1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398
|
/*
* hex.c
* $Id$
* generic tools for dealing with a hex mesh
*/
#include "hex.h"
#define FACE_INDEX(edge, vertex) (((edge)&6) | (((edge)&(vertex))!=0))
#define EDGE_BIT(face) (1<<((unsigned int)(face)>>1))
/* ------------------------------------------------------------------------ */
int hex_enter(HX_mesh *mesh, TK_ray *ray, long cell[],
real xy[][3], int tri[], real qp0[])
{
int bndy, edge, diag, face, invert, hit_miss, flag;
real *qp= ray->qp;
/* workspace for entry_setup, edge_test, and tri_traverse */
real dot[4];
int flags[3];
/* check that strides are consistent with block */
if (mesh->block != cell[1]) {
mesh->block= cell[1];
mesh->stride= mesh->blks[cell[1]].stride;
}
/* initialize xy for given cell, bndy face */
invert= tri[3]; /* stored from previous call */
face= (tri[0]&tri[1]&tri[2]) ^ (tri[0]|tri[1]|tri[2]);
bndy= face ^ 7;
bndy= FACE_INDEX(bndy,tri[0]^invert);
hex_face(mesh, cell[0], bndy, ray, invert, xy);
/* initialize dot, flags, possibly permute tri */
edge= entry_setup(ray, xy, tri, dot, flags);
if (qp0) {
qp0[ray->order[0]]= qp[0];
qp0[ray->order[1]]= qp[1];
qp0[ray->order[2]]= qp[2];
}
if (edge>1) return 2;
if ((tri[0]^face) == tri[1]) {
/* about to step across entry face diagonal */
diag= edge;
} else if ((tri[edge]^face) != tri[2]) {
/* about to step off of entry face, just crossed diagonal */
diag= 2;
} else {
/* about to step off of entry face, never crossed diagonal */
diag= !edge;
}
while (!(hit_miss= edge_test(xy, tri, dot, flags))) {
if (edge!=diag) {
/* step to next boundary face
* -- note that face and bndy are *not* inverted by invert */
int fedg;
if (diag!=2) edge= diag;
fedg= tri[edge]^tri[2];
face= FACE_INDEX(fedg,tri[edge]^invert);
flag= hex_step(mesh, cell, face);
/* handle mesh boundaries */
if (flag) {
int tri2= tri[2]; /* save original bndy face value */
tri[2]= tri[edge]^EDGE_BIT(bndy);
if (flag!=2) { /* handle corners that are "rounds" */
int tmp= bndy;
bndy= face;
face= tmp^1;
} else {
/* grab interior edge on reflecting face
* -- more work than strictly necessary, since ray_reflect
* will undo the partial projection
* -- a mess anyway owing to necessity of following check that
* tri[2] is actually a distinct point */
hex_edge(mesh, cell[0], bndy^1, face, ray, invert, xy);
if ((xy[tri[2]][0]==xy[tri[0]][0] &&
xy[tri[2]][1]==xy[tri[0]][1] &&
xy[tri[2]][2]==xy[tri[0]][2]) ||
(xy[tri[2]][0]==xy[tri[1]][0] &&
xy[tri[2]][1]==xy[tri[1]][1] &&
xy[tri[2]][2]==xy[tri[1]][2])) tri[2]= tri2^7;
/* finally reflect the ray */
ray_reflect(ray, xy, tri, dot, flags);
tri[2]= tri2; /* restore original bndy face value */
/* ray_reflect reprojected the face edge already,
* arrange for following hex_edge to reproject the
* opposite face */
face^= 1;
}
/* do not update invert here */
} else {
/* don't bother to check for "fillet" corners */
invert^= EDGE_BIT(face);
}
/* grab coordinates of next edge on new boundary face */
hex_edge(mesh, cell[0], bndy, face, ray, invert, xy);
/* if just crossed diagonal, reset diagonal flag */
if (diag==2) diag= edge;
} else {
/* step across face diagonal */
tri[2]^= EDGE_BIT(bndy)^7;
/* second tri_traverse always steps off face */
diag= 2;
}
/* cross the current triangle */
edge= tri_traverse(qp, xy, tri, dot);
}
if (hit_miss==2) return 1;
/* check that triangle orientation is correct for tet_traverse */
if ((xy[tri[1]][0]-xy[tri[0]][0])*(xy[tri[2]][1]-xy[tri[0]][1]) <
(xy[tri[1]][1]-xy[tri[0]][1])*(xy[tri[2]][0]-xy[tri[0]][0])) {
diag= tri[2];
tri[2]= tri[edge];
tri[edge]= diag;
}
/* allow xy scratch array to be interpreted correctly externally */
tri[3]= invert;
return 0;
}
/* ------------------------------------------------------------------------ */
/* enumerate all 24 orientations of a cube
* - orientations[o][0] = o>>2 (==f0)
* - orientations[o][2] = ((f0&4)?f0-4:f0+2) ^ ((o&2)?(f0&6)^6:0) ^ (o&1)
* - that is, the 2 bit of o tells whether ijk cyclic order preserved
* while the 1 bit tells if the min or max face has switched
*/
static int orientations[24][6]= {
{0,1,2,3,4,5}, {0,1,3,2,5,4}, {0,1,4,5,3,2}, {0,1,5,4,2,3},
{1,0,3,2,4,5}, {1,0,2,3,5,4}, {1,0,5,4,3,2}, {1,0,4,5,2,3},
{2,3,4,5,0,1}, {2,3,5,4,1,0}, {2,3,0,1,5,4}, {2,3,1,0,4,5},
{3,2,5,4,0,1}, {3,2,4,5,1,0}, {3,2,1,0,5,4}, {3,2,0,1,4,5},
{4,5,0,1,2,3}, {4,5,1,0,3,2}, {4,5,2,3,1,0}, {4,5,3,2,0,1},
{5,4,1,0,2,3}, {5,4,0,1,3,2}, {5,4,3,2,1,0}, {5,4,2,3,0,1}
};
static int orient_compose(int second, int first);
static int orient_compose(int second, int first)
{
int *o1= orientations[first];
int *o2= orientations[second];
/* destination of face 0 determines row in orientations array,
* when regarded as 6 rows of 4 columns
* low order two bits determined by destination of face 2 */
int f0= o2[o1[0]];
int lo= o2[o1[2]] ^ ((f0&4)? f0-4 : f0+2);
if (lo&4) lo^= 6; /* set 2 bit, not 4 bit */
return (f0<<2) | lo;
}
int hex_step(HX_mesh *mesh, long cell[], int face)
{
int i= ((unsigned int)(
face= orientations[mesh->orient][face]
))>>1;
long stride= mesh->stride[i];
long bound= mesh->bound[cell[0]-((face&1)?0:stride)][i];
if (!bound) {
/* usual case is to remain within current block */
if (!(face&1)) stride= -stride;
cell[0]+= stride;
} else if (bound<0) {
/* hit true boundary */
return -bound;
} else {
/* hit block boundary, must switch to new block */
HX_blkbnd *bnd= &mesh->bnds[bound-1];
long block= bnd->block;
mesh->block= block;
mesh->stride= mesh->blks[block].stride;
cell[0]= bnd->cell;
cell[1]= block;
if (bnd->orient) {
/* need to reset mesh->orient */
if (mesh->orient) {
/* object is to find orient such that
* orientations[orient][face] == bnd_orient[mesh_orient[face]]
* for every value of face */
mesh->orient= orient_compose(bnd->orient, mesh->orient);
} else {
mesh->orient= bnd->orient;
}
}
}
return 0;
}
static int faces[6][4]= {
{ 0, 2, 4, 6 }, { 1, 3, 5, 7 },
{ 0, 4, 1, 5 }, { 2, 6, 3, 7 },
{ 0, 1, 2, 3 }, { 4, 5, 6, 7 }};
static int edges[6][3]= {
{ 0, 1, 2 }, { 0, 1, 2 },
{ 1, 2, 0 }, { 1, 2, 0 },
{ 2, 0, 1 }, { 2, 0, 1 }};
void hex_face(HX_mesh *mesh, long cell, int face,
TK_ray *ray, int invert, real xy[][3])
{
real *p= ray->p;
real *qr= ray->qr;
int *order= ray->order;
int i, ix;
real (*mxyz)[3]= mesh->xyz;
int *fx= faces[(
face= orientations[mesh->orient][face]
)];
int *em= edges[face];
long im[4];
long m= cell - mesh->stride[0] - mesh->stride[1] - mesh->stride[2];
if (face&1) m+= mesh->stride[em[0]];
mxyz= mxyz+m; /* DEC cc doesn't like &mxyz[m] */
im[0]= 0;
im[1]= mesh->stride[em[1]];
im[2]= mesh->stride[em[2]];
im[3]= im[1]+im[2];
for (i=0 ; i<4 ; i++) {
ix= fx[i]^invert;
m= im[i];
xy[ix][2]= mxyz[m][order[2]] - p[2];
xy[ix][1]= mxyz[m][order[1]] - p[1] - xy[ix][2]*qr[1];
xy[ix][0]= mxyz[m][order[0]] - p[0] - xy[ix][2]*qr[0];
}
}
void hex_edge(HX_mesh *mesh, long cell, int bndy, int face,
TK_ray *ray, int invert, real xy[][3])
{
real *p= ray->p;
real *qr= ray->qr;
int *order= ray->order;
real (*mxyz)[3]= mesh->xyz+cell; /* DEC cc doesn't like &mesh->xyz[cell] */
int f= edges[(
face= orientations[mesh->orient][face]
)][0];
int b= edges[bndy][0];
int fb= edges[face^bndy^6][0];
long m= mesh->stride[fb];
int ix, x= 0;
if (face&1) x+= 1<<f;
else mxyz-= mesh->stride[f];
if (bndy&1) x+= 1<<b;
else mxyz-= mesh->stride[b];
ix= x^invert;
xy[ix][2]= mxyz[-m][order[2]] - p[2];
xy[ix][1]= mxyz[-m][order[1]] - p[1] - xy[ix][2]*qr[1];
xy[ix][0]= mxyz[-m][order[0]] - p[0] - xy[ix][2]*qr[0];
x+= 1<<fb;
ix= x^invert;
xy[ix][2]= mxyz[0][order[2]] - p[2];
xy[ix][1]= mxyz[0][order[1]] - p[1] - xy[ix][2]*qr[1];
xy[ix][0]= mxyz[0][order[0]] - p[0] - xy[ix][2]*qr[0];
}
static int triangle_flag= 0;
int hex_triang(int flag)
{
int old= triangle_flag;
if (flag==0 || flag==1) triangle_flag= flag;
return old;
}
#undef ABS
#define ABS(x) ((x)<0? -(x) : (x))
int hex_init(HX_mesh *mesh, long cell[], int tri[])
{
int i, j, k, edge, quad[4];
long s, ndx[4], d0, d1, p0, p1;
real v, l0, l1, tmp, dj, dk;
real (*xyz)[3]= mesh->xyz;
long start= mesh->start;
int face;
if (start>=0) {
face= start%6;
cell[0]= (start/= 6);
} else {
cell[0]= start= -1 - start;
face= -1;
}
for (s=0 ; s<mesh->nblks ; s++)
if (mesh->blks[s].first<=start && mesh->blks[s].final>start) break;
if (s>=mesh->nblks) return 1;
mesh->stride= mesh->blks[s].stride;
mesh->orient= 0;
mesh->block= cell[1]= s;
if (face<0) return 0;
i= ((unsigned int)face)>>1;
k= i? i-1 : 2;
j= i^k^3;
edge= 1<<i;
quad[0]= (face&1)? edge : 0;
quad[1]= quad[0] | (1<<j);
quad[2]= quad[0] | (1<<k);
quad[3]= quad[1] | quad[2];
s= ((face&1)? -mesh->stride[i] : mesh->stride[i]);
ndx[3]= cell[0] - ((face&1)? 0 : mesh->stride[i]);
ndx[2]= ndx[3] - mesh->stride[j];
ndx[1]= ndx[3] - mesh->stride[k];
ndx[0]= ndx[3] - mesh->stride[j] - mesh->stride[k];
if (triangle_flag) {
d0= 0; d1= 3; p0= 2; p1= 1;
} else {
d0= 1; d1= 2; p0= 0; p1= 3;
}
/* compute volume of cell to check mesh handedness,
* compute distances of corners from diagonal */
v= l0= l1= 0.;
for (i=0 ; i<3 ; i++) {
k= i? i-1 : 2;
j= k^i^3;
/* this actually gives 64*volume, v<0 for right-handed cell? */
v+= (xyz[ndx[1]][i]+xyz[ndx[0]][i]+xyz[ndx[3]][i]+xyz[ndx[2]][i] -
xyz[ndx[1]+s][i]-xyz[ndx[0]+s][i]-xyz[ndx[3]+s][i]-xyz[ndx[2]+s][i])*
((xyz[ndx[1]][j]-xyz[ndx[0]][j]+xyz[ndx[3]][j]-xyz[ndx[2]][j] +
xyz[ndx[1]+s][j]-xyz[ndx[0]+s][j]+xyz[ndx[3]+s][j]-xyz[ndx[2]+s][j])*
(xyz[ndx[2]][k]-xyz[ndx[0]][k]+xyz[ndx[3]][k]-xyz[ndx[1]][k] +
xyz[ndx[2]+s][k]-xyz[ndx[0]+s][k]+xyz[ndx[3]+s][k]-xyz[ndx[1]+s][k]) -
(xyz[ndx[1]][k]-xyz[ndx[0]][k]+xyz[ndx[3]][k]-xyz[ndx[2]][k] +
xyz[ndx[1]+s][k]-xyz[ndx[0]+s][k]+xyz[ndx[3]+s][k]-xyz[ndx[2]+s][k])*
(xyz[ndx[2]][j]-xyz[ndx[0]][j]+xyz[ndx[3]][j]-xyz[ndx[1]][j] +
xyz[ndx[2]+s][j]-xyz[ndx[0]+s][j]+xyz[ndx[3]+s][j]-xyz[ndx[1]+s][j]));
dj= xyz[ndx[d1]][j]-xyz[ndx[d0]][j];
dk= xyz[ndx[d1]][k]-xyz[ndx[d0]][k];
tmp= dj*(xyz[ndx[p0]][k]-xyz[ndx[d0]][k]) -
dk*(xyz[ndx[p0]][j]-xyz[ndx[d0]][j]);
l0+= ABS(tmp);
tmp= dj*(xyz[ndx[p1]][k]-xyz[ndx[d0]][k]) -
dk*(xyz[ndx[p1]][j]-xyz[ndx[d0]][j]);
l1+= ABS(tmp);
}
if (l0>l1) { /* points are p0, d0, d1 */
if (v>0.) { /* left-handed cell? */
tri[0]= quad[p0];
tri[1]= quad[d1];
tri[2]= quad[d0];
} else {
tri[0]= quad[p0];
tri[1]= quad[d0];
tri[2]= quad[d1];
}
} else { /* points are p1, d1, d0 */
if (v>0.) { /* left-handed cell? */
tri[0]= quad[p1];
tri[1]= quad[d0];
tri[2]= quad[d1];
} else {
tri[0]= quad[p1];
tri[1]= quad[d1];
tri[2]= quad[d0];
}
}
return 0;
}
/* ------------------------------------------------------------------------ */
int start_from_orig= 0;
int hex_startflag(int flag)
{
int oldflag= start_from_orig;
if (flag==0 || flag==1) start_from_orig= flag;
return oldflag;
}
/* ------------------------------------------------------------------------ */
|