| Geant4 Cross Reference |
1 // Copyright (C) 2010, Guy Barrand. All rights
2 // See the file tools.license for terms.
3
4 #ifndef tools_mat4
5 #define tools_mat4
6
7 #include "mat"
8
9 //#include <cmath>
10
11 namespace tools {
12
13 template <class T>
14 class mat4 : public mat<T,4> {
15 typedef mat<T,4> parent;
16 typedef mat<T,4> pr;
17 public:
18 #ifdef TOOLS_MEM
19 mat4(bool a_inc = true):parent(a_inc) {}
20 #else
21 mat4():parent() {}
22 #endif
23 mat4(const mat<T,4>& a_from):parent(a_from){
24 virtual ~mat4() {}
25 public:
26 mat4(const mat4& a_from):parent(a_from){}
27 mat4& operator=(const mat4& a_from){
28 parent::operator=(a_from);
29 return *this;
30 }
31 public:
32 mat4(const T& a_00,const T& a_01,const T& a_
33 const T& a_10,const T& a_11,const T& a_
34 const T& a_20,const T& a_21,const T& a_
35 const T& a_30,const T& a_31,const T& a_
36 {
37 set_matrix(a_00,a_01,a_02,a_03,
38 a_10,a_11,a_12,a_13,
39 a_20,a_21,a_22,a_23,
40 a_30,a_31,a_32,a_33);
41 }
42 public:
43 void set_matrix(const mat4<T>& a_m) {parent:
44 void set_matrix(
45 const T& a_00,const T& a_01,const T& a_02,
46 const T& a_10,const T& a_11,const T& a_12,
47 const T& a_20,const T& a_21,const T& a_22,
48 const T& a_30,const T& a_31,const T& a_32,
49 {
50 //a_<R><C>
51 //pr::m_vec[R + C * 4];
52 pr::m_vec[0] = a_00;pr::m_vec[4] = a_01;pr
53 pr::m_vec[1] = a_10;pr::m_vec[5] = a_11;pr
54 pr::m_vec[2] = a_20;pr::m_vec[6] = a_21;pr
55 pr::m_vec[3] = a_30;pr::m_vec[7] = a_31;pr
56 }
57
58 void set_scale(const T& a_s) {_set_scale(a_s
59 void set_scale(const T& a_1,const T& a_2,con
60 void set_translate(const T& a_x,const T& a_y
61 void set_rotate(const T& a_x,const T& a_y,co
62 _set_rotate(a_x,a_y,a_z,a_angle,pr::m_vec,
63 }
64 void set_ortho(const T& a_l,const T& a_r,
65 const T& a_b,const T& a_t,
66 const T& a_n,const T& a_f) {
67 // from man glOrtho.
68 T tx = -(a_r+a_l)/(a_r-a_l);
69 T ty = -(a_t+a_b)/(a_t-a_b);
70 T tz = -(a_f+a_n)/(a_f-a_n);
71
72 T a_00,a_01,a_02,a_03;
73 T a_10,a_11,a_12,a_13;
74 T a_20,a_21,a_22,a_23;
75 T a_30,a_31,a_32,a_33;
76 a_00 = 2/(a_r-a_l);a_01 = 0;a_02
77 a_10 = 0;a_11 = 2/(a_t-a_b);a_12
78 a_20 = 0;a_21 = 0;a_22
79 a_30 = 0;a_31 = 0;a_32
80 set_matrix(a_00,a_01,a_02,a_03, //1 row
81 a_10,a_11,a_12,a_13, //2 row
82 a_20,a_21,a_22,a_23, //3 row
83 a_30,a_31,a_32,a_33); //4 row
84
85 //NOTE : Z(x,y, z,1) = -2z/(f-n)+tz = [-2z
86 // W(x,y, z,1) = 1 -> Z/W = Z
87 // Z(x,y,-n,1) = -1
88 // Z(x,y,-f,1) = 1
89
90 // Z(x,y,-(f+n)/2,1) = 0
91
92 // X(x,0, z,1) = 2x/(r-l)+tx = [2x-r
93 // X(r,0, z,1) = 1
94
95 // the view direction is then (0,0,1) in t
96 }
97 void set_frustum(const T& a_l,const T& a_r,
98 const T& a_b,const T& a_t,
99 const T& a_n,const T& a_f)
100 // from man glFrustum.
101 T A = (a_r+a_l)/(a_r-a_l);
102 T B = (a_t+a_b)/(a_t-a_b);
103 T C = -(a_f+a_n)/(a_f-a_n);
104 T D = -(2*a_f*a_n)/(a_f-a_n);
105
106 T a_00,a_01,a_02,a_03;
107 T a_10,a_11,a_12,a_13;
108 T a_20,a_21,a_22,a_23;
109 T a_30,a_31,a_32,a_33;
110 a_00 = (2*a_n)/(a_r-a_l);a_01 =
111 a_10 = 0;a_11 = (2*a_n)/(a
112 a_20 = 0;a_21 =
113 a_30 = 0;a_31 =
114 set_matrix(a_00,a_01,a_02,a_03, //1 row
115 a_10,a_11,a_12,a_13, //2 row
116 a_20,a_21,a_22,a_23, //3 row
117 a_30,a_31,a_32,a_33); //4 row
118
119 //NOTE : Z(x,y, z,1) = C*z+D = -[(f+n)*z+2
120
121 // Z(x,y,-n,1) = -[-fn-nn+2fn]/(f-n)
122 // W(x,y,-n,1) = n
123 // -> Z/W(x,y,-n,1) = -1
124
125 // Z(x,y,-2fn/(f+n),1) = 0
126 // -> Z/W = 0
127
128 // Z(x,y,-f,1) = -[-ff-fn+2fn]/(f-n)
129 // W(x,y,-f,1) = f
130 // -> Z/W(x,y,-f,1) = 1
131
132 // X(x,0, z,1) = 2nx/(r-l)+z(r+l)/(r
133 // X(r,0,-n,1) = [nr-nl]/(r-l) = n
134 // W(r,0,-n,1) = n
135 // -> X/W(r,0,-n,1) = 1
136
137 // X(l,0,-n,1) = (2nl-n(r+l))/(r-l)
138 // W(l,0,-n,1) = n
139 // -> X/W(l,0,-n,1) = -1
140
141 // lrbt corners are in plane z=-1 at xy=+/
142
143 // eye ?
144 // eye before ? (0,0,z,1) -> (zA,zB,zC+D,-
145 // z=0 -> (0,0,D=-2fn(f-n),0)
146
147 }
148
149 void get_translate(T& a_x,T& a_y,T& a_z) con
150 a_x = pr::m_vec[12];
151 a_y = pr::m_vec[13];
152 a_z = pr::m_vec[14];
153 }
154
155 void no_translate() {
156 pr::m_vec[12] = 0;
157 pr::m_vec[13] = 0;
158 pr::m_vec[14] = 0;
159 }
160
161 //void set_translate_only(const T& a_x,const T
162 // pr::m_vec[12] = a_x;
163 // pr::m_vec[13] = a_y;
164 // pr::m_vec[14] = a_z;
165 //}
166
167 public:
168 void mul_4(T& a_x,T& a_y,T& a_z,T& a_p) cons
169 // a_[x,y,z,p] = this * a_[x,y,z,p]
170 //pr::m_vec[R + C * 4];
171 //pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m
172 //pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m
173 //pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m
174 //pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m
175 T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr
176 T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr
177 T z = pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr
178 T p = pr::m_vec[3]*a_x+pr::m_vec[7]*a_y+pr
179 a_x = x;
180 a_y = y;
181 a_z = z;
182 a_p = p;
183 }
184 void mul_4_opt(T& a_x,T& a_y,T& a_z,T& a_p,T
185 // a_[x,y,z,p] = this * a_[x,y,z,p]
186 //pr::m_vec[R + C * 4];
187 //pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m
188 //pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m
189 //pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m
190 //pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m
191 a_tmp[0] = pr::m_vec[0]*a_x+pr::m_vec[4]*a
192 a_tmp[1] = pr::m_vec[1]*a_x+pr::m_vec[5]*a
193 a_tmp[2] = pr::m_vec[2]*a_x+pr::m_vec[6]*a
194 a_tmp[3] = pr::m_vec[3]*a_x+pr::m_vec[7]*a
195 a_x = a_tmp[0];
196 a_y = a_tmp[1];
197 a_z = a_tmp[2];
198 a_p = a_tmp[3];
199 }
200 void mul_3(T& a_x,T& a_y,T& a_z) const {
201 // a_[x,y,z] = this * a_[x,y,z]
202 //pr::m_vec[R + C * 4];
203 //pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m
204 //pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m
205 //pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m
206 //pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m
207 T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr
208 T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr
209 T z = pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr
210 a_x = x;
211 a_y = y;
212 a_z = z;
213 }
214 void mul_3_opt(T& a_x,T& a_y,T& a_z,T a_tmp[
215 // a_[x,y,z] = this * a_[x,y,z]
216 //pr::m_vec[R + C * 4];
217 //pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m
218 //pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m
219 //pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m
220 //pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m
221 a_tmp[0] = pr::m_vec[0]*a_x+pr::m_vec[4]*a
222 a_tmp[1] = pr::m_vec[1]*a_x+pr::m_vec[5]*a
223 a_tmp[2] = pr::m_vec[2]*a_x+pr::m_vec[6]*a
224 a_x = a_tmp[0];
225 a_y = a_tmp[1];
226 a_z = a_tmp[2];
227 }
228 void mul_2(T& a_x,T& a_y) const {
229 // a_[x,y] = this * a_[x,y]
230 //pr::m_vec[R + C * 4];
231 //pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m
232 //pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m
233 //pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m
234 //pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m
235 T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr
236 T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr
237 a_x = x;
238 a_y = y;
239 }
240
241 void mul_dir_3(T& a_x,T& a_y,T& a_z) const {
242 // used to multiply normals.
243 // a_[x,y,z] = rot_part(this) * a_[x,y,z]
244
245 T x = pr::m_vec[0]*a_x+pr::m_vec[4]*a_y+pr
246 T y = pr::m_vec[1]*a_x+pr::m_vec[5]*a_y+pr
247 T z = pr::m_vec[2]*a_x+pr::m_vec[6]*a_y+pr
248 a_x = x;
249 a_y = y;
250 a_z = z;
251 }
252 void mul_dir_3_opt(T& a_x,T& a_y,T& a_z,T a_
253 // used to multiply normals.
254 // a_[x,y,z] = rot_part(this) * a_[x,y,z]
255
256 a_tmp[0] = pr::m_vec[0]*a_x+pr::m_vec[4]*a
257 a_tmp[1] = pr::m_vec[1]*a_x+pr::m_vec[5]*a
258 a_tmp[2] = pr::m_vec[2]*a_x+pr::m_vec[6]*a
259 a_x = a_tmp[0];
260 a_y = a_tmp[1];
261 a_z = a_tmp[2];
262 }
263
264 void mul_trans_3(T& a_x,T& a_y,T& a_z) const
265 // used in sg::healpix.
266 // a_[x,y,z] = trans_part(this) * a_[x,y,z
267 a_x += pr::m_vec[12];
268 a_y += pr::m_vec[13];
269 a_z += pr::m_vec[14];
270 }
271
272 template <class VEC>
273 void mul_dir_3(VEC& a_dir) const {mul_dir_3(
274
275 void mul_scale(const T& a_sx,const T& a_sy,c
276 // this = this * mat4_scale(a_s[x,y,z]
277 //pr::m_vec[R + C * 4];
278 //pr::m_vec[0]= 00;pr::m_vec[4] = 01;pr::m
279 //pr::m_vec[1]= 10;pr::m_vec[5] = 11;pr::m
280 //pr::m_vec[2]= 20;pr::m_vec[6] = 21;pr::m
281 //pr::m_vec[3]= 30;pr::m_vec[7] = 31;pr::m
282 pr::m_vec[0] *= a_sx;
283 pr::m_vec[1] *= a_sx;
284 pr::m_vec[2] *= a_sx;
285 pr::m_vec[3] *= a_sx;
286
287 pr::m_vec[4] *= a_sy;
288 pr::m_vec[5] *= a_sy;
289 pr::m_vec[6] *= a_sy;
290 pr::m_vec[7] *= a_sy;
291
292 pr::m_vec[ 8] *= a_sz;
293 pr::m_vec[ 9] *= a_sz;
294 pr::m_vec[10] *= a_sz;
295 pr::m_vec[11] *= a_sz;
296 }
297 void mul_scale(const T& a_s) {
298 pr::m_vec[0] *= a_s;
299 pr::m_vec[1] *= a_s;
300 pr::m_vec[2] *= a_s;
301 pr::m_vec[3] *= a_s;
302
303 pr::m_vec[4] *= a_s;
304 pr::m_vec[5] *= a_s;
305 pr::m_vec[6] *= a_s;
306 pr::m_vec[7] *= a_s;
307
308 pr::m_vec[ 8] *= a_s;
309 pr::m_vec[ 9] *= a_s;
310 pr::m_vec[10] *= a_s;
311 pr::m_vec[11] *= a_s;
312 }
313 void mul_translate(const T& a_x,const T& a_y
314 pr::m_vec[12] = pr::m_vec[0]*a_x+pr::m_vec
315 pr::m_vec[13] = pr::m_vec[1]*a_x+pr::m_vec
316 pr::m_vec[14] = pr::m_vec[2]*a_x+pr::m_vec
317 pr::m_vec[15] = pr::m_vec[3]*a_x+pr::m_vec
318 }
319
320 void mul_rotate(const T& a_x,const T& a_y,co
321 T rot[16];
322 _set_rotate(a_x,a_y,a_z,a_angle,rot,a_sin,
323 parent::_mul_mtx(rot);
324 }
325
326 void left_mul_rotate(const T& a_x,const T& a
327 T _m[16];
328 _set_rotate(a_x,a_y,a_z,a_angle,_m,a_sin,a
329 parent::_left_mul_mtx(_m);
330 }
331
332 void left_mul_scale(const T& a_x,const T& a_
333 T _m[16];
334 _set_scale(a_x,a_y,a_z,_m);
335 parent::_left_mul_mtx(_m);
336 }
337
338 void left_mul_translate(const T& a_x,const T
339 T _m[16];
340 _set_translate(a_x,a_y,a_z,_m);
341 parent::_left_mul_mtx(_m);
342 }
343
344 void v00(const T& a_value){pr::m_vec[0+0*4]
345 void v10(const T& a_value){pr::m_vec[1+0*4]
346 void v20(const T& a_value){pr::m_vec[2+0*4]
347 void v30(const T& a_value){pr::m_vec[3+0*4]
348
349 void v01(const T& a_value){pr::m_vec[0+1*4]
350 void v11(const T& a_value){pr::m_vec[1+1*4]
351 void v21(const T& a_value){pr::m_vec[2+1*4]
352 void v31(const T& a_value){pr::m_vec[3+1*4]
353
354 void v02(const T& a_value){pr::m_vec[0+2*4]
355 void v12(const T& a_value){pr::m_vec[1+2*4]
356 void v22(const T& a_value){pr::m_vec[2+2*4]
357 void v32(const T& a_value){pr::m_vec[3+2*4]
358
359 void v03(const T& a_value){pr::m_vec[0+3*4]
360 void v13(const T& a_value){pr::m_vec[1+3*4]
361 void v23(const T& a_value){pr::m_vec[2+3*4]
362 void v33(const T& a_value){pr::m_vec[3+3*4]
363
364 const T& v00() const {return pr::m_vec[0+0*4
365 const T& v10() const {return pr::m_vec[1+0*4
366 const T& v20() const {return pr::m_vec[2+0*4
367 const T& v30() const {return pr::m_vec[3+0*4
368
369 const T& v01() const {return pr::m_vec[0+1*4
370 const T& v11() const {return pr::m_vec[1+1*4
371 const T& v21() const {return pr::m_vec[2+1*4
372 const T& v31() const {return pr::m_vec[3+1*4
373
374 const T& v02() const {return pr::m_vec[0+2*4
375 const T& v12() const {return pr::m_vec[1+2*4
376 const T& v22() const {return pr::m_vec[2+2*4
377 const T& v32() const {return pr::m_vec[3+2*4
378
379 const T& v03() const {return pr::m_vec[0+3*4
380 const T& v13() const {return pr::m_vec[1+3*4
381 const T& v23() const {return pr::m_vec[2+3*4
382 const T& v33() const {return pr::m_vec[3+3*4
383
384 protected:
385 static void _set_translate(const T& a_x,cons
386 v[0] = T(1);v[4] = 0;v[ 8] = 0;v[12]
387 v[1] = 0;v[5] = T(1);v[ 9] = 0;v[13]
388 v[2] = 0;v[6] = 0;v[10] = T(1);v[14]
389 v[3] = 0;v[7] = 0;v[11] = 0;v[15]
390 }
391
392 static void _set_scale(const T& a_1,const T&
393 v[0] = a_1;v[4] = 0;v[ 8] = 0;v[12] =
394 v[1] = 0;v[5] = a_2;v[ 9] = 0;v[13] =
395 v[2] = 0;v[6] = 0;v[10] = a_3;v[14] =
396 v[3] = 0;v[7] = 0;v[11] = 0;v[15] =
397 }
398
399 static void _set_rotate(const T& a_x,const T
400 //WARNING : (a_x,a_y,a_z) must be a normal
401 // v[] = exp(-a_angle*n(a_x,a_y,a_z)*Rs).
402 T si = a_sin(a_angle);
403 T co = a_cos(a_angle);
404 T x = a_x;
405 T y = a_y;
406 T z = a_z;
407 T x2 = x*x;
408 T y2 = y*y;
409 T z2 = z*z;
410 T xy = x*y;
411 T xz = x*z;
412 T yz = y*z;
413 v[0] = x2+(1-x2)*co;v[4] = xy*(1-co)-z*si;
414 v[1] = xy*(1-co)+z*si;v[5] = y2+(1-y2)*co;
415 v[2] = xz*(1-co)-y*si;v[6] = yz*(1-co)+x*s
416 v[3] = 0;v[7] = 0;v[
417
418 // If :
419 // n =(x,y,z)
420 // n2 = x2+y2+z2 = 1
421 // n.E = x*E1+y*E2+z*E3
422 // with :
423 // E1 E2 E3
424 // 0 0 0 0 0 -1 0 1 0
425 // 0 0 1 0 0 0 -1 0 0
426 // 0 -1 0 1 0 0 0 0 0
427 //
428 // R(r,c) = cos(theta)*Id(r,c)+(1-cos(thet
429 //
430 // R = exp(-theta*(n.E)) // active rotatio
431
432 }
433
434 public:
435 void mul_mtx_rot_root(const T& a_00,const T&
436 const T& a_10,const T&
437 const T& a_20,const T&
438 {
439 T* tv = pr::m_vec;
440 //pr::m_vec[0] = 00;pr::m_vec[4] = 01;pr::
441 //pr::m_vec[1] = 10;pr::m_vec[5] = 11;pr::
442 //pr::m_vec[2] = 20;pr::m_vec[6] = 21;pr::
443 //pr::m_vec[3] = 30;pr::m_vec[7] = 31;pr::
444
445 T tv_0 = tv[0];
446 T tv_1 = tv[1];
447 T tv_2 = tv[2];
448 T tv_3 = tv[3];
449 T tv_4 = tv[4];
450 T tv_5 = tv[5];
451 T tv_6 = tv[6];
452 T tv_7 = tv[7];
453 T tv_8 = tv[8];
454 T tv_9 = tv[9];
455 T tv_10 = tv[10];
456 T tv_11 = tv[11];
457 T tv_12 = tv[12];
458 T tv_13 = tv[13];
459 T tv_14 = tv[14];
460 T tv_15 = tv[15];
461
462 T fv_0 = a_00;
463 T fv_1 = a_10;
464 T fv_2 = a_20;
465 //T fv_3 = 0;
466
467 T fv_4 = a_01;
468 T fv_5 = a_11;
469 T fv_6 = a_21;
470 //T fv_7 = 0;
471
472 T fv_8 = a_02;
473 T fv_9 = a_12;
474 T fv_10 = a_22;
475 //T fv_11 = 0;
476
477 //T fv_12 = 0;
478 //T fv_13 = 0;
479 //T fv_14 = 0;
480 //T fv_15 = 1;
481
482 tv[0] = tv_0*fv_0+tv_4*fv_1+ tv_8*fv_2;
483 tv[1] = tv_1*fv_0+tv_5*fv_1+ tv_9*fv_2;
484 tv[2] = tv_2*fv_0+tv_6*fv_1+tv_10*fv_2;
485 tv[3] = tv_3*fv_0+tv_7*fv_1+tv_11*fv_2;
486
487 tv[4] = tv_0*fv_4+tv_4*fv_5+ tv_8*fv_6;
488 tv[5] = tv_1*fv_4+tv_5*fv_5+ tv_9*fv_6;
489 tv[6] = tv_2*fv_4+tv_6*fv_5+tv_10*fv_6;
490 tv[7] = tv_3*fv_4+tv_7*fv_5+tv_11*fv_6;
491
492 tv[8] = tv_0*fv_8+tv_4*fv_9+ tv_8*fv_10;
493 tv[9] = tv_1*fv_8+tv_5*fv_9+ tv_9*fv_10;
494 tv[10] = tv_2*fv_8+tv_6*fv_9+tv_10*fv_10;
495 tv[11] = tv_3*fv_8+tv_7*fv_9+tv_11*fv_10;
496
497 tv[12] = tv_12;
498 tv[13] = tv_13;
499 tv[14] = tv_14;
500 tv[15] = tv_15;
501 }
502
503 template <class MAT3>
504 void set_mat3(MAT3& a_m3) {
505 a_m3.set_matrix(pr::m_vec[0],pr::m_vec[4],
506 pr::m_vec[1],pr::m_vec[5],
507 pr::m_vec[2],pr::m_vec[6],
508 }
509 private:static void check_instantiation() {mat
510 };
511
512 //////////////////////////////////////////////
513 /// common matrices : ////////////////////////
514 //////////////////////////////////////////////
515
516 #ifdef TOOLS_MEM
517 template <class T> inline const mat4<T>& mat4_
518 #else
519 template <class T> inline const mat4<T>& mat4_
520 #endif
521
522 /*
523 template <class T>
524 inline const mat4<T>& mat4_identity() {
525 static mat4<T> s_v(false);
526 static bool s_first = true;
527 if(s_first) {s_v.set_identity();s_first=fals
528 return s_v;
529 }
530 */
531
532 //for sf, mf :
533 template <class T>
534 inline const T* get_data(const mat4<T>& a_v) {
535
536 }
537
538 #include <ostream>
539
540 namespace tools {
541
542 template <class T>
543 inline std::ostream& operator<<(std::ostream&
544 const T* v = a_mtx.data();
545 a_out << v[0] << "," << v[4] << "," << v[ 8]
546 << v[1] << "," << v[5] << "," << v[ 9]
547 << v[2] << "," << v[6] << "," << v[10]
548 << v[3] << "," << v[7] << "," << v[11]
549 return a_out;
550 }
551
552 }
553
554 #endif