sofars/projection/
tpstv.rs

1/// In the tangent plane projection, given the star's rectangular
2/// coordinates and the direction cosines of the tangent point, solve
3/// for the direction cosines of the star.
4///
5/// Status:  support function.
6///
7/// Given:
8///    xi,eta  f64     rectangular coordinates of star image (Note 2)
9///    v0      [f64; 3]  tangent point's direction cosines
10///
11/// Returned:
12///    v       [f64; 3]  star's direction cosines
13///
14/// Notes:
15///
16/// 1) The tangent plane projection is also called the "gnomonic
17///    projection" and the "central projection".
18///
19/// 2) The eta axis points due north in the adopted coordinate system.
20///    If the direction cosines represent observed (RA,Dec), the tangent
21///    plane coordinates (xi,eta) are conventionally called the
22///    "standard coordinates".  If the direction cosines are with
23///    respect to a right-handed triad, (xi,eta) are also right-handed.
24///    The units of (xi,eta) are, effectively, radians at the tangent
25///    point.
26///
27/// 3) The method used is to complete the star vector in the (xi,eta)
28///    based triad and normalize it, then rotate the triad to put the
29///    tangent point at the pole with the x-axis aligned to zero
30///    longitude.  Writing (a0,b0) for the celestial spherical
31///    coordinates of the tangent point, the sequence of rotations is
32///    (b-pi/2) around the x-axis followed by (-a-pi/2) around the
33///    z-axis.
34///
35/// 4) If vector v0 is not of unit length, the returned vector v will
36///    be wrong.
37///
38/// 5) If vector v0 points at a pole, the returned vector v will be
39///    based on the arbitrary assumption that the longitude coordinate
40///    of the tangent point is zero.
41///
42/// 6) This function is a member of the following set:
43///
44///        spherical      vector         solve for
45///
46///        tpxes         tpxev          xi,eta
47///        tpsts       > tpstv <         star
48///        tpors         tporv          origin
49///
50/// References:
51///
52///    Calabretta M.R. & Greisen, E.W., 2002, "Representations of
53///    celestial coordinates in FITS", Astron.Astrophys. 395, 1077
54///
55///    Green, R.M., "Spherical Astronomy", Cambridge University Press,
56///    1987, Chapter 13.
57pub fn tpstv(xi: f64, eta: f64, v0: [f64; 3]) -> [f64; 3] {
58    let mut x = v0[0];
59    let y = v0[1];
60    let z = v0[2];
61
62    /* Deal with polar case. */
63    let mut r = (x * x + y * y).sqrt();
64    if r == 0.0 {
65        r = 1e-20;
66        x = r;
67    }
68
69    /* Star vector length to tangent plane. */
70    let f = (1.0 + xi * xi + eta * eta).sqrt();
71
72    /* Apply the transformation and normalize. */
73    let v_x = (x - (xi * y + eta * x * z) / r) / f;
74    let v_y = (y + (xi * x - eta * y * z) / r) / f;
75    let v_z = (z + eta * r) / f;
76
77    [v_x, v_y, v_z]
78}
sofars/projection/tpstv.rs

sofars/projection/
tpstv.rs
