arcsec-core 0.4.0

Plate-solving library behind the arcsec CLI: star detection, quad matching, blind solving and WCS fitting
Documentation 
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150

//! WCS solution derivation from plate constants.

use crate::math::coords::standard_equatorial;
use crate::types::{PlateConstants, WcsSolution};

/// Derive a WCS solution from solved plate constants.
///
/// # Arguments
/// - `ra_db`, `dec_db`: the reference position used to build the catalog quads (radians)
/// - `plate`: the solved plate constants (standard-coordinate arcsec per image pixel)
/// - `width`, `height`: image dimensions in pixels
#[must_use]
pub fn derive_wcs(
    ra_db: f64,
    dec_db: f64,
    plate: &PlateConstants,
    width: usize,
    height: usize,
) -> WcsSolution {
    let cx = (width as f64 - 1.0) * 0.5;
    let cy = (height as f64 - 1.0) * 0.5;

    // Standard coordinates (arcsec) of the image centre
    let x_std = plate.a * cx + plate.b * cy + plate.c;
    let y_std = plate.d * cx + plate.e * cy + plate.f;

    // Convert to RA/DEC using the tangent-plane inverse (cdelt=1 → arcsec units)
    let (ra0, dec0) = standard_equatorial(ra_db, dec_db, x_std, y_std, 1.0);

    // CD matrix [deg/pixel] (ASTAP sign convention)
    //   cd1_1 = -a/3600,  cd1_2 = -b/3600   (RA decreases eastward → negative sign)
    //   cd2_1 = +d/3600,  cd2_2 = +e/3600
    let cd1_1 = -plate.a / 3600.0;
    let cd1_2 = -plate.b / 3600.0;
    let cd2_1 = plate.d / 3600.0;
    let cd2_2 = plate.e / 3600.0;

    // Pixel scale [deg/pixel] and rotation [degrees]
    let cdelt1 = -(cd1_1 * cd1_1 + cd1_2 * cd1_2).sqrt(); // FITS: cdelt1 < 0 for east-to-right
    let cdelt2 = (cd2_1 * cd2_1 + cd2_2 * cd2_2).sqrt();
    let crota2 = cd2_1.atan2(cd2_2).to_degrees();

    WcsSolution {
        ra0,
        dec0,
        crpix1: cx + 1.0,
        crpix2: cy + 1.0,
        cd1_1,
        cd1_2,
        cd2_1,
        cd2_2,
        cdelt1,
        cdelt2,
        crota2,
        residual_rms: 0.0,
        stars_matched: 0,
        plate: plate.clone(),
        mag_limit: 0.0,
        search_dist_deg: 0.0,
        step_distances: Vec::new(),
        raw_matches: 0,
        matched_stars: Vec::new(),
        sip: None,
    }
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::math::coords::ang_sep;
    use core::f64::consts::PI;

    fn deg(d: f64) -> f64 {
        d * PI / 180.0
    }

    #[test]
    fn identity_wcs_near_zero() {
        // Identity plate constants: a=1, e=1, others=0 (1 arcsec/pixel, no rotation)
        let plate = PlateConstants {
            a: 1.0,
            b: 0.0,
            c: 0.0,
            d: 0.0,
            e: 1.0,
            f: 0.0,
        };
        let w = WcsSolution {
            ra0: 0.0,
            dec0: 0.0,
            ..derive_wcs(0.0, 0.0, &plate, 101, 101)
        };
        // Center standard coords should be (0, 0) → (ra0, dec0) ≈ reference position
        assert!(w.ra0.abs() < 1e-8, "ra0 = {}", w.ra0);
        assert!(w.dec0.abs() < 1e-8, "dec0 = {}", w.dec0);
        // cdelt should be ~1/3600 degrees
        assert!(
            (w.cdelt2 - 1.0 / 3600.0).abs() < 1e-10,
            "cdelt2 = {}",
            w.cdelt2
        );
    }

    #[test]
    fn center_ra_dec_reasonable() {
        // Plate constants with non-zero offset → center moves away from reference
        // a=1 arcsec/pix, e=1, c=100, f=200 → center offset (100, 200) arcsec from ref
        let plate = PlateConstants {
            a: 1.0,
            b: 0.0,
            c: 0.0,
            d: 0.0,
            e: 1.0,
            f: 0.0,
        };
        let ra_db = deg(45.0);
        let dec_db = deg(20.0);
        let wcs = derive_wcs(ra_db, dec_db, &plate, 101, 101);
        // The center should be close to (ra_db, dec_db) since c=f=0
        let sep = ang_sep(wcs.ra0, wcs.dec0, ra_db, dec_db);
        assert!(
            sep < deg(0.1),
            "center offset = {} arcsec",
            sep * 3600.0 * 180.0 / PI
        );
    }

    #[test]
    fn crpix_is_image_center() {
        let plate = PlateConstants {
            a: 1.0,
            b: 0.0,
            c: 0.0,
            d: 0.0,
            e: 1.0,
            f: 0.0,
        };
        let wcs = derive_wcs(0.0, 0.0, &plate, 200, 300);
        assert!(
            (wcs.crpix1 - 100.5).abs() < 1e-10,
            "crpix1 = {}",
            wcs.crpix1
        );
        assert!(
            (wcs.crpix2 - 150.5).abs() < 1e-10,
            "crpix2 = {}",
            wcs.crpix2
        );
    }
}