void radec_derivatives(double ra, double dec, double* dra, double* ddec) {
double cosd = cos(deg2rad(dec));
double cosra = cos(deg2rad(ra));
double sinra = sin(deg2rad(ra));
if (dra) {
dra[0] = cosd * -sinra;
dra[1] = cosd * cosra;
dra[2] = 0.0;
normalize_3(dra);
}
if (ddec) {
double sind = sin(deg2rad(dec));
ddec[0] = -sind * cosra;
ddec[1] = -sind * sinra;
ddec[2] = cosd;
normalize_3(ddec);
}
}
void tan_iwc2xyzarr(const tan_t* tan, double x, double y, double *xyz)
{
double rx, ry, rz;
double ix,iy,norm;
double jx,jy,jz;
// Mysterious factor of -1 correcting for vector directions below.
x = -deg2rad(x);
y = deg2rad(y);
// Take r to be the threespace vector of crval
radecdeg2xyz(tan->crval[0], tan->crval[1], &rx, &ry, &rz);
// printf("rx=%lf ry=%lf rz=%lf\n",rx,ry,rz);
// Form i = r cross north pole (0,0,1)
ix = ry;
iy = -rx;
// iz = 0
norm = hypot(ix, iy);
ix /= norm;
iy /= norm;
// printf("ix=%lf iy=%lf iz=0.0\n",ix,iy);
// printf("r.i = %lf\n",ix*rx+iy*ry);
// Form j = i cross r; iz=0 so some terms drop out
jx = iy * rz;
jy = - ix * rz;
jz = ix * ry - iy * rx;
// norm should already be 1, but normalize anyway
normalize(&jx, &jy, &jz);
// printf("jx=%lf jy=%lf jz=%lf\n",jx,jy,jz);
// printf("r.j = %lf\n",jx*rx+jy*ry+jz*rz);
// printf("i.j = %lf\n",ix*jx+iy*jy);
if (tan->sin) {
assert((x*x + y*y) < 1.0);
// Figure out what factor of r we have to add in to make the resulting length = 1
double rfrac = sqrt(1.0 - (x*x + y*y));
// Don't scale the projected x,y positions, just add in the right amount of r to
// bring it onto the unit sphere
xyz[0] = ix*x + jx*y + rx * rfrac;
xyz[1] = iy*x + jy*y + ry * rfrac;
xyz[2] = jz*y + rz * rfrac; // iz = 0
} else {
// Form the point on the tangent plane relative to observation point,
xyz[0] = ix*x + jx*y + rx;
xyz[1] = iy*x + jy*y + ry;
xyz[2] = jz*y + rz; // iz = 0
// and normalize back onto the unit sphere
normalize_3(xyz);
}
}
static
int fit_tan_wcs_solve(const double* starxyz,
const double* fieldxy,
const double* weights,
int N,
const double* crpix,
const tan_t* tanin,
tan_t* tanout,
double* p_scale) {
int i, j, k;
double field_cm[2] = {0, 0};
double cov[4] = {0, 0, 0, 0};
double R[4] = {0, 0, 0, 0};
double scale;
// projected star coordinates
double* p;
// relative field coordinates
double* f;
double pcm[2] = {0, 0};
double w = 0;
double totalw;
gsl_matrix* A;
gsl_matrix* U;
gsl_matrix* V;
gsl_vector* S;
gsl_vector* work;
gsl_matrix_view vcov;
gsl_matrix_view vR;
double crxyz[3];
double star_cm[3] = {0, 0, 0};
assert(((tanin != NULL) && (crpix != NULL)) || ((tanin == NULL) && (crpix == NULL)));
if (tanin) {
// default vals...
memcpy(tanout, tanin, sizeof(tan_t));
} else {
memset(tanout, 0, sizeof(tan_t));
}
// -allocate and fill "p" and "f" arrays. ("projected" and "field")
p = malloc(N * 2 * sizeof(double));
f = malloc(N * 2 * sizeof(double));
// -get field center-of-mass
totalw = 0.0;
for (i=0; i<N; i++) {
w = (weights ? weights[i] : 1.0);
field_cm[0] += w * fieldxy[i*2 + 0];
field_cm[1] += w * fieldxy[i*2 + 1];
totalw += w;
}
field_cm[0] /= totalw;
field_cm[1] /= totalw;
// Subtract it out.
for (i=0; i<N; i++) {
f[2*i+0] = fieldxy[2*i+0] - field_cm[0];
f[2*i+1] = fieldxy[2*i+1] - field_cm[1];
}
if (tanin) {
// Use original WCS to set the center of projection to the new crpix.
tan_pixelxy2xyzarr(tanin, crpix[0], crpix[1], crxyz);
for (i=0; i<N; i++) {
Unused anbool ok;
// -project the stars around crval
ok = star_coords(starxyz + i*3, crxyz, TRUE, p + 2*i, p + 2*i + 1);
assert(ok);
}
} else {
// -get the star center-of-mass (this will become the tangent point CRVAL)
for (i=0; i<N; i++) {
w = (weights ? weights[i] : 1.0);
star_cm[0] += w * starxyz[i*3 + 0];
star_cm[1] += w * starxyz[i*3 + 1];
star_cm[2] += w * starxyz[i*3 + 2];
}
normalize_3(star_cm);
// -project the stars around their center of mass
for (i=0; i<N; i++) {
Unused anbool ok;
ok = star_coords(starxyz + i*3, star_cm, TRUE, p + 2*i, p + 2*i + 1);
assert(ok);
}
}
// -compute the center of mass of the projected stars and subtract it out.
for (i=0; i<N; i++) {
w = (weights ? weights[i] : 1.0);
pcm[0] += w * p[2*i + 0];
pcm[1] += w * p[2*i + 1];
}
pcm[0] /= totalw;
pcm[1] /= totalw;
for (i=0; i<N; i++) {
p[2*i + 0] -= pcm[0];
p[2*i + 1] -= pcm[1];
}
// -compute the covariance between field positions and projected
// positions of the corresponding stars.
for (i=0; i<N; i++)
for (j=0; j<2; j++)
for (k=0; k<2; k++)
cov[j*2 + k] += p[i*2 + k] * f[i*2 + j];
for (i=0; i<4; i++)
assert(isfinite(cov[i]));
// -run SVD
V = gsl_matrix_alloc(2, 2);
S = gsl_vector_alloc(2);
work = gsl_vector_alloc(2);
vcov = gsl_matrix_view_array(cov, 2, 2);
vR = gsl_matrix_view_array(R, 2, 2);
A = &(vcov.matrix);
// The Jacobi version doesn't always compute an orthonormal U if S has zeros.
//gsl_linalg_SV_decomp_jacobi(A, V, S);
gsl_linalg_SV_decomp(A, V, S, work);
// the U result is written to A.
U = A;
gsl_vector_free(S);
gsl_vector_free(work);
// R = V U'
gsl_blas_dgemm(CblasNoTrans, CblasTrans, 1.0, V, U, 0.0, &(vR.matrix));
gsl_matrix_free(V);
for (i=0; i<4; i++)
assert(isfinite(R[i]));
// -compute scale: make the variances equal.
{
double pvar, fvar;
pvar = fvar = 0.0;
for (i=0; i<N; i++) {
w = (weights ? weights[i] : 1.0);
for (j=0; j<2; j++) {
pvar += w * square(p[i*2 + j]);
fvar += w * square(f[i*2 + j]);
}
}
scale = sqrt(pvar / fvar);
}
// -compute WCS parameters.
scale = rad2deg(scale);
tanout->cd[0][0] = R[0] * scale; // CD1_1
tanout->cd[0][1] = R[1] * scale; // CD1_2
tanout->cd[1][0] = R[2] * scale; // CD2_1
tanout->cd[1][1] = R[3] * scale; // CD2_2
assert(isfinite(tanout->cd[0][0]));
assert(isfinite(tanout->cd[0][1]));
assert(isfinite(tanout->cd[1][0]));
assert(isfinite(tanout->cd[1][1]));
if (tanin) {
// CRPIX is fixed.
tanout->crpix[0] = crpix[0];
tanout->crpix[1] = crpix[1];
// Set CRVAL temporarily...
tan_pixelxy2radec(tanin, crpix[0], crpix[1],
tanout->crval+0, tanout->crval+1);
// Shift CRVAL so that the center of the quad is in the right place.
{
double ix,iy;
double dx,dy;
double dxyz[3];
tan_pixelxy2iwc(tanout, field_cm[0], field_cm[1], &ix, &iy);
dx = rad2deg(pcm[0]) - ix;
dy = rad2deg(pcm[1]) - iy;
tan_iwc2xyzarr(tanout, dx, dy, dxyz);
xyzarr2radecdeg(dxyz, tanout->crval + 0, tanout->crval + 1);
}
} else {
tanout->crpix[0] = field_cm[0];
tanout->crpix[1] = field_cm[1];
xyzarr2radecdegarr(star_cm, tanout->crval);
// FIXME -- we ignore pcm. It should get added back in (after
// multiplication by CD in the appropriate units) to either crval or
// crpix. It's a very small correction probably of the same size
// as the other approximations we're making.
}
if (p_scale) *p_scale = scale;
free(p);
free(f);
return 0;
}
static void plot_targets(cairo_t* cairo, plot_args_t* pargs, plotann_t* ann) {
int i;
double cra, cdec;
plotstuff_get_radec_center_and_radius(pargs, &cra, &cdec, NULL);
for (i=0; i<bl_size(ann->targets); i++) {
target_t* tar = bl_access(ann->targets, i);
double px,py;
double cx,cy;
double dx,dy, r;
double ex,ey;
double ly, ry, tx, bx;
double distdeg;
anbool okquadrant;
char* txt;
logverb("Target: \"%s\" at (%g,%g)\n", tar->name, tar->ra, tar->dec);
okquadrant = plotstuff_radec2xy(pargs, tar->ra, tar->dec, &px, &py);
px -= 1;
py -= 1;
if (okquadrant &&
px >= 0 && px < pargs->W && py >= 0 && py < pargs->H) {
// inside the image!
logverb("Target \"%s\" is inside the image, at pixel (%g,%g)\n", tar->name, px, py);
plotstuff_stack_marker(pargs, px, py);
plotstuff_stack_text(pargs, cairo, tar->name, px, py);
continue;
}
// outside the image: find intersection point.
cx = pargs->W / 2.0;
cy = pargs->H / 2.0;
if (okquadrant) {
logverb("Target \"%s\" is outside the image, at pixel (%g,%g)\n", tar->name, px, py);
dx = px - cx;
dy = py - cy;
} else {
double cxyz[3];
double txyz[3];
double vec[3];
int j;
double ra,dec;
logverb("Target \"%s\" is way outside the image.\n", tar->name);
// fallback.
radecdeg2xyzarr(cra, cdec, cxyz);
radecdeg2xyzarr(tar->ra, tar->dec, txyz);
for (j=0; j<3; j++)
vec[j] = cxyz[j] + 0.1 * txyz[j];
normalize_3(vec);
xyzarr2radecdeg(vec, &ra, &dec);
okquadrant = plotstuff_radec2xy(pargs, ra, dec, &px, &py);
assert(okquadrant);
dx = px - cx;
dy = py - cy;
if ((dx*dx + dy*dy) < (cx*cx + cy*cy)) {
double scale = 3.0 * sqrt(cx*cx + cy*cy) / sqrt(dx*dx + dy*dy);
dx *= scale;
dy *= scale;
}
}
ly = (-(pargs->W/2.0) / dx) * dy + cy;
ry = ( (pargs->W/2.0) / dx) * dy + cy;
bx = (-(pargs->H/2.0) / dy) * dx + cx;
tx = ( (pargs->H/2.0) / dy) * dx + cx;
logverb("ly %g, ry %g, bx %g, tx %g\n", ly, ry, bx, tx);
if (px < cx && ly >= 0 && ly < pargs->H) {
ex = 0.0;
ey = ly;
} else if (px >= cx && ry >= 0 && ry < pargs->H) {
ex = pargs->W - 1;
ey = ry;
} else if (py < cy && bx >= 0 && bx < pargs->W) {
ex = bx;
ey = 0;
} else if (py >= cy && tx >= 0 && tx < pargs->W) {
ex = tx;
ey = pargs->H - 1;
} else {
logverb("None of the edges are in bounds: px,py=(%g,%g); ly=%g, ry=%g, bx=%g, tx=%g\n", px,py,ly,ry,bx,tx);
continue;
}
dx = ex - cx;
dy = ey - cy;
r = sqrt(dx*dx + dy*dy);
px = (r-100.0) / r * dx + cx;
py = (r-100.0) / r * dy + cy;
plotstuff_stack_arrow(pargs, px, py, ex, ey);
logverb("Arrow from (%g,%g) to (%g,%g)\n", px, py, ex, ey);
distdeg = deg_between_radecdeg(cra, cdec, tar->ra, tar->dec);
asprintf_safe(&txt, "%s: %.1f deg", tar->name, distdeg);
plotstuff_stack_text(pargs, cairo, txt, px, py);
}
}
static void plot_constellations(cairo_t* cairo, plot_args_t* pargs, plotann_t* ann) {
int i, N;
double ra,dec,radius;
double xyzf[3];
// Find the field center and radius
anwcs_get_radec_center_and_radius(pargs->wcs, &ra, &dec, &radius);
logverb("Plotting constellations: field center %g,%g, radius %g\n",
ra, dec, radius);
radecdeg2xyzarr(ra, dec, xyzf);
radius = deg2dist(radius);
N = constellations_n();
for (i=0; i<N; i++) {
int j, k;
// Find the approximate center and radius of this constellation
// and see if it overlaps with the field.
il* stars = constellations_get_unique_stars(i);
double xyzj[3];
double xyzc[3];
double maxr2 = 0;
dl* rds;
xyzc[0] = xyzc[1] = xyzc[2] = 0.0;
xyzj[0] = xyzj[1] = xyzj[2] = 0.0;
for (j=0; j<il_size(stars); j++) {
constellations_get_star_radec(il_get(stars, j), &ra, &dec);
radecdeg2xyzarr(ra, dec, xyzj);
for (k=0; k<3; k++)
xyzc[k] += xyzj[k];
}
normalize_3(xyzc);
for (j=0; j<il_size(stars); j++) {
constellations_get_star_radec(il_get(stars, j), &ra, &dec);
maxr2 = MAX(maxr2, distsq(xyzc, xyzj, 3));
}
il_free(stars);
maxr2 = square(sqrt(maxr2) + radius);
if (distsq(xyzf, xyzc, 3) > maxr2) {
xyzarr2radecdeg(xyzc, &ra, &dec);
logverb("Constellation %s (center %g,%g, radius %g) out of bounds\n",
constellations_get_shortname(i), ra, dec,
dist2deg(sqrt(maxr2) - radius));
logverb(" dist from field center to constellation center is %g deg\n",
distsq2deg(distsq(xyzf, xyzc, 3)));
logverb(" max radius: %g\n", distsq2deg(maxr2));
continue;
}
if (ann->constellation_pastel) {
float r,g,b;
xyzarr2radecdeg(xyzc, &ra, &dec);
color_for_radec(ra, dec, &r,&g,&b);
plotstuff_set_rgba2(pargs, r,g,b, 0.8);
plotstuff_builtin_apply(cairo, pargs);
}
// Phew, plot it.
if (ann->constellation_lines) {
rds = constellations_get_lines_radec(i);
logverb("Constellation %s: plotting %zu lines\n",
constellations_get_shortname(i), dl_size(rds)/4);
for (j=0; j<dl_size(rds)/4; j++) {
double r1,d1,r2,d2;
double r3,d3,r4,d4;
double off = ann->constellation_lines_offset;
r1 = dl_get(rds, j*4+0);
d1 = dl_get(rds, j*4+1);
r2 = dl_get(rds, j*4+2);
d2 = dl_get(rds, j*4+3);
if (anwcs_find_discontinuity(pargs->wcs, r1, d1, r2, d2,
&r3, &d3, &r4, &d4)) {
logverb("Discontinuous: %g,%g -- %g,%g\n", r1, d1, r2, d2);
logverb(" %g,%g == %g,%g\n", r3,d3, r4,d4);
plot_offset_line_rd(NULL, pargs, r1,d1,r3,d3, off, 0.);
plot_offset_line_rd(NULL, pargs, r4,d4,r2,d2, 0., off);
} else {
plot_offset_line_rd(NULL, pargs, r1,d1,r2,d2, off, off);
}
plotstuff_stroke(pargs);
}
dl_free(rds);
}
if (ann->constellation_labels ||
ann->constellation_markers) {
// Put the label at the center of mass of the stars that
// are in-bounds
int Nin = 0;
stars = constellations_get_unique_stars(i);
xyzc[0] = xyzc[1] = xyzc[2] = 0.0;
logverb("Labeling %s: %zu stars\n", constellations_get_shortname(i),
il_size(stars));
for (j=0; j<il_size(stars); j++) {
constellations_get_star_radec(il_get(stars, j), &ra, &dec);
if (!anwcs_radec_is_inside_image(pargs->wcs, ra, dec))
continue;
if (ann->constellation_markers)
plotstuff_marker_radec(pargs, ra, dec);
radecdeg2xyzarr(ra, dec, xyzj);
for (k=0; k<3; k++)
xyzc[k] += xyzj[k];
Nin++;
}
logverb(" %i stars in-bounds\n", Nin);
if (ann->constellation_labels && Nin) {
const char* label;
normalize_3(xyzc);
xyzarr2radecdeg(xyzc, &ra, &dec);
if (ann->constellation_labels_long)
label = constellations_get_longname(i);
else
label = constellations_get_shortname(i);
plotstuff_text_radec(pargs, ra, dec, label);
}
il_free(stars);
}
}
}
