoise { static public double noise(double x, double y, double z) { int X = (int)Math.floor(x) & 255, // FIND UNIT CUBE THAT Y = (int)Math.floor(y) & 255, // CONTAINS POINT. Z = (int)Math.floor(z) & 255; x -= Math.floor(x); // FIND RELATIVE X,Y,Z y -= Math.floor(y); // OF POINT IN CUBE. z -= Math.floor(z); double u = fade(x), // COMPUTE FADE CURVES v = fade(y), // FOR EACH OF X,Y,Z. w = fade(z); int A = p[X ]+Y, AA = p[A]+Z, AB = p[A+1]+Z, // HASH COORDINATES OF B = p[X+1]+Y, BA = p[B]+Z, BB = p[B+1]+Z; // THE 8 CUBE CORNERS, return lerp(w, lerp(v, lerp(u, grad(p[AA ], x , y , z ), // AND ADD grad(p[BA ], x-1, y , z )), // BLENDED lerp(u, grad(p[AB ], x , y-1, z ), // RESULTS grad(p[BB ], x-1, y-1, z ))),// FROM 8 lerp(v, lerp(u, grad(p[AA+1], x , y , z-1 ), // CORNERS grad(p[BA+1], x-1, y , z-1 )), // OF CUBE lerp(u, grad(p[AB+1], x , y-1, z-1 ), grad(p[BB+1], x-1, y-1, z-1 )))); } static double fade(double t) { return t * t * t * (t * (t * 6 - 15) + 10); } static double lerp(double t, double a, double b) { return a + t * (b - a); } static double grad(int hash, double x, double y, double z) { int h = hash & 15; // CONVERT LO 4 BITS OF HASH CODE double u = h<8 ? x : y, // INTO 12 GRADIENT DIRECTIONS. v = h<4 ? y : h==12||h==14 ? x : z; return ((h&1) == 0 ? u : -u) + ((h&2) == 0 ? v : -v); } static final int p[] = new int[512], permutation[] = { 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 }; static { for (int i=0; i < 256 ; i++) p[256+i] = p[i] = permutation[i]; } } * マンデルブロ集合 [#w81c919f] Z(n+1) = Z(n) * Z(n) + c ただし c = a + ib * ゲルストナー波 [#h9ca4d1d] http://www.fun.ac.jp/~sisp/old_report/2008/08/document08_A.pdf * Verlet(ベルレ)積分 [#bb0112b6] ある瞬間の位置をr0、次の瞬間の位置をr1として、さらに次の瞬間の位置をr2し、r1からr2へ移動する間の加速度の和をatとすると、 r2 = 2 * r1 - r0 + at * フィボナッチ数列 [#f53bb701] 1 1 2 3 5 8 13 21 34 55 89 144 233 377
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