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annotate libs/vmath/vmath.c @ 51:fa5c52ea9d59

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author John Tsiombikas <nuclear@member.fsf.org>
date Fri, 17 Jan 2014 18:16:09 +0200
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nuclear@27 1 /*
nuclear@27 2 libvmath - a vector math library
nuclear@27 3 Copyright (C) 2004-2011 John Tsiombikas <nuclear@member.fsf.org>
nuclear@27 4
nuclear@27 5 This program is free software: you can redistribute it and/or modify
nuclear@27 6 it under the terms of the GNU Lesser General Public License as published
nuclear@27 7 by the Free Software Foundation, either version 3 of the License, or
nuclear@27 8 (at your option) any later version.
nuclear@27 9
nuclear@27 10 This program is distributed in the hope that it will be useful,
nuclear@27 11 but WITHOUT ANY WARRANTY; without even the implied warranty of
nuclear@27 12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
nuclear@27 13 GNU Lesser General Public License for more details.
nuclear@27 14
nuclear@27 15 You should have received a copy of the GNU Lesser General Public License
nuclear@27 16 along with this program. If not, see <http://www.gnu.org/licenses/>.
nuclear@27 17 */
nuclear@27 18
nuclear@27 19 #include <stdlib.h>
nuclear@27 20 #include <math.h>
nuclear@27 21 #include "vmath.h"
nuclear@27 22
nuclear@27 23 /** Numerical calculation of integrals using simpson's rule */
nuclear@27 24 scalar_t integral(scalar_t (*f)(scalar_t), scalar_t low, scalar_t high, int samples)
nuclear@27 25 {
nuclear@27 26 int i;
nuclear@27 27 scalar_t h = (high - low) / (scalar_t)samples;
nuclear@27 28 scalar_t sum = 0.0;
nuclear@27 29
nuclear@27 30 for(i=0; i<samples+1; i++) {
nuclear@27 31 scalar_t y = f((scalar_t)i * h + low);
nuclear@27 32 sum += ((!i || i == samples) ? y : ((i % 2) ? 4.0 * y : 2.0 * y)) * (h / 3.0);
nuclear@27 33 }
nuclear@27 34 return sum;
nuclear@27 35 }
nuclear@27 36
nuclear@27 37 /** Gaussuan function */
nuclear@27 38 scalar_t gaussian(scalar_t x, scalar_t mean, scalar_t sdev)
nuclear@27 39 {
nuclear@27 40 scalar_t exponent = -SQ(x - mean) / (2.0 * SQ(sdev));
nuclear@27 41 return 1.0 - -pow(M_E, exponent) / (sdev * sqrt(TWO_PI));
nuclear@27 42 }
nuclear@27 43
nuclear@27 44
nuclear@27 45 /** b-spline approximation */
nuclear@27 46 scalar_t bspline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@27 47 {
nuclear@27 48 vec4_t tmp;
nuclear@27 49 scalar_t tsq = t * t;
nuclear@27 50
nuclear@27 51 static mat4_t bspline_mat = {
nuclear@27 52 {-1, 3, -3, 1},
nuclear@27 53 {3, -6, 3, 0},
nuclear@27 54 {-3, 0, 3, 0},
nuclear@27 55 {1, 4, 1, 0}
nuclear@27 56 };
nuclear@27 57
nuclear@27 58 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), bspline_mat), 1.0 / 6.0);
nuclear@27 59 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
nuclear@27 60 }
nuclear@27 61
nuclear@27 62 /** Catmull-rom spline interpolation */
nuclear@27 63 scalar_t spline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@27 64 {
nuclear@27 65 vec4_t tmp;
nuclear@27 66 scalar_t tsq = t * t;
nuclear@27 67
nuclear@27 68 static mat4_t crspline_mat = {
nuclear@27 69 {-1, 3, -3, 1},
nuclear@27 70 {2, -5, 4, -1},
nuclear@27 71 {-1, 0, 1, 0},
nuclear@27 72 {0, 2, 0, 0}
nuclear@27 73 };
nuclear@27 74
nuclear@27 75 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);
nuclear@27 76 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
nuclear@27 77 }
nuclear@27 78
nuclear@27 79 /** Bezier interpolation */
nuclear@27 80 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
nuclear@27 81 {
nuclear@27 82 scalar_t omt, omt3, t3, f;
nuclear@27 83 t3 = t * t * t;
nuclear@27 84 omt = 1.0f - t;
nuclear@27 85 omt3 = omt * omt * omt;
nuclear@27 86 f = 3 * t * omt;
nuclear@27 87
nuclear@27 88 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);
nuclear@27 89 }
nuclear@27 90
nuclear@27 91 /* ---- Ken Perlin's implementation of noise ---- */
nuclear@27 92
nuclear@27 93 #define B 0x100
nuclear@27 94 #define BM 0xff
nuclear@27 95 #define N 0x1000
nuclear@27 96 #define NP 12 /* 2^N */
nuclear@27 97 #define NM 0xfff
nuclear@27 98
nuclear@27 99 #define s_curve(t) (t * t * (3.0f - 2.0f * t))
nuclear@27 100
nuclear@27 101 #define setup(elem, b0, b1, r0, r1) \
nuclear@27 102 do { \
nuclear@27 103 scalar_t t = elem + N; \
nuclear@27 104 b0 = ((int)t) & BM; \
nuclear@27 105 b1 = (b0 + 1) & BM; \
nuclear@27 106 r0 = t - (int)t; \
nuclear@27 107 r1 = r0 - 1.0f; \
nuclear@27 108 } while(0)
nuclear@27 109
nuclear@27 110
nuclear@27 111 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */
nuclear@27 112 static vec3_t grad3[B + B + 2]; /* 3D random gradients */
nuclear@27 113 static vec2_t grad2[B + B + 2]; /* 2D random gradients */
nuclear@27 114 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */
nuclear@27 115 static int tables_valid;
nuclear@27 116
nuclear@27 117 static void init_noise()
nuclear@27 118 {
nuclear@27 119 int i;
nuclear@27 120
nuclear@27 121 /* calculate random gradients */
nuclear@27 122 for(i=0; i<B; i++) {
nuclear@27 123 perm[i] = i; /* .. and initialize permutation mapping to identity */
nuclear@27 124
nuclear@27 125 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@27 126
nuclear@27 127 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@27 128 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@27 129 grad2[i] = v2_normalize(grad2[i]);
nuclear@27 130
nuclear@27 131 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@27 132 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@27 133 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;
nuclear@27 134 grad3[i] = v3_normalize(grad3[i]);
nuclear@27 135 }
nuclear@27 136
nuclear@27 137 /* permute indices by swapping them randomly */
nuclear@27 138 for(i=0; i<B; i++) {
nuclear@27 139 int rand_idx = rand() % B;
nuclear@27 140
nuclear@27 141 int tmp = perm[i];
nuclear@27 142 perm[i] = perm[rand_idx];
nuclear@27 143 perm[rand_idx] = tmp;
nuclear@27 144 }
nuclear@27 145
nuclear@27 146 /* fill up the rest of the arrays by duplicating the existing gradients */
nuclear@27 147 /* and permutations */
nuclear@27 148 for(i=0; i<B+2; i++) {
nuclear@27 149 perm[B + i] = perm[i];
nuclear@27 150 grad1[B + i] = grad1[i];
nuclear@27 151 grad2[B + i] = grad2[i];
nuclear@27 152 grad3[B + i] = grad3[i];
nuclear@27 153 }
nuclear@27 154 }
nuclear@27 155
nuclear@27 156 scalar_t noise1(scalar_t x)
nuclear@27 157 {
nuclear@27 158 int bx0, bx1;
nuclear@27 159 scalar_t rx0, rx1, sx, u, v;
nuclear@27 160
nuclear@27 161 if(!tables_valid) {
nuclear@27 162 init_noise();
nuclear@27 163 tables_valid = 1;
nuclear@27 164 }
nuclear@27 165
nuclear@27 166 setup(x, bx0, bx1, rx0, rx1);
nuclear@27 167 sx = s_curve(rx0);
nuclear@27 168 u = rx0 * grad1[perm[bx0]];
nuclear@27 169 v = rx1 * grad1[perm[bx1]];
nuclear@27 170
nuclear@27 171 return lerp(u, v, sx);
nuclear@27 172 }
nuclear@27 173
nuclear@27 174 scalar_t noise2(scalar_t x, scalar_t y)
nuclear@27 175 {
nuclear@27 176 int i, j, b00, b10, b01, b11;
nuclear@27 177 int bx0, bx1, by0, by1;
nuclear@27 178 scalar_t rx0, rx1, ry0, ry1;
nuclear@27 179 scalar_t sx, sy, u, v, a, b;
nuclear@27 180
nuclear@27 181 if(!tables_valid) {
nuclear@27 182 init_noise();
nuclear@27 183 tables_valid = 1;
nuclear@27 184 }
nuclear@27 185
nuclear@27 186 setup(x, bx0, bx1, rx0, rx1);
nuclear@27 187 setup(y, by0, by1, ry0, ry1);
nuclear@27 188
nuclear@27 189 i = perm[bx0];
nuclear@27 190 j = perm[bx1];
nuclear@27 191
nuclear@27 192 b00 = perm[i + by0];
nuclear@27 193 b10 = perm[j + by0];
nuclear@27 194 b01 = perm[i + by1];
nuclear@27 195 b11 = perm[j + by1];
nuclear@27 196
nuclear@27 197 /* calculate hermite inteprolating factors */
nuclear@27 198 sx = s_curve(rx0);
nuclear@27 199 sy = s_curve(ry0);
nuclear@27 200
nuclear@27 201 /* interpolate along the left edge */
nuclear@27 202 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));
nuclear@27 203 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));
nuclear@27 204 a = lerp(u, v, sx);
nuclear@27 205
nuclear@27 206 /* interpolate along the right edge */
nuclear@27 207 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));
nuclear@27 208 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));
nuclear@27 209 b = lerp(u, v, sx);
nuclear@27 210
nuclear@27 211 /* interpolate between them */
nuclear@27 212 return lerp(a, b, sy);
nuclear@27 213 }
nuclear@27 214
nuclear@27 215 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)
nuclear@27 216 {
nuclear@27 217 int i, j;
nuclear@27 218 int bx0, bx1, by0, by1, bz0, bz1;
nuclear@27 219 int b00, b10, b01, b11;
nuclear@27 220 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;
nuclear@27 221 scalar_t sx, sy, sz;
nuclear@27 222 scalar_t u, v, a, b, c, d;
nuclear@27 223
nuclear@27 224 if(!tables_valid) {
nuclear@27 225 init_noise();
nuclear@27 226 tables_valid = 1;
nuclear@27 227 }
nuclear@27 228
nuclear@27 229 setup(x, bx0, bx1, rx0, rx1);
nuclear@27 230 setup(y, by0, by1, ry0, ry1);
nuclear@27 231 setup(z, bz0, bz1, rz0, rz1);
nuclear@27 232
nuclear@27 233 i = perm[bx0];
nuclear@27 234 j = perm[bx1];
nuclear@27 235
nuclear@27 236 b00 = perm[i + by0];
nuclear@27 237 b10 = perm[j + by0];
nuclear@27 238 b01 = perm[i + by1];
nuclear@27 239 b11 = perm[j + by1];
nuclear@27 240
nuclear@27 241 /* calculate hermite interpolating factors */
nuclear@27 242 sx = s_curve(rx0);
nuclear@27 243 sy = s_curve(ry0);
nuclear@27 244 sz = s_curve(rz0);
nuclear@27 245
nuclear@27 246 /* interpolate along the top slice of the cell */
nuclear@27 247 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));
nuclear@27 248 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));
nuclear@27 249 a = lerp(u, v, sx);
nuclear@27 250
nuclear@27 251 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));
nuclear@27 252 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));
nuclear@27 253 b = lerp(u, v, sx);
nuclear@27 254
nuclear@27 255 c = lerp(a, b, sy);
nuclear@27 256
nuclear@27 257 /* interpolate along the bottom slice of the cell */
nuclear@27 258 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));
nuclear@27 259 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));
nuclear@27 260 a = lerp(u, v, sx);
nuclear@27 261
nuclear@27 262 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));
nuclear@27 263 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));
nuclear@27 264 b = lerp(u, v, sx);
nuclear@27 265
nuclear@27 266 d = lerp(a, b, sy);
nuclear@27 267
nuclear@27 268 /* interpolate between slices */
nuclear@27 269 return lerp(c, d, sz);
nuclear@27 270 }
nuclear@27 271
nuclear@27 272 scalar_t fbm1(scalar_t x, int octaves)
nuclear@27 273 {
nuclear@27 274 int i;
nuclear@27 275 scalar_t res = 0.0f, freq = 1.0f;
nuclear@27 276 for(i=0; i<octaves; i++) {
nuclear@27 277 res += noise1(x * freq) / freq;
nuclear@27 278 freq *= 2.0f;
nuclear@27 279 }
nuclear@27 280 return res;
nuclear@27 281 }
nuclear@27 282
nuclear@27 283 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)
nuclear@27 284 {
nuclear@27 285 int i;
nuclear@27 286 scalar_t res = 0.0f, freq = 1.0f;
nuclear@27 287 for(i=0; i<octaves; i++) {
nuclear@27 288 res += noise2(x * freq, y * freq) / freq;
nuclear@27 289 freq *= 2.0f;
nuclear@27 290 }
nuclear@27 291 return res;
nuclear@27 292 }
nuclear@27 293
nuclear@27 294 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)
nuclear@27 295 {
nuclear@27 296 int i;
nuclear@27 297 scalar_t res = 0.0f, freq = 1.0f;
nuclear@27 298 for(i=0; i<octaves; i++) {
nuclear@27 299 res += noise3(x * freq, y * freq, z * freq) / freq;
nuclear@27 300 freq *= 2.0f;
nuclear@27 301 }
nuclear@27 302 return res;
nuclear@27 303 }
nuclear@27 304
nuclear@27 305 scalar_t turbulence1(scalar_t x, int octaves)
nuclear@27 306 {
nuclear@27 307 int i;
nuclear@27 308 scalar_t res = 0.0f, freq = 1.0f;
nuclear@27 309 for(i=0; i<octaves; i++) {
nuclear@27 310 res += fabs(noise1(x * freq) / freq);
nuclear@27 311 freq *= 2.0f;
nuclear@27 312 }
nuclear@27 313 return res;
nuclear@27 314 }
nuclear@27 315
nuclear@27 316 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)
nuclear@27 317 {
nuclear@27 318 int i;
nuclear@27 319 scalar_t res = 0.0f, freq = 1.0f;
nuclear@27 320 for(i=0; i<octaves; i++) {
nuclear@27 321 res += fabs(noise2(x * freq, y * freq) / freq);
nuclear@27 322 freq *= 2.0f;
nuclear@27 323 }
nuclear@27 324 return res;
nuclear@27 325 }
nuclear@27 326
nuclear@27 327 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)
nuclear@27 328 {
nuclear@27 329 int i;
nuclear@27 330 scalar_t res = 0.0f, freq = 1.0f;
nuclear@27 331 for(i=0; i<octaves; i++) {
nuclear@27 332 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);
nuclear@27 333 freq *= 2.0f;
nuclear@27 334 }
nuclear@27 335 return res;
nuclear@27 336 }