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/*
* hex24a.c
* $Id$
* use 24-tet decomposition to track rays through hex mesh
*/
#include "hex.h"
#define EDGE_BIT(face) (((face)&6)? ((face)&6) : 1)
/* ------------------------------------------------------------------------ */
void hex24_rays(HX_mesh *mesh, long n, real p[][3], real q[][3],
int body, TK_result *result)
{
TK_ray ray;
long cell[4], cell0[4];
real xy[15][3], matrix[5][3], qp0[3];
int tet[4], i, j, odd, tri0[4];
int use_enter= (mesh->start >= 0);
void (*tracker)(HX_mesh *, TK_ray *, long cell[],
real xy[][3], int tet[], TK_result *)=
body? hex24b_track : hex24f_track;
if (n<1) return;
ray_init(&ray, p[0], q[0], (void *)0);
for (i=0 ; i<5 ; i++) for (j=0 ; j<3 ; j++)
matrix[i][j]= (real)(i==j);
hex_init(mesh, cell, tet);
for (j=0 ; j<3 ; j++) tri0[j]= tet[j];
tet[3]= tri0[3]= 0;
for (j=0 ; j<4 ; j++) cell0[j]= cell[j];
for (odd=j=0 ; ; p++,q++) {
n--;
if (use_enter) i= hex_enter(mesh, &ray, cell, xy, tet, qp0);
else i= hex24_begin(mesh, &ray, cell, xy, tet);
if (!i) {
if (n && !start_from_orig && use_enter) {
for (j=0 ; j<3 ; j++) matrix[3][j]= qp0[j];
odd= update_transform(&ray, p[0], q[0], matrix, odd);
if (ray.qr[2]>0.) { tri0[0]= tet[0]; tri0[1]= tet[1]; }
else { tri0[0]= tet[1]; tri0[1]= tet[0]; }
tri0[2]= tet[2]; tri0[3]= tet[3];
for (j=0 ; j<4 ; j++) cell0[j]= cell[j];
}
if (use_enter) i= hex24_enter(xy, tet);
if (!i) tracker(mesh, &ray, cell, xy, tet, result);
}
if (i) ray_store(result, cell[0], (real)i, 1);
if (!n) break;
ray_init(&ray, p[1], q[1], matrix);
for (j=0 ; j<4 ; j++) tet[j]= tri0[j];
for (j=0 ; j<4 ; j++) cell[j]= cell0[j];
}
}
/* ------------------------------------------------------------------------ */
int hex24_enter(real xy[][3], int tet[])
{
int invert= tet[3]; /* invert flag from hex_enter */
int i, corner;
int fourth= tet[0]^tet[1]^tet[2];
int edge= (tet[0]&tet[1]&tet[2]) ^ (tet[0]|tet[1]|tet[2]) ^ 7;
/* initialize tet[3] and corner */
corner= fourth^7;
if ((corner^edge)==tet[2]) corner= 2;
else corner= (corner^edge)==tet[1];
tet[3]= ((tet[0]&edge)!=0) | (edge&6) | 8;
/* load face center into xy scratch space */
for (i=0 ; i<3 ; i++)
xy[tet[3]][i]=
0.25*(xy[tet[0]][i]+xy[tet[1]][i]+xy[tet[2]][i]+xy[fourth][i]);
if (tet_traverse(xy, tet)==corner) { /* rare */
tet[3]= fourth;
if (tet_traverse(xy, tet)==corner) return 4; /* really rare */
}
tet[3]= invert;
return 0;
}
/* ------------------------------------------------------------------------ */
void hex24f_track(HX_mesh *mesh, TK_ray *ray, long cell[],
real xy[][3], int tet[], TK_result *result)
{
real s;
int center, edge, face, flag;
int invert= tet[3]; /* invert flag from hex_enter, hex24_enter */
static real dummy= 0.;
real *qp_compute= result? 0 : &dummy;
/* initialize tet[3], center, and face */
if (tet[2]&8) center= 2;
else center= (tet[1]&8)!=0;
face= tet[center]&7;
edge= EDGE_BIT(face);
if (!(edge&invert)) face^= 1;
flag= (center==2)? 0 : center+1;
tet[3]= tet[flag]^tet[3-flag-center]^edge^7;
tet[3]= 8 | (tet[3]&6) | ((tet[3]&tet[flag])!=0);
/* store initial point */
ray_store(result, cell[0], ray->qr[2]*tri_intersect(xy, tet), 1);
for (;;) {
/* grab new face of current cell */
hex_face(mesh, cell[0], face, ray, invert, xy);
hex24_face(face, invert, xy, 0);
/* track ray through hex using face-centered 24-tet decomposition
* there are three types of tets:
* (0) edge tets have two adjacent hex corners and the two hex
* face centers adjacent to that edge
* (1) body tets have four face centers (part of the central octahedron)
* (2) corner tets have one hex corner and the three adjacent hex
* face centers
* this loop is only on edge tets */
for (tet_traverse(xy,tet) ; !(tet[3]&8) ; tet_traverse(xy,tet)) {
if (tet[2]&8) edge= (tet[1]&8)? tet[0] : tet[1];
else edge= tet[2];
edge^= tet[3]; /* of edge tet just traversed */
/* get third face center for this corner tet and track through */
tet[3]= 8 | (edge&6) | ((edge&tet[3])==0);
tet_traverse(xy, tet);
if (!(tet[3]&8)) {
/* track through central octahedron
* arbitrarily choose face opposite tet[0] as fourth
* -- tet[1] or tet[2] would work just as well */
tet[3]= tet[0]^1;
edge= tet[0]&6; /* 0, 2, or 4 axis of octahedron */
for (tet_traverse(xy,tet) ; (tet[3]&6)!=edge ; tet_traverse(xy,tet))
tet[3]^= 1;
/* track across exit corner tet */
if (tet[0]&1) tet[3]= EDGE_BIT(tet[0]);
else tet[3]= 0;
if (tet[1]&1) tet[3]|= EDGE_BIT(tet[1]);
if (tet[2]&1) tet[3]|= EDGE_BIT(tet[2]);
tet_traverse(xy, tet);
}
/* back in an edge tet from corner tet */
edge= EDGE_BIT(tet[3]);
if (tet[2]&8) tet[3]= (tet[1]&8)? tet[0] : tet[1];
else tet[3]= tet[2];
tet[3]^= edge;
}
s= ray->qr[2]*tri_intersect(xy, tet);
if (!result && s>0.) break; /* reached hex24_begin goal point */
ray_store(result, cell[0], s, 0);
if (tet[2]&8) center= 2;
else center= (tet[1]&8)!=0;
face= (tet[center]&7);
edge= EDGE_BIT(face);
if (edge&invert) face^= 1;
flag= hex_step(mesh, cell, face);
if (flag) {
if (flag!=2) break;
if (ray_reflect(ray, xy, tet, qp_compute, (int *)0)) {
int i= center? center-1 : 2;
int j= i^center^3;
int t= tet[i];
tet[i]= tet[j];
tet[j]= t;
}
hex_face(mesh, cell[0], face^1, ray, invert, xy);
hex24_face(face^1, invert, xy, 0);
} else {
invert^= edge;
}
}
}
/* ------------------------------------------------------------------------ */
void hex24b_track(HX_mesh *mesh, TK_ray *ray, long cell[],
real xy[][3], int tet[], TK_result *result)
{
real s;
int i, center, edge, face, flag;
int invert= tet[3]; /* invert flag from hex_enter, hex24_enter */
static real dummy= 0.;
real *qp_compute= result? 0 : &dummy;
/* initialize tet[3], center, edge, and face */
if (tet[2]&8) center= 2;
else center= (tet[1]&8)!=0;
face= tet[center]&7;
edge= EDGE_BIT(face);
if (!(edge&invert)) face^= 1;
tet[3]= 14;
/* store initial point */
ray_store(result, cell[0], ray->qr[2]*tri_intersect(xy, tet), 1);
for (;;) {
/* grab new face of current cell */
hex_face(mesh, cell[0], face, ray, invert, xy);
hex24_face(face, invert, xy, 1);
/* track ray through hex using body-centered 24-tet decomposition
* each of the 24 tets is identical; they all consist of two
* corners, one face center, and the body center of the hex
* initially the body center xy[14] is the apex tet[3]
* when tet_traverse discards xy[14] we exit the hex */
for (i=tet_traverse(xy,tet) ; tet[3]!=14 ; i=tet_traverse(xy,tet)) {
if (center==i) {
/* move to a new face */
int v0= (tet[0]&8)!=0; /* v0, v1 are the two hex corners */
int v1= (v0 || (tet[1]&8))? 2 : 1;
edge^= tet[v0]^tet[v1]^7;
tet[3]= 8 | (edge&6) | ((tet[v0]&edge)!=0);
center= 3;
} else {
/* remain on current face,
* discarded point flips to diagonally opposite corner */
tet[3]^= edge^7;
if (center==3) center= i;
}
}
if (center==3) center= i;
s= ray->qr[2]*tri_intersect(xy, tet);
if (!result && s>0.) break; /* reached hex24_begin goal point */
ray_store(result, cell[0], s, 0);
face= (tet[center]&7);
edge= EDGE_BIT(face);
if (edge&invert) face^= 1;
flag= hex_step(mesh, cell, face);
if (flag) {
if (flag!=2) break;
if (ray_reflect(ray, xy, tet, qp_compute, (int *)0)) {
int i= center? center-1 : 2;
int j= i^center^3;
int t= tet[i];
tet[i]= tet[j];
tet[j]= t;
}
hex_face(mesh, cell[0], face^1, ray, invert, xy);
hex24_face(face^1, invert, xy, 1);
} else {
invert^= edge;
}
}
}
/* ------------------------------------------------------------------------ */
static void face0(real xy[][3]);
static void face1(real xy[][3]);
static void face2(real xy[][3]);
static void face3(real xy[][3]);
static void face4(real xy[][3]);
static void face5(real xy[][3]);
static void (*facen[6])(real xy[][3])= {
&face0, &face1, &face2, &face3, &face4, &face5 };
void hex24_face(int face, int invert, real xy[][3], int body)
{
int i;
if (EDGE_BIT(face)&invert) face^= 1; /* convert from mesh to xy index */
facen[face](xy);
if (body) {
face|= 8;
for (i=0 ; i<3 ; i++) xy[14][i]= 0.5*(xy[face][i]+xy[face^1][i]);
}
}
static void face0(real xy[][3])
{
int i;
for (i=0 ; i<3 ; i++) {
xy[12][i]= 0.25*(xy[0][i]+xy[1][i]+xy[2][i]+xy[3][i]);
xy[11][i]= 0.25*(xy[2][i]+xy[3][i]+xy[6][i]+xy[7][i]);
xy[13][i]= 0.25*(xy[4][i]+xy[5][i]+xy[6][i]+xy[7][i]);
xy[10][i]= 0.25*(xy[0][i]+xy[1][i]+xy[4][i]+xy[5][i]);
xy[8][i]= 0.25*(xy[0][i]+xy[2][i]+xy[4][i]+xy[6][i]);
}
}
static void face1(real xy[][3])
{
int i;
for (i=0 ; i<3 ; i++) {
xy[12][i]= 0.25*(xy[0][i]+xy[1][i]+xy[2][i]+xy[3][i]);
xy[11][i]= 0.25*(xy[2][i]+xy[3][i]+xy[6][i]+xy[7][i]);
xy[13][i]= 0.25*(xy[4][i]+xy[5][i]+xy[6][i]+xy[7][i]);
xy[10][i]= 0.25*(xy[0][i]+xy[1][i]+xy[4][i]+xy[5][i]);
xy[9][i]= 0.25*(xy[1][i]+xy[3][i]+xy[5][i]+xy[7][i]);
}
}
static void face2(real xy[][3])
{
int i;
for (i=0 ; i<3 ; i++) {
xy[8][i]= 0.25*(xy[0][i]+xy[2][i]+xy[4][i]+xy[6][i]);
xy[13][i]= 0.25*(xy[4][i]+xy[5][i]+xy[6][i]+xy[7][i]);
xy[9][i]= 0.25*(xy[1][i]+xy[3][i]+xy[5][i]+xy[7][i]);
xy[12][i]= 0.25*(xy[0][i]+xy[1][i]+xy[2][i]+xy[3][i]);
xy[10][i]= 0.25*(xy[0][i]+xy[1][i]+xy[4][i]+xy[5][i]);
}
}
static void face3(real xy[][3])
{
int i;
for (i=0 ; i<3 ; i++) {
xy[8][i]= 0.25*(xy[0][i]+xy[2][i]+xy[4][i]+xy[6][i]);
xy[13][i]= 0.25*(xy[4][i]+xy[5][i]+xy[6][i]+xy[7][i]);
xy[9][i]= 0.25*(xy[1][i]+xy[3][i]+xy[5][i]+xy[7][i]);
xy[12][i]= 0.25*(xy[0][i]+xy[1][i]+xy[2][i]+xy[3][i]);
xy[11][i]= 0.25*(xy[2][i]+xy[3][i]+xy[6][i]+xy[7][i]);
}
}
static void face4(real xy[][3])
{
int i;
for (i=0 ; i<3 ; i++) {
xy[10][i]= 0.25*(xy[0][i]+xy[1][i]+xy[4][i]+xy[5][i]);
xy[9][i]= 0.25*(xy[1][i]+xy[3][i]+xy[5][i]+xy[7][i]);
xy[11][i]= 0.25*(xy[2][i]+xy[3][i]+xy[6][i]+xy[7][i]);
xy[8][i]= 0.25*(xy[0][i]+xy[2][i]+xy[4][i]+xy[6][i]);
xy[12][i]= 0.25*(xy[0][i]+xy[1][i]+xy[2][i]+xy[3][i]);
}
}
static void face5(real xy[][3])
{
int i;
for (i=0 ; i<3 ; i++) {
xy[10][i]= 0.25*(xy[0][i]+xy[1][i]+xy[4][i]+xy[5][i]);
xy[9][i]= 0.25*(xy[1][i]+xy[3][i]+xy[5][i]+xy[7][i]);
xy[11][i]= 0.25*(xy[2][i]+xy[3][i]+xy[6][i]+xy[7][i]);
xy[8][i]= 0.25*(xy[0][i]+xy[2][i]+xy[4][i]+xy[6][i]);
xy[13][i]= 0.25*(xy[4][i]+xy[5][i]+xy[6][i]+xy[7][i]);
}
}
/* ------------------------------------------------------------------------ */
static int hex24_pierce(HX_mesh *mesh, TK_ray *ray, long cell,
real xy[][3], int tri[]);
int hex24_begin(HX_mesh *mesh, TK_ray *ray, long cell[],
real xy[][3], int tri[])
{
int i, j;
long k;
real ctop, p[3], q[3];
/* check that strides are consistent with block */
if (mesh->block != cell[1]) {
mesh->block= cell[1];
mesh->stride= mesh->blks[cell[1]].stride;
}
/* find centroid of initial cell, store in xy[0] */
for (i=0 ; i<3 ; i++) {
xy[0][i]= 0.0;
for (j=0 ; j<8 ; j++) {
k= cell[0];
if (j&1) k-= mesh->stride[0];
if (j&2) k-= mesh->stride[1];
if (j&4) k-= mesh->stride[2];
xy[0][i]+= mesh->xyz[k][i];
}
xy[0][i]*= 0.125;
}
/* compute direction from centroid of cell to ray->p */
for (i=0, ctop=0.0 ; i<3 ; i++) {
j= ray->order[i];
q[j]= ray->p[i] - xy[0][j]; /* will become ray1.q */
ctop+= q[j]*q[j];
p[j]= ray->p[i]; /* will become ray1.p */
}
if (ctop) {
/* invent a fake ray from centroid to ray->p */
TK_ray ray1;
extern double sqrt(double);
real matrix[5][3], qp0[3];
ctop= 1./sqrt(ctop);
for (i=0 ; i<3 ; i++) q[i]*= ctop;
ray_init(&ray1, p, q, (void *)0);
/* find face triangle through which fake ray enters cell[0]
* -- this may fail only if centroid not inside cell[0] */
if (hex24_pierce(mesh, &ray1, cell[0], xy, tri)) return 1;
/* initialize ray1.qp to any vector perpendicular to q */
qp0[ray1.order[0]]= ray1.qp[0]= 0.;
ray1.qp[1]= q[ray1.order[2]];
ray1.qp[2]= -q[ray1.order[1]];
ctop= 1./sqrt(ray1.qp[1]*ray1.qp[1] + ray1.qp[2]*ray1.qp[2]);
qp0[ray1.order[1]]= (ray1.qp[1]*= ctop);
qp0[ray1.order[2]]= (ray1.qp[2]*= ctop);
for (i=0 ; i<5 ; i++) for (j=0 ; j<3 ; j++)
matrix[i][j]= (real)(i==j);
/* track fake ray to cell containing ray->p */
hex24f_track(mesh, &ray1, cell, xy, tri, (TK_result *)0);
/* re-initialize original ray to be consistent with any
* reflections suffered during tracking */
for (j=0 ; j<3 ; j++) matrix[3][j]= qp0[j];
update_transform(&ray1, p, q, matrix, 0);
for (j=0 ; j<3 ; j++) q[j]= ray->q[j];
ray_init(ray, p, q, matrix);
}
/* find entry face triangle
* -- failure here is a bug or rounding error? */
return hex24_pierce(mesh, ray, cell[0], xy, tri);
}
static void pierce24_setup(real xy[][3], int tri[], int t);
static int hex24_pierce(HX_mesh *mesh, TK_ray *ray, long cell,
real xy[][3], int tri[])
{
int t, t_min, test_tri[3];
real s, s_min;
/* the importance of tri[3] is that the call to the tracker
* following this entry routine will assume that only one face
* (determined by tri[3]) of the xy array has been loaded
* - unlike the hex_enter entry point routine, this routine loads
* all 8 corners of the cell, and so must merely set tri[3]
* to be consistent with the current meaning of the points in xy */
tri[3]= 0;
/* move all 8 points of cell into xy scratch array */
hex_face(mesh, cell, 0, ray, tri[3], xy);
hex_face(mesh, cell, 1, ray, tri[3], xy);
for (t=0 ; t<3 ; t++) xy[8][t]=
0.25*(xy[0][t]+xy[2][t]+xy[4][t]+xy[6][t]);
hex24_face(1, tri[3], xy, 0);
/* check all 24 face triangles for entry and exit points
* -- remember most negative s */
t_min= -1;
s_min= 1.e35;
for (t=0 ; t<24 ; t++) {
pierce24_setup(xy, test_tri, t);
if (tri_contains(xy, test_tri)) {
s= ray->qr[2]*tri_intersect(xy, test_tri);
if (s < s_min) s_min= s, t_min= t;
}
}
if (t_min < 0) return 1;
pierce24_setup(xy, tri, t_min);
return 0;
}
static void pierce24_setup(real xy[][3], int tri[], int t)
{
/* based on hex_init */
int face= ((unsigned int)t)>>2;
int i= ((unsigned int)face)>>1;
int k= i? i-1 : 2;
int quad[4];
quad[0]= (t&4)? (1<<i) : 0;
quad[1]= quad[0] | (1<<(i^k^3));
/* this time, put them in cyclic order */
quad[3]= quad[0] | (1<<k);
quad[2]= quad[1] | quad[3];
t= t&3;
tri[0]= quad[t++]; tri[1]= quad[(t&4)? 0 : t];
tri[2]= 8 | face;
tri_check(xy, tri);
}
/* ------------------------------------------------------------------------ */
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