VizieR help - FAQ - Tutorial

The x,y (relative coordinates from the center) represent the arc projection. It means that, if r is the relative angular distance between the point and the center of the projection, and a the position angle (North through East) of the point relative to the center, the relative coordinates are:

x = r ⋅ sin(a)
y = r ⋅ cos(a)

Assuming the center of the projection at (RA0=0, Dec0=0) (i.e. Cartesian position of the center is (1,0,0)), from the Cartesian coordinates of the point:

(u, v, w) = (cosDec⋅cosRA, cosDec⋅sinRA, sinDec)

the projections are:

x = cos–1(u) ⋅ v/sqrt(v2+w2)
y = cos–1(u) ⋅ w/sqrt(v2+w2)

i.e. a is the position angle of the point (v,w) .

When the center of projection is another position (RA0, DE0), a rotation is performed to bring the center of the projection to the chosen position, using the rotation matrix:

 cosDec0⋅cosRA0 cosDec0⋅sinRA0 sinDec0
 –sinRA0           cosRA0		      0 
–sinDec0⋅cosRA0–sinDec0⋅sinRA0 cosDec0 


The reverse transformation (RA and Dec from x and y) are derived by the formulae, if r is the distance (r = sqrt(x2+ y2)):

u = cos(r)
v = x sin(r)/r
w = y sin(r)/r

the reverse rotation (with the transposed rotation matrix) is performed, and the (u, v, w) vector is transformed into the exact position.

Note that the computations of

   Dec=Dec_0 + y 
   RA=RA_0 + x / cos(Dec)
   

are only asymptotically correct, at very small distances from the projection center.


last update: ls: cannot access '0.htx': Operation not permitted ls: cannot access '1.htx': Operation not permitted ls: cannot access '1g.htx': Operation not permitted ls: cannot access '2.htx': Operation not permitted ls: cannot access '3.htx': Operation not permitted ls: cannot access '4.htx': Operation not permitted ls: cannot access '5.htx': Operation not permitted ls: cannot access 'DirSearch.htx': Operation not permitted ls: cannot access 'ac2000.htx': Operation not permitted ls: cannot access 'adapt.htx': Operation not permitted ls: cannot access 'args.htx': Operation not permitted ls: cannot access 'batchmode.htx': Operation not permitted ls: cannot access 'colors.htx': Operation not permitted ls: cannot access 'cst.htx': Operation not permitted ls: cannot access 'customcol.htx': Operation not permitted ls: cannot access 'customcol1.htx': Operation not permitted ls: cannot access 'f_bgcat.htx': Operation not permitted ls: cannot access 'f_bgdat.htx': Operation not permitted ls: cannot access 'f_bgtit.htx': Operation not permitted ls: cannot access 'f_goviz.htx': Operation not permitted ls: cannot access 'f_script.htx': Operation not permitted ls: cannot access 'faq.htx': Operation not permitted ls: cannot access 'file.htx': Operation not permitted ls: cannot access 'footprint.htx': Operation not permitted ls: cannot access 'gsc.intro.htx': Operation not permitted ls: cannot access 'gsc1.2.intro.htx': Operation not permitted ls: cannot access 'gsc1.3.intro.htx': Operation not permitted ls: cannot access 'head.htx': Operation not permitted ls: cannot access 'history.htx': Operation not permitted ls: cannot access 'index.htx': Operation not permitted ls: cannot access 'intro.htx': Operation not permitted ls: cannot access 'menu.htx': Operation not permitted ls: cannot access 'navbar.htx': Operation not permitted ls: cannot access 'output.htx': Operation not permitted ls: cannot access 'query_setup.htx': Operation not permitted ls: cannot access 'syntax.htx': Operation not permitted ls: cannot access 'tail.htx': Operation not permitted ls: cannot access 'ucd_example.htx': Operation not permitted ls: cannot access 'vizjoin.htx': Operation not permitted ls: cannot access 'xy.htx': Operation not permitted