1 // (c) bernhard schupp 1997 - 1998 2 #ifndef MAPP_CUBE_3D_H_INCLUDED 3 #define MAPP_CUBE_3D_H_INCLUDED 4 5 #include <cmath> 6 7 #include "gitter_sti.h" 8 9 namespace ALUGrid 10 { 11 12 class LinearMapping; // in mapp_tetra_3d.h 13 14 class TrilinearMapping 15 { 16 static const alucoord_t _epsilon; 17 18 const alucoord_t (&p0)[ 3 ], (&p1)[ 3 ], (&p2)[ 3 ], (&p3)[ 3 ]; 19 const alucoord_t (&p4)[ 3 ], (&p5)[ 3 ], (&p6)[ 3 ], (&p7)[ 3 ]; 20 alucoord_t a [ 8 ][ 3 ]; 21 alucoord_t Df [ 3 ][ 3 ]; 22 alucoord_t Dfi [ 3 ][ 3 ]; 23 alucoord_t DetDf; 24 void linear (const alucoord_t (&)[3]); 25 void inverse (const alucoord_t (&)[3]); 26 public : 27 inline TrilinearMapping (const alucoord_t (&)[3], const alucoord_t (&)[3], const alucoord_t (&)[3], const alucoord_t (&)[3], 28 const alucoord_t (&)[3], const alucoord_t (&)[3], const alucoord_t (&)[3], const alucoord_t (&)[3]); 29 inline TrilinearMapping (const TrilinearMapping &); ~TrilinearMapping()30 ~TrilinearMapping () {} 31 alucoord_t det (const alucoord_t (&)[3]); 32 inline void map2world (const alucoord_t (&)[3], alucoord_t (&)[3]) const; 33 inline void map2world (const alucoord_t , const alucoord_t , const alucoord_t , alucoord_t (&)[3]) const; 34 void world2map (const alucoord_t (&)[3], alucoord_t (&)[3]); 35 barycenter(const alucoord_t (& p0)[3],const alucoord_t (& p1)[3],const alucoord_t (& p2)[3],const alucoord_t (& p3)[3],const alucoord_t (& p4)[3],const alucoord_t (& p5)[3],const alucoord_t (& p6)[3],const alucoord_t (& p7)[3],alucoord_t (& barycenter)[3])36 static inline void barycenter(const alucoord_t (&p0)[3], const alucoord_t (&p1)[3], const alucoord_t (&p2)[3], const alucoord_t (&p3)[3], 37 const alucoord_t (&p4)[3], const alucoord_t (&p5)[3], const alucoord_t (&p6)[3], const alucoord_t (&p7)[3], 38 alucoord_t (&barycenter)[3]) 39 { 40 barycenter[0] = 0.125 * (p0[0] + p1[0] + p2[0] + p3[0] + p4[0] + p5[0] + p6[0] + p7[0]); 41 barycenter[1] = 0.125 * (p0[1] + p1[1] + p2[1] + p3[1] + p4[1] + p5[1] + p6[1] + p7[1]); 42 barycenter[2] = 0.125 * (p0[2] + p1[2] + p2[2] + p3[2] + p4[2] + p5[2] + p6[2] + p7[2]); 43 44 #ifdef ALUGRIDDEBUG 45 { 46 TrilinearMapping map(p0,p1,p2,p3,p4,p5,p6,p7); 47 alucoord_t p[3]; 48 map.map2world(.0, .0, .0, p); 49 for(int j=0; j<3; ++j) 50 { 51 alugrid_assert ( fabs(barycenter[j] - p[j]) < 1e-8 ); 52 } 53 } 54 #endif 55 } 56 57 // returns true if mapping is affine 58 inline bool affine() const; 59 }; 60 61 class QuadraturCube3Dbasis 62 { 63 protected: 64 static const alucoord_t _p2 [4][3]; 65 static const alucoord_t _p3 [8][3]; 66 }; 67 68 struct VolumeCalc 69 { 70 typedef alucoord_t val_t; 71 typedef int arg_t; 72 73 val_t operator() ( const alucoord_t (&)[ 3 ], const arg_t & ); 74 val_t operator() ( const alucoord_t (&)[ 4 ], const LinearMapping &, const arg_t & ); 75 }; 76 77 struct SurfaceCalc 78 { 79 public: 80 typedef alucoord_t val_t; 81 typedef int arg_t; 82 val_t operator() ( const alucoord_t (&)[ 2 ], const alucoord_t (&)[ 3 ], const arg_t & ); 83 val_t operator() ( const alucoord_t (&)[ 3 ], const alucoord_t (&)[ 3 ], const arg_t & ); 84 }; 85 86 template< class A > class QuadraturCube3D : private QuadraturCube3Dbasis { 87 private : 88 TrilinearMapping _map; 89 public : QuadraturCube3D(const TrilinearMapping & m)90 QuadraturCube3D (const TrilinearMapping & m) : _map (m) {} ~QuadraturCube3D()91 ~QuadraturCube3D () {} 92 typedef typename A::val_t val_t; 93 typedef typename A::arg_t arg_t; 94 inline val_t integrate2 (val_t, const arg_t & = arg_t ()); 95 inline val_t integrate3 (val_t, const arg_t & = arg_t ()); 96 }; 97 98 template< class A > class QuadraturCube3D_1 : private QuadraturCube3Dbasis { 99 private : 100 TrilinearMapping _map; 101 public : QuadraturCube3D_1(const TrilinearMapping & m)102 QuadraturCube3D_1 (const TrilinearMapping & m) : _map (m) {} ~QuadraturCube3D_1()103 ~QuadraturCube3D_1 () {} 104 typedef typename A::val_t val_t; 105 typedef typename A::arg_t arg_t; 106 inline val_t integrate2 (val_t, const arg_t & = arg_t ()); 107 inline val_t integrate3 (val_t, const arg_t & = arg_t ()); 108 }; 109 110 class BilinearSurfaceMapping { 111 const alucoord_t (&_p0)[3], (&_p1)[3], (&_p2)[3], (&_p3)[3]; 112 alucoord_t _b [4][3]; 113 alucoord_t _n [3][3]; 114 public : 115 inline BilinearSurfaceMapping (const alucoord_t (&)[3], const alucoord_t (&)[3], const alucoord_t (&)[3], const alucoord_t (&)[3]); 116 inline BilinearSurfaceMapping (const BilinearSurfaceMapping &); ~BilinearSurfaceMapping()117 ~BilinearSurfaceMapping () {} 118 inline void map2world(const alucoord_t (&)[2], alucoord_t (&)[3]) const; 119 inline void map2world(alucoord_t x, alucoord_t y, alucoord_t (&w)[3]) const; 120 inline void normal(const alucoord_t (&)[2], alucoord_t (&)[3]) const; 121 barycenter(const alucoord_t (& p0)[3],const alucoord_t (& p1)[3],const alucoord_t (& p2)[3],const alucoord_t (& p3)[3],alucoord_t (& barycenter)[3])122 static inline void barycenter(const alucoord_t (&p0)[3], const alucoord_t (&p1)[3], const alucoord_t (&p2)[3], const alucoord_t (&p3)[3], 123 alucoord_t (&barycenter)[3]) 124 { 125 barycenter[0] = 0.25 * (p0[0] + p1[0] + p2[0] + p3[0]); 126 barycenter[1] = 0.25 * (p0[1] + p1[1] + p2[1] + p3[1]); 127 barycenter[2] = 0.25 * (p0[2] + p1[2] + p2[2] + p3[2]); 128 129 #ifdef ALUGRIDDEBUG 130 { 131 BilinearSurfaceMapping map(p0,p1,p2,p3); 132 alucoord_t p[3]; 133 map.map2world(.0, .0, p); 134 for(int j=0; j<3; ++j) 135 { 136 alugrid_assert ( fabs(barycenter[j] - p[j]) < 1e-8 ); 137 } 138 } 139 #endif 140 } 141 }; 142 143 class QuadraturCube2Dbasis { 144 protected : 145 static const alucoord_t _p1 [2]; 146 static const alucoord_t _p3 [4][2]; 147 }; 148 149 template< class A > class QuadraturCube2D : private QuadraturCube2Dbasis { 150 BilinearSurfaceMapping _map; 151 public: QuadraturCube2D(const BilinearSurfaceMapping & m)152 QuadraturCube2D(const BilinearSurfaceMapping & m) : _map (m) {} ~QuadraturCube2D()153 ~QuadraturCube2D() {} 154 typedef typename A::val_t val_t; 155 typedef typename A::arg_t arg_t; 156 inline val_t integrate1 (val_t, const arg_t & = arg_t()); 157 inline val_t integrate3 (val_t, const arg_t & = arg_t()); 158 inline val_t integrate (val_t, const arg_t & = arg_t(), int = 1); 159 }; 160 161 template< class A > class QuadraturCube2D_1 : private QuadraturCube2Dbasis { 162 BilinearSurfaceMapping _map; 163 public: QuadraturCube2D_1(const BilinearSurfaceMapping & m)164 QuadraturCube2D_1(const BilinearSurfaceMapping & m) : _map (m) {} ~QuadraturCube2D_1()165 ~QuadraturCube2D_1() {} 166 typedef typename A::val_t val_t; 167 typedef typename A::arg_t arg_t; 168 inline val_t integrate1 (val_t, const arg_t & = arg_t()); 169 inline val_t integrate3 (val_t, const arg_t & = arg_t()); 170 inline val_t integrate (val_t, const arg_t & = arg_t(), int = 1); 171 }; 172 173 // 174 // # # # # # # # ###### 175 // # ## # # # ## # # 176 // # # # # # # # # # ##### 177 // # # # # # # # # # # 178 // # # ## # # # ## # 179 // # # # ###### # # # ###### 180 // 181 182 TrilinearMapping(const alucoord_t (& x0)[3],const alucoord_t (& x1)[3],const alucoord_t (& x2)[3],const alucoord_t (& x3)[3],const alucoord_t (& x4)[3],const alucoord_t (& x5)[3],const alucoord_t (& x6)[3],const alucoord_t (& x7)[3])183 inline TrilinearMapping::TrilinearMapping (const alucoord_t (&x0)[3], const alucoord_t (&x1)[3], 184 const alucoord_t (&x2)[3], const alucoord_t (&x3)[3], const alucoord_t (&x4)[3], 185 const alucoord_t (&x5)[3], const alucoord_t (&x6)[3], const alucoord_t (&x7)[3]) 186 : p0(x0), p1(x1), p2(x2), p3(x3), p4(x4), p5(x5), p6(x6), p7(x7) { 187 a [0][0] = p3 [0]; 188 a [0][1] = p3 [1]; 189 a [0][2] = p3 [2]; 190 a [1][0] = p0 [0] - p3 [0]; 191 a [1][1] = p0 [1] - p3 [1]; 192 a [1][2] = p0 [2] - p3 [2]; 193 a [2][0] = p2 [0] - p3 [0]; 194 a [2][1] = p2 [1] - p3 [1]; 195 a [2][2] = p2 [2] - p3 [2]; 196 a [3][0] = p7 [0] - p3 [0]; 197 a [3][1] = p7 [1] - p3 [1]; 198 a [3][2] = p7 [2] - p3 [2]; 199 a [4][0] = p1 [0] - p2 [0] - a [1][0]; 200 a [4][1] = p1 [1] - p2 [1] - a [1][1]; 201 a [4][2] = p1 [2] - p2 [2] - a [1][2]; 202 a [5][0] = p6 [0] - p7 [0] - a [2][0]; 203 a [5][1] = p6 [1] - p7 [1] - a [2][1]; 204 a [5][2] = p6 [2] - p7 [2] - a [2][2]; 205 a [6][0] = p4 [0] - p0 [0] - a [3][0]; 206 a [6][1] = p4 [1] - p0 [1] - a [3][1]; 207 a [6][2] = p4 [2] - p0 [2] - a [3][2]; 208 a [7][0] = p5 [0] - p4 [0] + p7 [0] - p6 [0] - p1 [0] + p0 [0] + a [2][0]; 209 a [7][1] = p5 [1] - p4 [1] + p7 [1] - p6 [1] - p1 [1] + p0 [1] + a [2][1]; 210 a [7][2] = p5 [2] - p4 [2] + p7 [2] - p6 [2] - p1 [2] + p0 [2] + a [2][2]; 211 return; 212 } 213 TrilinearMapping(const TrilinearMapping & map)214 inline TrilinearMapping::TrilinearMapping (const TrilinearMapping & map) 215 : p0(map.p0), p1(map.p1), p2(map.p2), p3(map.p3), p4(map.p4), p5(map.p5), p6(map.p6), p7(map.p7) { 216 for (int i = 0; i < 8; i ++) 217 for (int j = 0; j < 3; j ++) 218 a [i][j] = map.a [i][j]; 219 return; 220 } 221 map2world(const alucoord_t (& p)[3],alucoord_t (& world)[3])222 inline void TrilinearMapping::map2world(const alucoord_t (&p)[3], alucoord_t (&world)[3]) const { 223 alucoord_t x = .5 * (p [0] + 1.); 224 alucoord_t y = .5 * (p [1] + 1.); 225 alucoord_t z = .5 * (p [2] + 1.); 226 alucoord_t t3 = y * z; 227 alucoord_t t8 = x * z; 228 alucoord_t t13 = x * y; 229 alucoord_t t123 = x * t3; 230 world [0] = a [0][0] + a [1][0] * x + a [2][0] * y + a [3][0] * z + a [4][0] * t13 + a [5][0] * t3 + a [6][0] * t8 + a [7][0] * t123; 231 world [1] = a [0][1] + a [1][1] * x + a [2][1] * y + a [3][1] * z + a [4][1] * t13 + a [5][1] * t3 + a [6][1] * t8 + a [7][1] * t123; 232 world [2] = a [0][2] + a [1][2] * x + a [2][2] * y + a [3][2] * z + a [4][2] * t13 + a [5][2] * t3 + a [6][2] * t8 + a [7][2] * t123; 233 return; 234 } 235 map2world(const alucoord_t x1,const alucoord_t x2,const alucoord_t x3,alucoord_t (& world)[3])236 inline void TrilinearMapping::map2world(const alucoord_t x1, const alucoord_t x2, const alucoord_t x3, alucoord_t (&world)[3]) const { 237 alucoord_t map [3]; 238 map [0] = x1; 239 map [1] = x2; 240 map [2] = x3; 241 map2world (map, world); 242 return; 243 } 244 affine()245 inline bool TrilinearMapping::affine () const 246 { 247 alucoord_t sum = 0.0; 248 // summ all factor from non-linaer terms 249 for(int i=4; i<8; ++i) 250 { 251 for(int j=0; j<3; ++j) 252 { 253 sum += fabs(a[i][j]); 254 } 255 } 256 257 // mapping is affine when all higher terms are zero 258 return (sum < _epsilon); 259 } 260 integrate2(val_t base,const arg_t & x)261 template< class A > inline typename QuadraturCube3D < A >::val_t QuadraturCube3D < A >::integrate2 (val_t base, const arg_t & x) { 262 263 // Exakt f"ur Polynome vom Grad <= 2 264 // auf dem W"urfel [-1,1]x[-1,1]x[-1,1], V([-1,1]^3) = 8.0 265 266 for(int i = 0; i < 4; i ++) { 267 val_t t = A()( _p2 [i], x); 268 base += (t *= ( _map.det ( _p2 [i]) * 2.0)); 269 } 270 return base; 271 } 272 integrate3(val_t base,const arg_t & x)273 template< class A > inline typename QuadraturCube3D < A >::val_t QuadraturCube3D < A >::integrate3 (val_t base, const arg_t & x) { 274 275 // exakt f"ur Polynome vom Grad <= 3 276 277 for(int i = 0; i < 8; i ++ ) { 278 val_t t = A()( _p3 [i], x); 279 base += (t *= _map.det ( _p3 [i])); 280 } 281 return base; 282 } 283 integrate2(val_t base,const arg_t & x)284 template< class A > inline typename QuadraturCube3D_1 < A >::val_t QuadraturCube3D_1 < A >::integrate2 (val_t base, const arg_t & x) { 285 286 // Exakt f"ur Polynome vom Grad <= 2 287 // auf dem W"urfel [-1,1]x[-1,1]x[-1,1], V([-1,1]^3) = 8.0 288 289 for(int i = 0; i < 4; i ++) { 290 val_t t = A()( _p2 [i], _map, x); 291 base += (t *= ( _map.det ( _p2 [i]) * 2.0)); 292 } 293 return base; 294 } 295 integrate3(val_t base,const arg_t & x)296 template< class A > inline typename QuadraturCube3D_1 < A >::val_t QuadraturCube3D_1 < A >::integrate3 (val_t base, const arg_t & x) { 297 298 // exakt f"ur Polynome vom Grad <= 3 299 300 for(int i = 0; i < 8; i ++ ) { 301 val_t t = A()( _p3 [i], _map, x); 302 base += (t *= _map.det ( _p3 [i])); 303 } 304 return base; 305 } 306 operator()307 inline VolumeCalc::val_t VolumeCalc::operator () (const alucoord_t (&)[3], const arg_t &) { 308 return 1.0; 309 } 310 operator()311 inline VolumeCalc::val_t VolumeCalc::operator () (const alucoord_t (&)[4], const LinearMapping &, const arg_t &) { 312 return 1.0; 313 } 314 BilinearSurfaceMapping(const alucoord_t (& x0)[3],const alucoord_t (& x1)[3],const alucoord_t (& x2)[3],const alucoord_t (& x3)[3])315 inline BilinearSurfaceMapping::BilinearSurfaceMapping (const alucoord_t (&x0)[3], const alucoord_t (&x1)[3], const alucoord_t (&x2)[3], const alucoord_t (&x3)[3]) 316 : _p0 (x0), _p1 (x1), _p2 (x2), _p3 (x3) { 317 _b [0][0] = _p0 [0]; 318 _b [0][1] = _p0 [1]; 319 _b [0][2] = _p0 [2]; 320 _b [1][0] = _p3 [0] - _p0 [0]; 321 _b [1][1] = _p3 [1] - _p0 [1]; 322 _b [1][2] = _p3 [2] - _p0 [2]; 323 _b [2][0] = _p1 [0] - _p0 [0]; 324 _b [2][1] = _p1 [1] - _p0 [1]; 325 _b [2][2] = _p1 [2] - _p0 [2]; 326 _b [3][0] = _p2 [0] - _p1 [0] - _b [1][0]; 327 _b [3][1] = _p2 [1] - _p1 [1] - _b [1][1]; 328 _b [3][2] = _p2 [2] - _p1 [2] - _b [1][2]; 329 _n [0][0] = _b [1][1] * _b [2][2] - _b [1][2] * _b [2][1]; 330 _n [0][1] = _b [1][2] * _b [2][0] - _b [1][0] * _b [2][2]; 331 _n [0][2] = _b [1][0] * _b [2][1] - _b [1][1] * _b [2][0]; 332 _n [1][0] = _b [1][1] * _b [3][2] - _b [1][2] * _b [3][1]; 333 _n [1][1] = _b [1][2] * _b [3][0] - _b [1][0] * _b [3][2]; 334 _n [1][2] = _b [1][0] * _b [3][1] - _b [1][1] * _b [3][0]; 335 _n [2][0] = _b [3][1] * _b [2][2] - _b [3][2] * _b [2][1]; 336 _n [2][1] = _b [3][2] * _b [2][0] - _b [3][0] * _b [2][2]; 337 _n [2][2] = _b [3][0] * _b [2][1] - _b [3][1] * _b [2][0]; 338 return; 339 } 340 BilinearSurfaceMapping(const BilinearSurfaceMapping & m)341 inline BilinearSurfaceMapping::BilinearSurfaceMapping (const BilinearSurfaceMapping & m) 342 : _p0(m._p0), _p1(m._p1), _p2(m._p2), _p3(m._p3) { 343 {for (int i = 0; i < 4; i ++) 344 for (int j = 0; j < 3; j ++ ) 345 _b [i][j] = m._b [i][j]; 346 } 347 {for (int i = 0; i < 3; i ++) 348 for (int j = 0; j < 3; j ++ ) 349 _n [i][j] = m._n [i][j]; 350 } 351 return; 352 } 353 map2world(const alucoord_t (& map)[2],alucoord_t (& wld)[3])354 inline void BilinearSurfaceMapping::map2world (const alucoord_t (&map)[2], alucoord_t (&wld)[3]) const { 355 alucoord_t x = .5 * (map [0] + 1.0); 356 alucoord_t y = .5 * (map [1] + 1.0); 357 alucoord_t xy = x * y; 358 wld[0] = _b [0][0] + x * _b [1][0] + y * _b [2][0] + xy * _b [3][0]; 359 wld[1] = _b [0][1] + x * _b [1][1] + y * _b [2][1] + xy * _b [3][1]; 360 wld[2] = _b [0][2] + x * _b [1][2] + y * _b [2][2] + xy * _b [3][2]; 361 return; 362 } 363 map2world(alucoord_t x,alucoord_t y,alucoord_t (& w)[3])364 inline void BilinearSurfaceMapping::map2world (alucoord_t x, alucoord_t y, alucoord_t (&w)[3]) const { 365 alucoord_t p [2]; 366 p [0] = x; 367 p [1] = y; 368 map2world (p,w); 369 return; 370 } 371 normal(const alucoord_t (& map)[2],alucoord_t (& normal)[3])372 inline void BilinearSurfaceMapping::normal (const alucoord_t (&map)[2], alucoord_t (&normal)[3]) const { 373 alucoord_t x = .5 * (map [0] + 1.0); 374 alucoord_t y = .5 * (map [1] + 1.0); 375 normal [0] = -( _n [0][0] + _n [1][0] * x + _n [2][0] * y); 376 normal [1] = -( _n [0][1] + _n [1][1] * x + _n [2][1] * y); 377 normal [2] = -( _n [0][2] + _n [1][2] * x + _n [2][2] * y); 378 return; 379 } 380 integrate1(val_t base,const arg_t & x)381 template< class A > typename QuadraturCube2D < A >::val_t QuadraturCube2D < A >::integrate1 (val_t base, const arg_t & x) { 382 alucoord_t n [3]; 383 _map.normal (_p1,n); 384 return base + A () (_p1,n,x); 385 } 386 integrate3(val_t base,const arg_t & x)387 template< class A > typename QuadraturCube2D < A >::val_t QuadraturCube2D < A >::integrate3 (val_t base, const arg_t & x) { 388 const alucoord_t quarter = 1.0/4.0; 389 val_t res; 390 for(int i = 0; i < 4; i ++) { 391 alucoord_t n [3]; 392 _map.normal (_p3 [i],n); 393 val_t tmp = A () ( _p3 [i],n,x); 394 base += (tmp *= quarter); 395 } 396 return base; 397 } 398 integrate(val_t base,const arg_t & x,int resolution)399 template< class A > typename QuadraturCube2D < A >::val_t QuadraturCube2D < A >::integrate(val_t base, const arg_t & x, int resolution) { 400 alucoord_t w = 1.0/alucoord_t (resolution * resolution); 401 alucoord_t delta = 2.0/alucoord_t (resolution); 402 for(int i = 0; i < resolution; i ++) { 403 alucoord_t p [2]; 404 p [0] = delta * (alucoord_t (i) + .5) - 1.0; 405 for(int j = 0; j < resolution; j ++) { 406 alucoord_t n [3]; 407 p [1] = delta * (alucoord_t (j) + .5) - 1.0; 408 _map.normal (p,n); 409 val_t tmp = A () (p,n,x); 410 tmp *= w; 411 base += tmp; 412 } 413 } 414 return base; 415 } 416 integrate1(val_t base,const arg_t & x)417 template< class A > typename QuadraturCube2D_1 < A >::val_t QuadraturCube2D_1< A >::integrate1 ( val_t base, const arg_t &x ) 418 { 419 return base + A()( _p1,_map, x ); 420 } 421 422 template< class A > integrate3(val_t base,const arg_t & x)423 typename QuadraturCube2D_1 < A >::val_t QuadraturCube2D_1< A >::integrate3 ( val_t base, const arg_t & x ) 424 { 425 const alucoord_t quarter = 1.0/4.0; 426 val_t res; 427 for(int i = 0; i < 4; i ++) { 428 val_t tmp = A () ( _p3 [i],_map,x); 429 base += (tmp *= quarter); 430 } 431 return base; 432 } 433 434 template< class A > integrate(val_t base,const arg_t & x,int resolution)435 typename QuadraturCube2D_1 < A >::val_t QuadraturCube2D_1 < A >::integrate(val_t base, const arg_t & x, int resolution) 436 { 437 alucoord_t w = 1.0/alucoord_t (resolution * resolution); 438 alucoord_t delta = 2.0/alucoord_t (resolution); 439 for(int i = 0; i < resolution; i ++) { 440 alucoord_t p [2]; 441 p [0] = delta * (alucoord_t (i) + .5) - 1.0; 442 for(int j = 0; j < resolution; j ++) { 443 p [1] = delta * (alucoord_t (j) + .5) - 1.0; 444 val_t tmp = A () (p,_map,x); 445 tmp *= w; 446 base += tmp; 447 } 448 } 449 return base; 450 } 451 operator()452 inline SurfaceCalc::val_t SurfaceCalc::operator()(const alucoord_t (&)[2], const alucoord_t (&n)[3], const arg_t &) 453 { 454 return sqrt (n [0] * n [0] + n [1] * n [1] + n [2] * n [2]); 455 } 456 operator()457 inline SurfaceCalc::val_t SurfaceCalc::operator()(const alucoord_t (&)[3], const alucoord_t (&n)[3], const arg_t &) 458 { 459 return sqrt (n [0] * n [0] + n [1] * n [1] + n [2] * n [2]); 460 } 461 462 } // namespace ALUGrid 463 464 #endif // #ifndef MAPP_CUBE_3D_H_INCLUDED 465