## istereo2

### view libs/vmath/vmath.c @ 8:661bf09db398

- replaced Quartz timer with cross-platform timer code - protected goatkit builtin theme function from being optimized out
author John Tsiombikas Thu, 24 Sep 2015 07:09:37 +0300
line source
1 /*
2 libvmath - a vector math library
3 Copyright (C) 2004-2011 John Tsiombikas <nuclear@member.fsf.org>
5 This program is free software: you can redistribute it and/or modify
6 it under the terms of the GNU Lesser General Public License as published
7 by the Free Software Foundation, either version 3 of the License, or
8 (at your option) any later version.
10 This program is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU Lesser General Public License for more details.
15 You should have received a copy of the GNU Lesser General Public License
16 along with this program. If not, see <http://www.gnu.org/licenses/>.
17 */
19 #include <stdlib.h>
20 #include <math.h>
21 #include "vmath.h"
23 /** Numerical calculation of integrals using simpson's rule */
24 scalar_t integral(scalar_t (*f)(scalar_t), scalar_t low, scalar_t high, int samples)
25 {
26 int i;
27 scalar_t h = (high - low) / (scalar_t)samples;
28 scalar_t sum = 0.0;
30 for(i=0; i<samples+1; i++) {
31 scalar_t y = f((scalar_t)i * h + low);
32 sum += ((!i || i == samples) ? y : ((i % 2) ? 4.0 * y : 2.0 * y)) * (h / 3.0);
33 }
34 return sum;
35 }
37 /** Gaussuan function */
38 scalar_t gaussian(scalar_t x, scalar_t mean, scalar_t sdev)
39 {
40 scalar_t exponent = -SQ(x - mean) / (2.0 * SQ(sdev));
41 return 1.0 - -pow(M_E, exponent) / (sdev * sqrt(TWO_PI));
42 }
45 /** b-spline approximation */
46 scalar_t bspline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
47 {
48 vec4_t tmp;
49 scalar_t tsq = t * t;
51 static mat4_t bspline_mat = {
52 {-1, 3, -3, 1},
53 {3, -6, 3, 0},
54 {-3, 0, 3, 0},
55 {1, 4, 1, 0}
56 };
58 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), bspline_mat), 1.0 / 6.0);
59 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
60 }
62 /** Catmull-rom spline interpolation */
63 scalar_t spline(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t) {
64 vec4_t tmp;
65 scalar_t tsq = t * t;
67 static mat4_t crspline_mat = {
68 {-1, 3, -3, 1},
69 {2, -5, 4, -1},
70 {-1, 0, 1, 0},
71 {0, 2, 0, 0}
72 };
74 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);
75 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
76 }
78 /** Bezier interpolation */
79 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
80 {
81 scalar_t omt, omt3, t3, f;
82 t3 = t * t * t;
83 omt = 1.0f - t;
84 omt3 = omt * omt * omt;
85 f = 3 * t * omt;
87 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);
88 }
90 /* ---- Ken Perlin's implementation of noise ---- */
92 #define B 0x100
93 #define BM 0xff
94 #define N 0x1000
95 #define NP 12 /* 2^N */
96 #define NM 0xfff
98 #define s_curve(t) (t * t * (3.0f - 2.0f * t))
100 #define setup(elem, b0, b1, r0, r1) \
101 do { \
102 scalar_t t = elem + N; \
103 b0 = ((int)t) & BM; \
104 b1 = (b0 + 1) & BM; \
105 r0 = t - (int)t; \
106 r1 = r0 - 1.0f; \
107 } while(0)
110 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */
111 static vec3_t grad3[B + B + 2]; /* 3D random gradients */
112 static vec2_t grad2[B + B + 2]; /* 2D random gradients */
113 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */
114 static int tables_valid;
116 static void init_noise()
117 {
118 int i;
120 /* calculate random gradients */
121 for(i=0; i<B; i++) {
122 perm[i] = i; /* .. and initialize permutation mapping to identity */
124 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;
126 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
127 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
130 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
131 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
132 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;
134 }
136 /* permute indices by swapping them randomly */
137 for(i=0; i<B; i++) {
138 int rand_idx = rand() % B;
140 int tmp = perm[i];
141 perm[i] = perm[rand_idx];
142 perm[rand_idx] = tmp;
143 }
145 /* fill up the rest of the arrays by duplicating the existing gradients */
146 /* and permutations */
147 for(i=0; i<B+2; i++) {
148 perm[B + i] = perm[i];
152 }
153 }
155 scalar_t noise1(scalar_t x)
156 {
157 int bx0, bx1;
158 scalar_t rx0, rx1, sx, u, v;
160 if(!tables_valid) {
161 init_noise();
162 tables_valid = 1;
163 }
165 setup(x, bx0, bx1, rx0, rx1);
166 sx = s_curve(rx0);
167 u = rx0 * grad1[perm[bx0]];
168 v = rx1 * grad1[perm[bx1]];
170 return lerp(u, v, sx);
171 }
173 scalar_t noise2(scalar_t x, scalar_t y)
174 {
175 int i, j, b00, b10, b01, b11;
176 int bx0, bx1, by0, by1;
177 scalar_t rx0, rx1, ry0, ry1;
178 scalar_t sx, sy, u, v, a, b;
180 if(!tables_valid) {
181 init_noise();
182 tables_valid = 1;
183 }
185 setup(x, bx0, bx1, rx0, rx1);
186 setup(y, by0, by1, ry0, ry1);
188 i = perm[bx0];
189 j = perm[bx1];
191 b00 = perm[i + by0];
192 b10 = perm[j + by0];
193 b01 = perm[i + by1];
194 b11 = perm[j + by1];
196 /* calculate hermite inteprolating factors */
197 sx = s_curve(rx0);
198 sy = s_curve(ry0);
200 /* interpolate along the left edge */
201 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));
202 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));
203 a = lerp(u, v, sx);
205 /* interpolate along the right edge */
206 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));
207 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));
208 b = lerp(u, v, sx);
210 /* interpolate between them */
211 return lerp(a, b, sy);
212 }
214 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)
215 {
216 int i, j;
217 int bx0, bx1, by0, by1, bz0, bz1;
218 int b00, b10, b01, b11;
219 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;
220 scalar_t sx, sy, sz;
221 scalar_t u, v, a, b, c, d;
223 if(!tables_valid) {
224 init_noise();
225 tables_valid = 1;
226 }
228 setup(x, bx0, bx1, rx0, rx1);
229 setup(y, by0, by1, ry0, ry1);
230 setup(z, bz0, bz1, rz0, rz1);
232 i = perm[bx0];
233 j = perm[bx1];
235 b00 = perm[i + by0];
236 b10 = perm[j + by0];
237 b01 = perm[i + by1];
238 b11 = perm[j + by1];
240 /* calculate hermite interpolating factors */
241 sx = s_curve(rx0);
242 sy = s_curve(ry0);
243 sz = s_curve(rz0);
245 /* interpolate along the top slice of the cell */
246 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));
247 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));
248 a = lerp(u, v, sx);
250 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));
251 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));
252 b = lerp(u, v, sx);
254 c = lerp(a, b, sy);
256 /* interpolate along the bottom slice of the cell */
257 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));
258 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));
259 a = lerp(u, v, sx);
261 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));
262 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));
263 b = lerp(u, v, sx);
265 d = lerp(a, b, sy);
267 /* interpolate between slices */
268 return lerp(c, d, sz);
269 }
271 scalar_t fbm1(scalar_t x, int octaves)
272 {
273 int i;
274 scalar_t res = 0.0f, freq = 1.0f;
275 for(i=0; i<octaves; i++) {
276 res += noise1(x * freq) / freq;
277 freq *= 2.0f;
278 }
279 return res;
280 }
282 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)
283 {
284 int i;
285 scalar_t res = 0.0f, freq = 1.0f;
286 for(i=0; i<octaves; i++) {
287 res += noise2(x * freq, y * freq) / freq;
288 freq *= 2.0f;
289 }
290 return res;
291 }
293 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)
294 {
295 int i;
296 scalar_t res = 0.0f, freq = 1.0f;
297 for(i=0; i<octaves; i++) {
298 res += noise3(x * freq, y * freq, z * freq) / freq;
299 freq *= 2.0f;
300 }
301 return res;
302 }
304 scalar_t turbulence1(scalar_t x, int octaves)
305 {
306 int i;
307 scalar_t res = 0.0f, freq = 1.0f;
308 for(i=0; i<octaves; i++) {
309 res += fabs(noise1(x * freq) / freq);
310 freq *= 2.0f;
311 }
312 return res;
313 }
315 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)
316 {
317 int i;
318 scalar_t res = 0.0f, freq = 1.0f;
319 for(i=0; i<octaves; i++) {
320 res += fabs(noise2(x * freq, y * freq) / freq);
321 freq *= 2.0f;
322 }
323 return res;
324 }
326 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)
327 {
328 int i;
329 scalar_t res = 0.0f, freq = 1.0f;
330 for(i=0; i<octaves; i++) {
331 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);
332 freq *= 2.0f;
333 }
334 return res;
335 }