Spherical Geometry

Table of contents

• Basic information
• Examples
  • Filtering stars by constellation
  • GeCAA theory task
• Library state

Basic information

A library for handling geometry on the surface of a sphere.

This library combines spherical and vector geometry to perform operations with points, great circles, great circle arcs, and spherical polygons. A great circle is an equivalent of a straight line in planar geometry - it is the shortest path between two points on a sphere.

Doing geometry on a sphere requires using spherical trigonometry and being very careful when taking arcsin etc. to get angles, as one often gets false results.

Examples

More examples can be found in the examples folder. The unit tests can also serve as ones.

Filtering stars by constellation

This uses the Polygon API, checking if each of the stars is inside the tested constellation polygon.

Testing all constellations on the sky, all of them worked without any issues (stars deemed to be inside the constellation are marked in green).

GeCAA theory task

Below is an example of solving the GeCAA 2020 Theory task 7 analytically.

use spherical_geometry::{SphericalPoint, GreatCircle};

fn gecaa_2020_theory_7() {
    let delta = 10e-2;

    let start_1 = SphericalPoint::new(-PI / 2.0, 0.0);
    let end_1 = SphericalPoint::new(0.0, 15.0 * PI / 180.0);
    let circle_1 = GreatCircle::new(start_1, end_1).expect("The points are fairly far away");

    let start_2 = SphericalPoint::new(-210.0 * PI / 180.0, 23.5 * PI / 180.0); // Switch RA direction as the question measures azimuth from north to east
    let end_2 = SphericalPoint::new(-255.0 * PI / 180.0, 75.0 * PI / 180.0); // Switch RA direction as the question measures azimuth from north to east
    let circle_2 = GreatCircle::new(start_2, end_2).expect("The points are fairly far away");

    let intersections = circle_1.intersect_great_circle(&circle_2).expect("The paths are not parallel");

    let [(ra_1, dec_1), (ra_2, dec_2)] = if intersections[0].ra < intersections[1].ra {
        [(intersections[1].ra, intersections[1].dec), (intersections[0].ra, intersections[0].dec)]
    } else {
        [(intersections[0].ra, intersections[0].dec), (intersections[1].ra, intersections[1].dec)]
    };

    let (ra_1_corr, dec_1_corr) = ((360.0 - 21.94) * PI / 180.0, 13.96 * PI / 180.0); // Once again switch RA direction as the question measures azimuth from north to east
    let (ra_2_corr, dec_2_corr) = ((360.0 - 201.94) * PI / 180.0, -13.96 * PI / 180.0); // Once again switch RA direction as the question measures azimuth from north to east

    assert!((ra_1_corr - ra_1).abs() < delta && (dec_1_corr - dec_1).abs() < delta);
    assert!((ra_2_corr - ra_2).abs() < delta && (dec_2_corr - dec_2).abs() < delta);
}

Library state

The library is in active development, more features are expected to be added, see the table below for planned features. The API should not change much from the current state, but there are no guarantees.

State key:

• 🟢 - fully implemented
• 🟡 - partially implemented
• 🟠 - implemented, but partially broken
• 🔴 - not yet implemented