static void
fill_colortbl(unsigned char *lo_rgb, unsigned char *hi_rgb)
{
int i;
double a, b;
#if BLEND_USING_HSV
fastf_t lo_hsv[3], hi_hsv[3];
fastf_t hsv[3];
bu_rgb_to_hsv(lo_rgb, lo_hsv);
bu_rgb_to_hsv(hi_rgb, hi_hsv);
#endif
for (i = 0; i < MAX_COLORTBL; ++i) {
b = ((double) i) / (MAX_COLORTBL - 1);
a = 1.0 - b;
#if BLEND_USING_HSV
VBLEND2(hsv, a, lo_hsv, b, hi_hsv);
bu_hsv_to_rgb(hsv, colortbl[i]);
#else
VBLEND2(colortbl[i], a, lo_rgb, b, hi_rgb);
#endif
}
}
static void
val_To_RGB(cell_val cv, unsigned char *rgb)
{
double val;
if (color_flag) {
COPYRGB(rgb, cv.v_color);
return;
}
val = (cv.v_scalar - dom_min) * dom_cvt;
if ((boolean_flag && !ZERO(cv.v_scalar - bool_val))
|| (val < SMALL_FASTF) || (val > 10.0))
{
COPYRGB(rgb, BACKGROUND);
} else if (ZERO(val)) {
COPYRGB(rgb, WHITE);
} else {
int idx;
double rem;
double res;
if (interp_flag) {
vect_t prev_hsv;
vect_t hsv;
vect_t next_hsv;
idx = val + 0.01; /* convert to range [0 to 10] */
if ((rem = val - (double) idx) < 0.0) /* remainder */
rem = 0.0;
res = 1.0 - rem;
#if BLEND_USING_HSV
bu_rgb_to_hsv(colortbl[idx], prev_hsv);
bu_rgb_to_hsv(colortbl[idx+1], next_hsv);
VBLEND2(hsv, res, prev_hsv, rem, next_hsv);
bu_hsv_to_rgb(hsv, rgb);
#else
VBLEND2(rgb, res, colortbl[idx], rem, colortbl[idx+1]);
#endif
} else {
idx = val + 0.51;
COPYRGB(rgb, colortbl[idx]);
}
}
return;
}
void
quat_slerp(fastf_t *qout, const fastf_t *q1, const fastf_t *q2, double f)
{
double omega;
double cos_omega;
double invsin;
register double s1, s2;
cos_omega = QDOT( q1, q2 );
if ( (1.0 + cos_omega) > 1.0e-5 ) {
/* cos_omega > -0.99999 */
if ( (1.0 - cos_omega) > 1.0e-5 ) {
/* usual case */
omega = acos(cos_omega); /* XXX atan2? */
invsin = 1.0 / sin(omega);
s1 = sin( (1.0-f)*omega ) * invsin;
s2 = sin( f*omega ) * invsin;
} else {
/*
* cos_omega > 0.99999
* The ends are very close to each other,
* use linear interpolation, to avoid divide-by-zero
*/
s1 = 1.0 - f;
s2 = f;
}
QBLEND2( qout, s1, q1, s2, q2 );
} else {
/*
* cos_omega == -1, omega = M_PI.
* The ends are nearly opposite, 180 degrees (M_PI) apart.
*/
/* (I have no idea what permuting the elements accomplishes,
* perhaps it creates a perpendicular? */
qout[X] = -q1[Y];
qout[Y] = q1[X];
qout[Z] = -q1[W];
s1 = sin( (0.5-f) * M_PI );
s2 = sin( f * M_PI );
VBLEND2( qout, s1, q1, s2, qout );
qout[W] = q1[Z];
}
}
/*
* M A I N ( )
*/
int
main (int argc, char **argv)
{
char *inbuf; /* The input scanline */
char *outbuf; /* " output " */
char *in, *out; /* Pointers into inbuf and outbuf */
fastf_t twice_r1r2;
fastf_t squares;
fastf_t scale_fac;
fastf_t theta;
fastf_t x; /* Scale factor for pixel blending */
int i; /* Pixel index in inbuf */
int j; /* " " " outbuf */
long int row;
long int row_width;
if (!get_args( argc, argv ))
{
(void) fputs(usage, stderr);
bu_exit (1, NULL);
}
if (solid_type == SPHERE)
{
(void) fprintf(stderr, "Sphere scaling not yet implemented\n");
bu_exit (1, NULL);
}
else if (solid_type != TORUS)
{
(void) fprintf(stderr, "Illegal solid type %d\n", solid_type);
bu_exit (0, NULL);
}
/*
* Autosize the input if appropriate
*/
if (fileinput && autosize)
{
unsigned long int w, h;
if (fb_common_file_size(&w, &h, file_name, 3))
{
file_width = (long)w;
file_height = (long)h;
}
else
(void) fprintf(stderr, "texturescale: unable to autosize\n");
}
/*
* Initialize some runtime constants
*/
twice_r1r2 = 2 * r1 * r2;
squares = r1 * r1 + r2 * r2;
scale_fac = file_width / (r1 + r2);
/*
* Allocate 1-scanline buffers for input and output
*/
outbuf = bu_malloc(3*file_width, "outbuf");
inbuf = bu_malloc(3*file_width, "inbuf");
/*
* Do the filtering
*/
for (row = 0; row < file_height; ++row)
{
/*
* Read an input scanline
*/
if (! read_row(inbuf, file_width, infp))
{
perror(file_name);
(void) fprintf(stderr, "texturescale: fread() error\n");
bu_exit (1, NULL);
}
/*
* Determine how much of the input scanline we want
*/
theta = 2 * bn_pi * row / file_height;
row_width = scale_fac * sqrt(squares - twice_r1r2 * cos(theta));
in = inbuf + ((file_width - row_width) / 2) * 3;
out = outbuf;
/*
* Scale the input scanline into the output scanline
*/
for (i = j = 1; j <= file_width; ++j)
{
if (i * file_width < j * row_width)
{
x = j - (i * file_width) / row_width;
VBLEND2(out, (1.0 - x), in, x, in + 3);
++i;
in += 3;
}
else
VMOVE(out, in);
out += 3;
}
/*
* Write the output scanline
*/
if (fwrite(outbuf, 3, file_width, stdout) != file_width)
{
perror("stdout");
bu_exit (2, NULL);
}
}
bu_exit (1, NULL);
}
/**
* 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
bn_math_cmd(ClientData clientData, Tcl_Interp *interp, int argc, char **argv)
{
void (*math_func)();
struct bu_vls result;
math_func = (void (*)())clientData; /* object-to-function cast */
bu_vls_init(&result);
if (math_func == bn_mat_mul) {
mat_t o, a, b;
if (argc < 3 || bn_decode_mat(a, argv[1]) < 16 ||
bn_decode_mat(b, argv[2]) < 16) {
bu_vls_printf(&result, "usage: %s matA matB", argv[0]);
goto error;
}
bn_mat_mul(o, a, b);
bn_encode_mat(&result, o);
} else if (math_func == bn_mat_inv || math_func == bn_mat_trn) {
mat_t o, a;
if (argc < 2 || bn_decode_mat(a, argv[1]) < 16) {
bu_vls_printf(&result, "usage: %s mat", argv[0]);
goto error;
}
(*math_func)(o, a);
bn_encode_mat(&result, o);
} else if (math_func == bn_matXvec) {
mat_t m;
hvect_t i, o;
if (argc < 3 || bn_decode_mat(m, argv[1]) < 16 ||
bn_decode_hvect(i, argv[2]) < 4) {
bu_vls_printf(&result, "usage: %s mat hvect", argv[0]);
goto error;
}
bn_matXvec(o, m, i);
bn_encode_hvect(&result, o);
} else if (math_func == bn_mat4x3pnt) {
mat_t m;
point_t i, o;
if (argc < 3 || bn_decode_mat(m, argv[1]) < 16 ||
bn_decode_vect(i, argv[2]) < 3) {
bu_vls_printf(&result, "usage: %s mat point", argv[0]);
goto error;
}
bn_mat4x3pnt(o, m, i);
bn_encode_vect(&result, o);
} else if (math_func == bn_mat4x3vec) {
mat_t m;
vect_t i, o;
if (argc < 3 || bn_decode_mat(m, argv[1]) < 16 ||
bn_decode_vect(i, argv[2]) < 3) {
bu_vls_printf(&result, "usage: %s mat vect", argv[0]);
goto error;
}
bn_mat4x3vec(o, m, i);
bn_encode_vect(&result, o);
} else if (math_func == bn_hdivide) {
hvect_t i;
vect_t o;
if (argc < 2 || bn_decode_hvect(i, argv[1]) < 4) {
bu_vls_printf(&result, "usage: %s hvect", argv[0]);
goto error;
}
bn_hdivide(o, i);
bn_encode_vect(&result, o);
} else if (math_func == bn_vjoin1) {
point_t o;
point_t b, d;
fastf_t c;
if (argc < 4) {
bu_vls_printf(&result, "usage: %s pnt scale dir", argv[0]);
goto error;
}
if ( bn_decode_vect(b, argv[1]) < 3) goto error;
if (Tcl_GetDouble(interp, argv[2], &c) != TCL_OK) goto error;
if ( bn_decode_vect(d, argv[3]) < 3) goto error;
VJOIN1( o, b, c, d ); /* bn_vjoin1( o, b, c, d ) */
bn_encode_vect(&result, o);
} else if ( math_func == bn_vblend) {
point_t a, c, e;
fastf_t b, d;
if ( argc < 5 ) {
bu_vls_printf(&result, "usage: %s scale pnt scale pnt", argv[0]);
goto error;
}
if ( Tcl_GetDouble(interp, argv[1], &b) != TCL_OK) goto error;
if ( bn_decode_vect( c, argv[2] ) < 3) goto error;
if ( Tcl_GetDouble(interp, argv[3], &d) != TCL_OK) goto error;
if ( bn_decode_vect( e, argv[4] ) < 3) goto error;
VBLEND2( a, b, c, d, e )
bn_encode_vect( &result, a );
} else if (math_func == bn_mat_ae) {
mat_t o;
double az, el;
if (argc < 3) {
bu_vls_printf(&result, "usage: %s azimuth elevation", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[1], &az) != TCL_OK) goto error;
if (Tcl_GetDouble(interp, argv[2], &el) != TCL_OK) goto error;
bn_mat_ae(o, (fastf_t)az, (fastf_t)el);
bn_encode_mat(&result, o);
} else if (math_func == bn_ae_vec) {
fastf_t az, el;
vect_t v;
if (argc < 2 || bn_decode_vect(v, argv[1]) < 3) {
bu_vls_printf(&result, "usage: %s vect", argv[0]);
goto error;
}
bn_ae_vec(&az, &el, v);
bu_vls_printf(&result, "%g %g", az, el);
} else if (math_func == bn_aet_vec) {
fastf_t az, el, twist, accuracy;
vect_t vec_ae, vec_twist;
if (argc < 4 || bn_decode_vect(vec_ae, argv[1]) < 3 ||
bn_decode_vect(vec_twist, argv[2]) < 3 ||
sscanf(argv[3], "%lf", &accuracy) < 1) {
bu_vls_printf(&result, "usage: %s vec_ae vec_twist accuracy",
argv[0]);
goto error;
}
bn_aet_vec(&az, &el, &twist, vec_ae, vec_twist, accuracy);
bu_vls_printf(&result, "%g %g %g", az, el, twist);
} else if (math_func == bn_mat_angles) {
mat_t o;
double alpha, beta, ggamma;
if (argc < 4) {
bu_vls_printf(&result, "usage: %s alpha beta gamma", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[1], &alpha) != TCL_OK) goto error;
if (Tcl_GetDouble(interp, argv[2], &beta) != TCL_OK) goto error;
if (Tcl_GetDouble(interp, argv[3], &ggamma) != TCL_OK) goto error;
bn_mat_angles(o, alpha, beta, ggamma);
bn_encode_mat(&result, o);
} else if (math_func == bn_eigen2x2) {
fastf_t val1, val2;
vect_t vec1, vec2;
double a, b, c;
if (argc < 4) {
bu_vls_printf(&result, "usage: %s a b c", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[1], &a) != TCL_OK) goto error;
if (Tcl_GetDouble(interp, argv[2], &c) != TCL_OK) goto error;
if (Tcl_GetDouble(interp, argv[3], &b) != TCL_OK) goto error;
bn_eigen2x2(&val1, &val2, vec1, vec2, (fastf_t)a, (fastf_t)b,
(fastf_t)c);
bu_vls_printf(&result, "%g %g {%g %g %g} {%g %g %g}", val1, val2,
V3ARGS(vec1), V3ARGS(vec2));
} else if (math_func == bn_mat_fromto) {
mat_t o;
vect_t from, to;
if (argc < 3 || bn_decode_vect(from, argv[1]) < 3 ||
bn_decode_vect(to, argv[2]) < 3) {
bu_vls_printf(&result, "usage: %s vecFrom vecTo", argv[0]);
goto error;
}
bn_mat_fromto(o, from, to);
bn_encode_mat(&result, o);
} else if (math_func == bn_mat_xrot || math_func == bn_mat_yrot ||
math_func == bn_mat_zrot) {
mat_t o;
double s, c;
if (argc < 3) {
bu_vls_printf(&result, "usage: %s sinAngle cosAngle", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[1], &s) != TCL_OK) goto error;
if (Tcl_GetDouble(interp, argv[2], &c) != TCL_OK) goto error;
(*math_func)(o, s, c);
bn_encode_mat(&result, o);
} else if (math_func == bn_mat_lookat) {
mat_t o;
vect_t dir;
int yflip;
if (argc < 3 || bn_decode_vect(dir, argv[1]) < 3) {
bu_vls_printf(&result, "usage: %s dir yflip", argv[0]);
goto error;
}
if (Tcl_GetBoolean(interp, argv[2], &yflip) != TCL_OK) goto error;
bn_mat_lookat(o, dir, yflip);
bn_encode_mat(&result, o);
} else if (math_func == bn_vec_ortho || math_func == bn_vec_perp) {
vect_t ov, vec;
if (argc < 2 || bn_decode_vect(vec, argv[1]) < 3) {
bu_vls_printf(&result, "usage: %s vec", argv[0]);
goto error;
}
(*math_func)(ov, vec);
bn_encode_vect(&result, ov);
} else if (math_func == bn_mat_scale_about_pt_wrapper) {
mat_t o;
vect_t v;
double scale;
int status;
if (argc < 3 || bn_decode_vect(v, argv[1]) < 3) {
bu_vls_printf(&result, "usage: %s pt scale", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[2], &scale) != TCL_OK) goto error;
bn_mat_scale_about_pt_wrapper(&status, o, v, scale);
if (status != 0) {
bu_vls_printf(&result, "error performing calculation");
goto error;
}
bn_encode_mat(&result, o);
} else if (math_func == bn_mat_xform_about_pt) {
mat_t o, xform;
vect_t v;
if (argc < 3 || bn_decode_mat(xform, argv[1]) < 16 ||
bn_decode_vect(v, argv[2]) < 3) {
bu_vls_printf(&result, "usage: %s xform pt", argv[0]);
goto error;
}
bn_mat_xform_about_pt(o, xform, v);
bn_encode_mat(&result, o);
} else if (math_func == bn_mat_arb_rot) {
mat_t o;
point_t pt;
vect_t dir;
double angle;
if (argc < 4 || bn_decode_vect(pt, argv[1]) < 3 ||
bn_decode_vect(dir, argv[2]) < 3) {
bu_vls_printf(&result, "usage: %s pt dir angle", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[3], &angle) != TCL_OK)
return TCL_ERROR;
bn_mat_arb_rot(o, pt, dir, (fastf_t)angle);
bn_encode_mat(&result, o);
} else if (math_func == quat_mat2quat) {
mat_t mat;
quat_t quat;
if (argc < 2 || bn_decode_mat(mat, argv[1]) < 16) {
bu_vls_printf(&result, "usage: %s mat", argv[0]);
goto error;
}
quat_mat2quat(quat, mat);
bn_encode_quat(&result, quat);
} else if (math_func == quat_quat2mat) {
mat_t mat;
quat_t quat;
if (argc < 2 || bn_decode_quat(quat, argv[1]) < 4) {
bu_vls_printf(&result, "usage: %s quat", argv[0]);
goto error;
}
quat_quat2mat(mat, quat);
bn_encode_mat(&result, mat);
} else if (math_func == bn_quat_distance_wrapper) {
quat_t q1, q2;
double d;
if (argc < 3 || bn_decode_quat(q1, argv[1]) < 4 ||
bn_decode_quat(q2, argv[2]) < 4) {
bu_vls_printf(&result, "usage: %s quatA quatB", argv[0]);
goto error;
}
bn_quat_distance_wrapper(&d, q1, q2);
bu_vls_printf(&result, "%g", d);
} else if (math_func == quat_double || math_func == quat_bisect ||
math_func == quat_make_nearest) {
quat_t oqot, q1, q2;
if (argc < 3 || bn_decode_quat(q1, argv[1]) < 4 ||
bn_decode_quat(q2, argv[2]) < 4) {
bu_vls_printf(&result, "usage: %s quatA quatB", argv[0]);
goto error;
}
(*math_func)(oqot, q1, q2);
bn_encode_quat(&result, oqot);
} else if (math_func == quat_slerp) {
quat_t oq, q1, q2;
double d;
if (argc < 4 || bn_decode_quat(q1, argv[1]) < 4 ||
bn_decode_quat(q2, argv[2]) < 4) {
bu_vls_printf(&result, "usage: %s quat1 quat2 factor", argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[3], &d) != TCL_OK) goto error;
quat_slerp(oq, q1, q2, d);
bn_encode_quat(&result, oq);
} else if (math_func == quat_sberp) {
quat_t oq, q1, qa, qb, q2;
double d;
if (argc < 6 || bn_decode_quat(q1, argv[1]) < 4 ||
bn_decode_quat(qa, argv[2]) < 4 || bn_decode_quat(qb, argv[3]) < 4 ||
bn_decode_quat(q2, argv[4]) < 4) {
bu_vls_printf(&result, "usage: %s quat1 quatA quatB quat2 factor",
argv[0]);
goto error;
}
if (Tcl_GetDouble(interp, argv[5], &d) != TCL_OK) goto error;
quat_sberp(oq, q1, qa, qb, q2, d);
bn_encode_quat(&result, oq);
} else if (math_func == quat_exp || math_func == quat_log) {
quat_t qout, qin;
if (argc < 2 || bn_decode_quat(qin, argv[1]) < 4) {
bu_vls_printf(&result, "usage: %s quat", argv[0]);
goto error;
}
(*math_func)(qout, qin);
bn_encode_quat(&result, qout);
} else if (math_func == (void (*)())bn_isect_line3_line3) {
double t, u;
point_t pt, a;
vect_t dir, c;
int i;
static const struct bn_tol tol = {
BN_TOL_MAGIC, 0.005, 0.005*0.005, 1e-6, 1-1e-6
};
if (argc != 5) {
bu_vls_printf(&result,
"Usage: bn_isect_line3_line3 pt dir pt dir (%d args specified)",
argc-1);
goto error;
}
if (bn_decode_vect(pt, argv[1]) < 3) {
bu_vls_printf(&result, "bn_isect_line3_line3 no pt: %s\n", argv[0]);
goto error;
}
if (bn_decode_vect(dir, argv[2]) < 3) {
bu_vls_printf(&result, "bn_isect_line3_line3 no dir: %s\n", argv[0]);
goto error;
}
if (bn_decode_vect(a, argv[3]) < 3) {
bu_vls_printf(&result, "bn_isect_line3_line3 no a pt: %s\n", argv[0]);
goto error;
}
if (bn_decode_vect(c, argv[4]) < 3) {
bu_vls_printf(&result, "bn_isect_line3_line3 no c dir: %s\n", argv[0]);
goto error;
}
i = bn_isect_line3_line3(&t, &u, pt, dir, a, c, &tol);
if (i != 1) {
bu_vls_printf(&result, "bn_isect_line3_line3 no intersection: %s\n", argv[0]);
goto error;
}
VJOIN1(a, pt, t, dir);
bn_encode_vect(&result, a);
} else if (math_func == (void (*)())bn_isect_line2_line2) {
double dist[2];
point_t pt, a;
vect_t dir, c;
int i;
static const struct bn_tol tol = {
BN_TOL_MAGIC, 0.005, 0.005*0.005, 1e-6, 1-1e-6
};
if (argc != 5) {
bu_vls_printf(&result,
"Usage: bn_isect_line2_line2 pt dir pt dir (%d args specified)",
argc-1);
goto error;
}
/* i = bn_isect_line2_line2 {0 0} {1 0} {1 1} {0 -1} */
VSETALL(pt, 0.0);
VSETALL(dir, 0.0);
VSETALL(a, 0.0);
VSETALL(c, 0.0);
if (bn_decode_vect(pt, argv[1]) < 2) {
bu_vls_printf(&result, "bn_isect_line2_line2 no pt: %s\n", argv[0]);
goto error;
}
if (bn_decode_vect(dir, argv[2]) < 2) {
bu_vls_printf(&result, "bn_isect_line2_line2 no dir: %s\n", argv[0]);
goto error;
}
if (bn_decode_vect(a, argv[3]) < 2) {
bu_vls_printf(&result, "bn_isect_line2_line2 no a pt: %s\n", argv[0]);
goto error;
}
if (bn_decode_vect(c, argv[4]) < 2) {
bu_vls_printf(&result, "bn_isect_line2_line2 no c dir: %s\n", argv[0]);
goto error;
}
i = bn_isect_line2_line2(dist, pt, dir, a, c, &tol);
if (i != 1) {
bu_vls_printf(&result, "bn_isect_line2_line2 no intersection: %s\n", argv[0]);
goto error;
}
VJOIN1(a, pt, dist[0], dir);
bu_vls_printf(&result, "%g %g", a[0], a[1]);
} else {
bu_vls_printf(&result, "libbn/bn_tcl.c: math function %s not supported yet\n", argv[0]);
goto error;
}
Tcl_AppendResult(interp, bu_vls_addr(&result), (char *)NULL);
bu_vls_free(&result);
return TCL_OK;
error:
Tcl_AppendResult(interp, bu_vls_addr(&result), (char *)NULL);
bu_vls_free(&result);
return TCL_ERROR;
}
static void bn_vblend(mat_t a, fastf_t b, mat_t c, fastf_t d, mat_t e)
{
VBLEND2( a, b, c, d, e );
}