/**
* Intersect a ray with a revolve. If an intersection occurs, a struct
* seg will be acquired and filled in.
*
* Returns -
* 0 MISS
* >0 HIT
*/
int
rt_revolve_shot(struct soltab *stp, struct xray *rp, struct application *ap, struct seg *seghead)
{
struct revolve_specific *rev =
(struct revolve_specific *)stp->st_specific;
struct seg *segp;
struct hit *hitp;
struct hit *hits[MAX_HITS], hit[MAX_HITS];
size_t i, j, nseg, nhits;
int in, out;
fastf_t k, m, h, aa, bb;
point_t dp, pr, xlated;
vect_t vr, ur, norm, normS, normE;
fastf_t start, end, angle;
vect_t dir;
point_t hit1, hit2;
point2d_t hit2d, pt1, pt2;
fastf_t a, b, c, disc, k1, k2, t1, t2;
uint32_t *lng;
struct line_seg *lsg;
struct carc_seg *csg;
nhits = 0;
for (i=0; i<MAX_HITS; i++) hits[i] = &hit[i];
vr[X] = VDOT(rev->xUnit, rp->r_dir);
vr[Y] = VDOT(rev->yUnit, rp->r_dir);
vr[Z] = VDOT(rev->zUnit, rp->r_dir);
VSUB2(xlated, rp->r_pt, rev->v3d);
pr[X] = VDOT(rev->xUnit, xlated);
pr[Y] = VDOT(rev->yUnit, xlated);
pr[Z] = VDOT(rev->zUnit, xlated);
VMOVE(ur, vr);
VUNITIZE(ur);
if (rev->ang < M_2PI) {
VREVERSE(normS, rev->yUnit); /* start normal */
start = (VDOT(normS, rev->v3d) - VDOT(normS, rp->r_pt)) / VDOT(normS, rp->r_dir);
VCROSS(normE, rev->zUnit, rev->rEnd); /* end normal */
end = (VDOT(normE, rev->v3d) - VDOT(normE, rp->r_pt)) / VDOT(normE, rp->r_dir);
VJOIN1(hit1, pr, start, vr);
hit2d[Y] = hit1[Z];
hit2d[X] = sqrt(hit1[X]*hit1[X] + hit1[Y]*hit1[Y]);
VJOIN1(hit2, xlated, start, rp->r_dir);
if (VDOT(rev->xUnit, hit2) < 0) {
/* set the sign of the 2D point's x coord */
hit2d[X] = -hit2d[X];
}
if (rt_sketch_contains(rev->skt, hit2d)) {
hit2d[X] = -hit2d[X];
if (rev->ang > M_PI && rt_sketch_contains(rev->skt, hit2d)) {
/* skip it */
} else {
hitp = hits[nhits++];
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = start;
hitp->hit_surfno = (hit2d[X]>0) ? START_FACE_NEG : START_FACE_POS;
VSET(hitp->hit_vpriv, -hit2d[X], hit2d[Y], 0);
}
}
VJOIN1(hit1, pr, end, vr);
hit2d[Y] = hit1[Z];
hit2d[X] = sqrt(hit1[X]*hit1[X] + hit1[Y]*hit1[Y]);
VJOIN1(hit2, xlated, end, rp->r_dir);
if (VDOT(rev->rEnd, hit2) < 0) {
/* set the sign of the 2D point's x coord */
hit2d[X] = -hit2d[X];
}
if (rt_sketch_contains(rev->skt, hit2d)) {
hit2d[X] = -hit2d[X];
if (rev->ang > M_PI && rt_sketch_contains(rev->skt, hit2d)) {
/* skip it */
} else {
if (nhits >= MAX_HITS) return -1; /* too many hits */
hitp = hits[nhits++];
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = end;
hitp->hit_surfno = (hit2d[X]>0) ? END_FACE_NEG : END_FACE_POS;
VSET(hitp->hit_vpriv, -hit2d[X], hit2d[Y], 0);
}
}
}
/**
* calculate hyperbola parameters
*
* [ (x*x) / aa^2 ] - [ (y-h)^2 / bb^2 ] = 1
*
* x = aa cosh(t - k);
* y = h + bb sinh(t - k);
*/
VREVERSE(dp, pr);
VSET(norm, ur[X], ur[Y], 0);
k = VDOT(dp, norm) / VDOT(ur, norm);
h = pr[Z] + k*vr[Z];
if (NEAR_EQUAL(fabs(ur[Z]), 1.0, RT_DOT_TOL)) {
aa = sqrt(pr[X]*pr[X] + pr[Y]*pr[Y]);
bb = MAX_FASTF;
} else {
aa = sqrt((pr[X] + k*vr[X])*(pr[X] + k*vr[X]) + (pr[Y] + k*vr[Y])*(pr[Y] + k*vr[Y]));
bb = sqrt(aa*aa * (1.0/(1 - ur[Z]*ur[Z]) - 1.0));
}
/**
* if (ur[Z] == 1) {
* bb = inf;
* // ray becomes a line parallel to sketch's y-axis instead of a hyberbola
* }
* if (ur[Z] == 0) {
* bb = 0;
* // ray becomes a line parallel to sketch's x-axis instead of a hyperbola
* // all hits must have x > aa
* }
*/
/* handle open sketches */
if (!NEAR_ZERO(ur[Z], RT_DOT_TOL)) {
for (i=0; i<rev->skt->vert_count && rev->ends[i] != -1; i++) {
V2MOVE(pt1, rev->skt->verts[rev->ends[i]]);
hit2d[Y] = pt1[Y];
if (NEAR_EQUAL(fabs(ur[Z]), 1.0, RT_DOT_TOL)) {
/* ur[Z] == 1 */
hit2d[X] = aa;
} else {
hit2d[X] = aa*sqrt((hit2d[Y]-h)*(hit2d[Y]-h)/(bb*bb) + 1);
}
if (pt1[X] < 0) hit2d[X] = -fabs(hit2d[X]);
if (fabs(hit2d[X]) < fabs(pt1[X])) {
/* valid hit */
if (nhits >= MAX_HITS) return -1; /* too many hits */
hitp = hits[nhits++];
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = (hit2d[Y] - pr[Z]) / vr[Z];
hitp->hit_surfno = HORIZ_SURF;
VJOIN1(hitp->hit_vpriv, pr, hitp->hit_dist, vr);
hitp->hit_point[X] = hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
angle = atan2(hitp->hit_vpriv[Y], hitp->hit_vpriv[X]);
if (pt1[X] < 0) {
angle += M_PI;
} else if (angle < 0) {
angle += M_2PI;
}
hit2d[X] = -hit2d[X];
if (angle > rev->ang) {
nhits--;
continue;
} else if ((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d)
&& hit2d[X] > 0) {
nhits--;
continue;
}
/* X and Y are used for uv(), Z is used for norm() */
hitp->hit_vpriv[X] = pt1[X];
hitp->hit_vpriv[Y] = angle;
if (i+1 < rev->skt->vert_count && rev->ends[i+1] != -1 &&
NEAR_EQUAL(rev->skt->verts[rev->ends[i]][Y],
rev->skt->verts[rev->ends[i+1]][Y], SMALL)) {
hitp->hit_vpriv[Z] = rev->skt->verts[rev->ends[i+1]][X];
i++;
if (fabs(hit2d[X]) < fabs(hitp->hit_vpriv[Z])) {
nhits--;
}
} else {
hitp->hit_vpriv[Z] = 0;
}
}
}
}
/* find hyperbola intersection with each sketch segment */
nseg = rev->skt->curve.count;
for (i=0; i<nseg; i++) {
lng = (uint32_t *)rev->skt->curve.segment[i];
switch (*lng) {
case CURVE_LSEG_MAGIC:
lsg = (struct line_seg *)lng;
V2MOVE(pt1, rev->skt->verts[lsg->start]);
V2MOVE(pt2, rev->skt->verts[lsg->end]);
V2SUB2(dir, pt2, pt1);
if (ZERO(dir[X])) {
m = 1.0;
} else {
m = dir[Y] / dir[X];
}
if (NEAR_EQUAL(fabs(ur[Z]), 1.0, RT_DOT_TOL)) {
/* ray is vertical line at x=aa */
if (FMIN(pt1[X], pt2[X]) < aa && aa < FMAX(pt1[X], pt2[X])) {
/* check the positive side of the sketch (x > 0) */
k1 = (m * (aa - pt1[X]) + pt1[Y] - pr[Z]) / vr[Z];
VJOIN1(hit1, pr, k1, vr);
angle = atan2(hit1[Y], hit1[X]);
hit2d[X] = -aa; /* use neg to check for overlap in contains() */
hit2d[Y] = hit1[Z];
if (angle < 0) {
angle += M_2PI;
}
if (angle < rev->ang &&
!((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d))) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit1);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = -1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k1;
hitp->hit_surfno = i;
}
}
if (FMIN(pt1[X], pt2[X]) < -aa && -aa < FMAX(pt1[X], pt2[X])) {
/* check negative side of the sketch (x < 0) */
k1 = (m * (-aa - pt1[X]) + pt1[Y] - pr[Z]) / vr[Z];
VJOIN1(hit1, pr, k1, vr);
angle = atan2(hit1[Y], hit1[X]);
hit2d[X] = aa; /* use neg to check for overlap in contains() */
hit2d[Y] = hit1[Z];
if (angle < 0) {
angle += M_PI;
}
if (angle < rev->ang &&
!((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d))) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit1);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = 1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k1;
hitp->hit_surfno = i;
}
}
} else if (NEAR_ZERO(ur[Z], RT_DOT_TOL)) {
/* ray is horizontal line at y = h; hit2d[X] > aa */
if (FMIN(pt1[Y], pt2[Y]) < h && h < FMAX(pt1[Y], pt2[Y])) {
if (ZERO(m)) {
hit2d[X] = pt1[X];
} else {
hit2d[X] = pt1[X] + (h-pt1[Y])/m;
}
hit2d[Y] = h;
if (fabs(hit2d[X]) > aa) {
k1 = k + sqrt(hit2d[X]*hit2d[X] - aa*aa);
k2 = k - sqrt(hit2d[X]*hit2d[X] - aa*aa);
VJOIN1(hit1, pr, k1, vr);
angle = atan2(hit1[Y], hit1[X]);
if (hit2d[X] < 0) {
angle += M_PI;
} else if (angle < 0) {
angle += M_2PI;
}
hit2d[X] = -hit2d[X];
if (angle < rev->ang &&
!((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d))) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit1);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = (hit2d[X]>0) ? 1.0/m : -1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k1;
hitp->hit_surfno = i;
}
VJOIN1(hit2, pr, k2, vr);
angle = atan2(hit2[Y], hit2[X]);
if (-hit2d[X] < 0) {
angle += M_PI;
} else if (angle < 0) {
angle += M_2PI;
}
if (angle < rev->ang &&
!((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d))) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit2);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = (hit2d[X]>0) ? 1.0/m : -1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k2;
hitp->hit_surfno = i;
}
}
}
} else {
a = dir[X]*dir[X]/(aa*aa) - dir[Y]*dir[Y]/(bb*bb);
b = 2*(dir[X]*pt1[X]/(aa*aa) - dir[Y]*(pt1[Y]-h)/(bb*bb));
c = pt1[X]*pt1[X]/(aa*aa) - (pt1[Y]-h)*(pt1[Y]-h)/(bb*bb) - 1;
disc = b*b - (4.0 * a * c);
if (!NEAR_ZERO(a, RT_PCOEF_TOL)) {
if (disc > 0) {
disc = sqrt(disc);
t1 = (-b + disc) / (2.0 * a);
t2 = (-b - disc) / (2.0 * a);
k1 = (pt1[Y]-pr[Z] + t1*dir[Y])/vr[Z];
k2 = (pt1[Y]-pr[Z] + t2*dir[Y])/vr[Z];
if (t1 > 0 && t1 < 1) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
VJOIN1(hit1, pr, k1, vr);
angle = atan2(hit1[Y], hit1[X]);
V2JOIN1(hit2d, pt1, t1, dir);
if (hit2d[X] < 0) {
angle += M_PI;
} else if (angle < 0) {
angle += M_2PI;
}
hit2d[X] = -hit2d[X];
if (angle < rev->ang) {
if ((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d)) {
/* overlap, so ignore it */
} else {
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit1);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = (hit2d[X]>0) ? 1.0/m : -1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k1;
hitp->hit_surfno = i;
}
}
}
if (t2 > 0 && t2 < 1) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
VJOIN1(hit2, pr, k2, vr);
angle = atan2(hit2[Y], hit2[X]);
V2JOIN1(hit2d, pt1, t2, dir);
if (hit2d[X] < 0) {
angle += M_PI;
} else if (angle < 0) {
angle += M_2PI;
}
hit2d[X] = -hit2d[X];
if (angle < rev->ang) {
if ((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d)) {
/* overlap, so ignore it */
} else {
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit2);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = (hit2d[X]>0) ? 1.0/m : -1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k2;
hitp->hit_surfno = i;
}
}
}
}
} else if (!NEAR_ZERO(b, RT_PCOEF_TOL)) {
t1 = -c / b;
k1 = (pt1[Y]-pr[Z] + t1*dir[Y])/vr[Z];
if (t1 > 0 && t1 < 1) {
if (nhits >= MAX_HITS) return -1; /* too many hits */
VJOIN1(hit1, pr, k1, vr);
angle = atan2(hit1[Y], hit1[X]);
V2JOIN1(hit2d, pt1, t1, dir);
if (hit2d[X] < 0) {
angle += M_PI;
} else if (angle < 0) {
angle += M_2PI;
}
hit2d[X] = -hit2d[X];
if (angle < rev->ang) {
if ((angle + M_PI < rev->ang || angle - M_PI > 0)
&& rt_sketch_contains(rev->skt, hit2d)) {
/* overlap, so ignore it */
} else {
hitp = hits[nhits++];
hitp->hit_point[X] = -hit2d[X];
hitp->hit_point[Y] = hit2d[Y];
hitp->hit_point[Z] = 0;
VMOVE(hitp->hit_vpriv, hit1);
if (ZERO(m)) {
hitp->hit_vpriv[Z] = 0.0;
} else {
hitp->hit_vpriv[Z] = (hit2d[X]>0) ? 1.0/m : -1.0/m;
}
hitp->hit_magic = RT_HIT_MAGIC;
hitp->hit_dist = k1;
hitp->hit_surfno = i;
}
}
}
}
}
break;
case CURVE_CARC_MAGIC:
/*
circle: (x-cx)^2 + (y-cy)^2 = cr^2
x = (1/2cx)y^2 + (-cy/cx)y + (1/2cx)(cy^2 + cx^2 - cr^2) + (1/2cx)(x^2)
x = f(y) + (1/2cx)x^2
hyperbola:
[(x-hx)/a]^2 - [(y-hy)/b]^2 = 1
x^2 = (a^2/b^2)y^2 + (-2*hy*a^2/b^2)y + (hy^2 * a^2/b^2) + a^2
x^2 = g(y)
plug the second equation into the first to get:
x = f(y) + (1/2cx)g(y)
then square that to get:
x^2 = {f(y) + (1/2cx)g(y)}^2 = g(y)
move all to one side to get:
0 = {f(y) + (1/2cx)g(y)}^2 - g(y)
this is a fourth order polynomial in y.
*/
{
bn_poly_t circleX; /* f(y) */
bn_poly_t hypXsq; /* g(y) */
bn_poly_t hypXsq_scaled; /* g(y) / (2*cx) */
bn_poly_t sum; /* f(y) + g(y)/(2cx) */
bn_poly_t sum_sq; /* {f(y) + g(y)/(2cx)}^2 */
bn_poly_t answer; /* {f(y) + g(y)/(2cx)}^2 - g(y) */
bn_complex_t roots[4];
int rootcnt;
fastf_t cx, cy, crsq = 0; /* carc's (x, y) coords and radius^2 */
point2d_t center, radius;
/* calculate circle parameters */
csg = (struct carc_seg *)lng;
if (csg->radius <= 0.0) {
/* full circle, "end" is center and "start" is on the circle */
V2MOVE(center, rev->skt->verts[csg->end]);
V2SUB2(radius, rev->skt->verts[csg->start], center);
crsq = MAG2SQ(radius);
} else {
point_t startpt, endpt, midpt;
vect_t s_to_m;
vect_t bisector;
vect_t vertical;
fastf_t distance;
fastf_t magsq_s2m;
VSET(vertical, 0, 0, 1);
V2MOVE(startpt, rev->skt->verts[csg->start]);
startpt[Z] = 0.0;
V2MOVE(endpt, rev->skt->verts[csg->end]);
endpt[Z] = 0.0;
VBLEND2(midpt, 0.5, startpt, 0.5, endpt);
VSUB2(s_to_m, midpt, startpt);
VCROSS(bisector, vertical, s_to_m);
VUNITIZE(bisector);
magsq_s2m = MAGSQ(s_to_m);
if (magsq_s2m > csg->radius*csg->radius) {
fastf_t max_radius;
max_radius = sqrt(magsq_s2m);
if (NEAR_EQUAL(max_radius, csg->radius, RT_LEN_TOL)) {
csg->radius = max_radius;
} else {
bu_log("Impossible radius for circular arc in extrusion (%s), is %g, cannot be more than %g!\n",
stp->st_dp->d_namep, csg->radius, sqrt(magsq_s2m));
bu_log("Difference is %g\n", max_radius - csg->radius);
return -1;
}
}
distance = sqrt(csg->radius*csg->radius - magsq_s2m);
/* save arc center */
if (csg->center_is_left) {
V2JOIN1(center, midpt, distance, bisector);
} else {
V2JOIN1(center, midpt, -distance, bisector);
}
}
cx = center[X];
cy = center[Y];
circleX.dgr = 2;
hypXsq.dgr = 2;
hypXsq_scaled.dgr = 2;
sum.dgr = 2;
sum_sq.dgr = 4;
answer.dgr = 4;
circleX.cf[0] = (cy*cy + cx*cx - crsq)/(2.0*cx);
circleX.cf[1] = -cy/cx;
circleX.cf[2] = 1/(2.0*cx);
hypXsq_scaled.cf[0] = hypXsq.cf[0] = aa*aa + h*h*aa*aa/(bb*bb);
hypXsq_scaled.cf[1] = hypXsq.cf[1] = -2.0*h*aa*aa/(bb*bb);
hypXsq_scaled.cf[2] = hypXsq.cf[2] = (aa*aa)/(bb*bb);
bn_poly_scale(&hypXsq_scaled, 1.0 / (2.0 * cx));
bn_poly_add(&sum, &hypXsq_scaled, &circleX);
bn_poly_mul(&sum_sq, &sum, &sum);
bn_poly_sub(&answer, &sum_sq, &hypXsq);
/* It is known that the equation is 4th order. Therefore, if the
* root finder returns other than 4 roots, error.
*/
rootcnt = rt_poly_roots(&answer, roots, stp->st_dp->d_namep);
if (rootcnt != 4) {
if (rootcnt > 0) {
bu_log("tor: rt_poly_roots() 4!=%d\n", rootcnt);
bn_pr_roots(stp->st_name, roots, rootcnt);
} else if (rootcnt < 0) {
static int reported=0;
bu_log("The root solver failed to converge on a solution for %s\n", stp->st_dp->d_namep);
if (!reported) {
VPRINT("while shooting from:\t", rp->r_pt);
VPRINT("while shooting at:\t", rp->r_dir);
bu_log("Additional torus convergence failure details will be suppressed.\n");
reported=1;
}
}
}
break;
}
case CURVE_BEZIER_MAGIC:
break;
case CURVE_NURB_MAGIC:
break;
default:
bu_log("rt_revolve_prep: ERROR: unrecognized segment type!\n");
break;
}
}
if (nhits%2 != 0) {
bu_log("odd number of hits: %zu\n", nhits);
for (i=0; i<nhits; i++) {
bu_log("\t(%6.2f, %6.2f)\t%6.2f\t%2d\n",
hits[i]->hit_point[X], hits[i]->hit_point[Y], hits[i]->hit_dist, hits[i]->hit_surfno);
}
return -1;
}
/* sort hitpoints (an arbitrary number of hits depending on sketch) */
for (i=0; i<nhits; i+=2) {
in = out = -1;
for (j=0; j<nhits; j++) {
if (hits[j] == NULL) continue;
if (in == -1) {
in = j;
continue;
}
/* store shortest dist as 'in', second shortest as 'out' */
if (hits[j]->hit_dist <= hits[in]->hit_dist) {
out = in;
in = j;
} else if (out == -1 || hits[j]->hit_dist <= hits[out]->hit_dist) {
out = j;
}
}
if (in == -1 || out == -1) {
bu_log("failed to find valid segment. nhits: %zu\n", nhits);
break;
}
if (ZERO(hits[in]->hit_dist - hits[out]->hit_dist)) {
hits[in] = NULL;
hits[out] = NULL;
continue;
}
RT_GET_SEG(segp, ap->a_resource);
segp->seg_stp = stp;
segp->seg_in = *hits[in];
hits[in] = NULL;
segp->seg_out = *hits[out];
hits[out] = NULL;
BU_LIST_INSERT(&(seghead->l), &(segp->l));
}
return nhits;
}
int
rt_poly_roots(register bn_poly_t *eqn, /* equation to be solved */
register bn_complex_t roots[], /* space to put roots found */
const char *name) /* name of the primitive being checked */
{
register size_t n; /* number of roots found */
fastf_t factor; /* scaling factor for copy */
/* Remove leading coefficients which are too close to zero,
* to prevent the polynomial factoring from blowing up, below.
*/
while (ZERO(eqn->cf[0])) {
for (n=0; n <= eqn->dgr; n++) {
eqn->cf[n] = eqn->cf[n+1];
}
if (--eqn->dgr <= 0)
return 0;
}
/* Factor the polynomial so the first coefficient is one
* for ease of handling.
*/
factor = 1.0 / eqn->cf[0];
(void) bn_poly_scale(eqn, factor);
n = 0; /* Number of roots found */
/* A trailing coefficient of zero indicates that zero
* is a root of the equation.
*/
while (ZERO(eqn->cf[eqn->dgr])) {
roots[n].re = roots[n].im = 0.0;
--eqn->dgr;
++n;
}
while (eqn->dgr > 2) {
if (eqn->dgr == 4) {
if (bn_poly_quartic_roots(&roots[n], eqn)) {
if (rt_poly_checkroots(eqn, &roots[n], 4) == 0) {
return n+4;
}
}
} else if (eqn->dgr == 3) {
if (bn_poly_cubic_roots(&roots[n], eqn)) {
if (rt_poly_checkroots(eqn, &roots[n], 3) == 0) {
return n+3;
}
}
}
/*
* Set initial guess for root to almost zero.
* This method requires a small nudge off the real axis.
*/
bn_cx_cons(&roots[n], 0.0, SMALL);
if ((rt_poly_findroot(eqn, &roots[n], name)) < 0)
return n; /* return those we found, anyways */
if (fabs(roots[n].im) > 1.0e-5* fabs(roots[n].re)) {
/* If root is complex, its complex conjugate is
* also a root since complex roots come in con-
* jugate pairs when all coefficients are real.
*/
++n;
roots[n] = roots[n-1];
bn_cx_conj(&roots[n]);
} else {
/* Change 'practically real' to real */
roots[n].im = 0.0;
}
rt_poly_deflate(eqn, &roots[n]);
++n;
}
/* For polynomials of lower degree, iterative techniques
* are an inefficient way to find the roots.
*/
if (eqn->dgr == 1) {
roots[n].re = -(eqn->cf[1]);
roots[n].im = 0.0;
++n;
} else if (eqn->dgr == 2) {
bn_poly_quadratic_roots(&roots[n], eqn);
n += 2;
}
return n;
}
