goat3d

view libs/vmath/vmath.c @ 40:a5c5cec3cb88

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- added mesh attribute and face append functions - added Int4 constructor - continued the blender exporter - fixed a bug in clean_filename which made it produce unterminated strings - renamed clean_filename to goat3d_clean_filename and made it extern - added call to goat3d_clean_filename in the mesh XML export code to cleanup ctm filenames
author John Tsiombikas <nuclear@member.fsf.org>
date Sun, 13 Oct 2013 10:14:19 +0300
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1 /*
2 libvmath - a vector math library
3 Copyright (C) 2004-2011 John Tsiombikas <nuclear@member.fsf.org>
4
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.
9
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.
14
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 */
18
19 #include <stdlib.h>
20 #include <math.h>
21 #include "vmath.h"
22
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;
29
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 }
36
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 }
43
44
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;
50
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 };
57
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 }
61
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 {
65 vec4_t tmp;
66 scalar_t tsq = t * t;
67
68 static mat4_t crspline_mat = {
69 {-1, 3, -3, 1},
70 {2, -5, 4, -1},
71 {-1, 0, 1, 0},
72 {0, 2, 0, 0}
73 };
74
75 tmp = v4_scale(v4_transform(v4_cons(a, b, c, d), crspline_mat), 0.5);
76 return v4_dot(v4_cons(tsq * t, tsq, t, 1.0), tmp);
77 }
78
79 /** Bezier interpolation */
80 scalar_t bezier(scalar_t a, scalar_t b, scalar_t c, scalar_t d, scalar_t t)
81 {
82 scalar_t omt, omt3, t3, f;
83 t3 = t * t * t;
84 omt = 1.0f - t;
85 omt3 = omt * omt * omt;
86 f = 3 * t * omt;
87
88 return (a * omt3) + (b * f * omt) + (c * f * t) + (d * t3);
89 }
90
91 /* ---- Ken Perlin's implementation of noise ---- */
92
93 #define B 0x100
94 #define BM 0xff
95 #define N 0x1000
96 #define NP 12 /* 2^N */
97 #define NM 0xfff
98
99 #define s_curve(t) (t * t * (3.0f - 2.0f * t))
100
101 #define setup(elem, b0, b1, r0, r1) \
102 do { \
103 scalar_t t = elem + N; \
104 b0 = ((int)t) & BM; \
105 b1 = (b0 + 1) & BM; \
106 r0 = t - (int)t; \
107 r1 = r0 - 1.0f; \
108 } while(0)
109
110
111 static int perm[B + B + 2]; /* permuted index from g_n onto themselves */
112 static vec3_t grad3[B + B + 2]; /* 3D random gradients */
113 static vec2_t grad2[B + B + 2]; /* 2D random gradients */
114 static scalar_t grad1[B + B + 2]; /* 1D random ... slopes */
115 static int tables_valid;
116
117 static void init_noise()
118 {
119 int i;
120
121 /* calculate random gradients */
122 for(i=0; i<B; i++) {
123 perm[i] = i; /* .. and initialize permutation mapping to identity */
124
125 grad1[i] = (scalar_t)((rand() % (B + B)) - B) / B;
126
127 grad2[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
128 grad2[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
129 grad2[i] = v2_normalize(grad2[i]);
130
131 grad3[i].x = (scalar_t)((rand() % (B + B)) - B) / B;
132 grad3[i].y = (scalar_t)((rand() % (B + B)) - B) / B;
133 grad3[i].z = (scalar_t)((rand() % (B + B)) - B) / B;
134 grad3[i] = v3_normalize(grad3[i]);
135 }
136
137 /* permute indices by swapping them randomly */
138 for(i=0; i<B; i++) {
139 int rand_idx = rand() % B;
140
141 int tmp = perm[i];
142 perm[i] = perm[rand_idx];
143 perm[rand_idx] = tmp;
144 }
145
146 /* fill up the rest of the arrays by duplicating the existing gradients */
147 /* and permutations */
148 for(i=0; i<B+2; i++) {
149 perm[B + i] = perm[i];
150 grad1[B + i] = grad1[i];
151 grad2[B + i] = grad2[i];
152 grad3[B + i] = grad3[i];
153 }
154 }
155
156 scalar_t noise1(scalar_t x)
157 {
158 int bx0, bx1;
159 scalar_t rx0, rx1, sx, u, v;
160
161 if(!tables_valid) {
162 init_noise();
163 tables_valid = 1;
164 }
165
166 setup(x, bx0, bx1, rx0, rx1);
167 sx = s_curve(rx0);
168 u = rx0 * grad1[perm[bx0]];
169 v = rx1 * grad1[perm[bx1]];
170
171 return lerp(u, v, sx);
172 }
173
174 scalar_t noise2(scalar_t x, scalar_t y)
175 {
176 int i, j, b00, b10, b01, b11;
177 int bx0, bx1, by0, by1;
178 scalar_t rx0, rx1, ry0, ry1;
179 scalar_t sx, sy, u, v, a, b;
180
181 if(!tables_valid) {
182 init_noise();
183 tables_valid = 1;
184 }
185
186 setup(x, bx0, bx1, rx0, rx1);
187 setup(y, by0, by1, ry0, ry1);
188
189 i = perm[bx0];
190 j = perm[bx1];
191
192 b00 = perm[i + by0];
193 b10 = perm[j + by0];
194 b01 = perm[i + by1];
195 b11 = perm[j + by1];
196
197 /* calculate hermite inteprolating factors */
198 sx = s_curve(rx0);
199 sy = s_curve(ry0);
200
201 /* interpolate along the left edge */
202 u = v2_dot(grad2[b00], v2_cons(rx0, ry0));
203 v = v2_dot(grad2[b10], v2_cons(rx1, ry0));
204 a = lerp(u, v, sx);
205
206 /* interpolate along the right edge */
207 u = v2_dot(grad2[b01], v2_cons(rx0, ry1));
208 v = v2_dot(grad2[b11], v2_cons(rx1, ry1));
209 b = lerp(u, v, sx);
210
211 /* interpolate between them */
212 return lerp(a, b, sy);
213 }
214
215 scalar_t noise3(scalar_t x, scalar_t y, scalar_t z)
216 {
217 int i, j;
218 int bx0, bx1, by0, by1, bz0, bz1;
219 int b00, b10, b01, b11;
220 scalar_t rx0, rx1, ry0, ry1, rz0, rz1;
221 scalar_t sx, sy, sz;
222 scalar_t u, v, a, b, c, d;
223
224 if(!tables_valid) {
225 init_noise();
226 tables_valid = 1;
227 }
228
229 setup(x, bx0, bx1, rx0, rx1);
230 setup(y, by0, by1, ry0, ry1);
231 setup(z, bz0, bz1, rz0, rz1);
232
233 i = perm[bx0];
234 j = perm[bx1];
235
236 b00 = perm[i + by0];
237 b10 = perm[j + by0];
238 b01 = perm[i + by1];
239 b11 = perm[j + by1];
240
241 /* calculate hermite interpolating factors */
242 sx = s_curve(rx0);
243 sy = s_curve(ry0);
244 sz = s_curve(rz0);
245
246 /* interpolate along the top slice of the cell */
247 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz0));
248 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz0));
249 a = lerp(u, v, sx);
250
251 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz0));
252 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz0));
253 b = lerp(u, v, sx);
254
255 c = lerp(a, b, sy);
256
257 /* interpolate along the bottom slice of the cell */
258 u = v3_dot(grad3[b00 + bz0], v3_cons(rx0, ry0, rz1));
259 v = v3_dot(grad3[b10 + bz0], v3_cons(rx1, ry0, rz1));
260 a = lerp(u, v, sx);
261
262 u = v3_dot(grad3[b01 + bz0], v3_cons(rx0, ry1, rz1));
263 v = v3_dot(grad3[b11 + bz0], v3_cons(rx1, ry1, rz1));
264 b = lerp(u, v, sx);
265
266 d = lerp(a, b, sy);
267
268 /* interpolate between slices */
269 return lerp(c, d, sz);
270 }
271
272 scalar_t fbm1(scalar_t x, int octaves)
273 {
274 int i;
275 scalar_t res = 0.0f, freq = 1.0f;
276 for(i=0; i<octaves; i++) {
277 res += noise1(x * freq) / freq;
278 freq *= 2.0f;
279 }
280 return res;
281 }
282
283 scalar_t fbm2(scalar_t x, scalar_t y, int octaves)
284 {
285 int i;
286 scalar_t res = 0.0f, freq = 1.0f;
287 for(i=0; i<octaves; i++) {
288 res += noise2(x * freq, y * freq) / freq;
289 freq *= 2.0f;
290 }
291 return res;
292 }
293
294 scalar_t fbm3(scalar_t x, scalar_t y, scalar_t z, int octaves)
295 {
296 int i;
297 scalar_t res = 0.0f, freq = 1.0f;
298 for(i=0; i<octaves; i++) {
299 res += noise3(x * freq, y * freq, z * freq) / freq;
300 freq *= 2.0f;
301 }
302 return res;
303 }
304
305 scalar_t turbulence1(scalar_t x, int octaves)
306 {
307 int i;
308 scalar_t res = 0.0f, freq = 1.0f;
309 for(i=0; i<octaves; i++) {
310 res += fabs(noise1(x * freq) / freq);
311 freq *= 2.0f;
312 }
313 return res;
314 }
315
316 scalar_t turbulence2(scalar_t x, scalar_t y, int octaves)
317 {
318 int i;
319 scalar_t res = 0.0f, freq = 1.0f;
320 for(i=0; i<octaves; i++) {
321 res += fabs(noise2(x * freq, y * freq) / freq);
322 freq *= 2.0f;
323 }
324 return res;
325 }
326
327 scalar_t turbulence3(scalar_t x, scalar_t y, scalar_t z, int octaves)
328 {
329 int i;
330 scalar_t res = 0.0f, freq = 1.0f;
331 for(i=0; i<octaves; i++) {
332 res += fabs(noise3(x * freq, y * freq, z * freq) / freq);
333 freq *= 2.0f;
334 }
335 return res;
336 }