200 lines
7.4 KiB
Rust
200 lines
7.4 KiB
Rust
//! Tests for footprint geometry and coverage fractions.
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//!
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//! 覆盖区几何与覆盖比例的测试。
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use apsis_coverage::{
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Footprint, central_angle_between, footprint, footprint_area, footprint_central_angle,
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footprint_edge_elevation, footprint_fraction, point_in_footprint,
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};
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use apsis_math::Vec3;
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use core::f64::consts::{FRAC_PI_2, PI};
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/// The Earth equatorial radius, in kilometers.
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///
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/// 地球赤道半径，单位为千米。
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const BODY_RADIUS: f64 = 6_378.137;
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/// A low Earth orbit at 550 km altitude.
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///
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/// 550 km 高度的低轨。
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const LOW_ORBIT: f64 = BODY_RADIUS + 550.0;
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/// A geostationary radius.
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///
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/// 地球静止轨道半径。
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const GEOSTATIONARY: f64 = 42_164.0;
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const TOLERANCE: f64 = 1e-9;
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#[test]
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fn the_footprint_at_a_ten_degree_mask_matches_a_hand_computation() {
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// A 550 km satellite at a ten degree mask has a central angle of
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// 14.9566 degrees, a surface radius of 1664.965 km, and an area of
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// 8 659 493.8 square kilometers.
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// 十度遮蔽下 550 km 卫星的中心角为 14.9566 度，地表半径为 1664.965 km，面积为
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// 8 659 493.8 平方千米。
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let mask = 10.0_f64.to_radians();
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let footprint = footprint(LOW_ORBIT, BODY_RADIUS, mask).expect("valid");
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assert!((footprint.central_angle.to_degrees() - 14.956_635_124_957_29).abs() < 1e-9);
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assert!((footprint.surface_radius() - 1_664.965_006_091_034_9).abs() < 1e-6);
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assert!((footprint.area() - 8_659_493.809_336_036).abs() < 1e-3);
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assert!((footprint.fraction_of_surface() - 0.016_939_280_322_558_092).abs() < 1e-12);
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}
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#[test]
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fn the_area_matches_the_spherical_cap_relation() {
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let footprint = footprint(LOW_ORBIT, BODY_RADIUS, 0.3).expect("valid");
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let expected = 2.0 * PI * BODY_RADIUS * BODY_RADIUS * (1.0 - footprint.central_angle.cos());
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assert!((footprint.area() - expected).abs() < TOLERANCE);
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}
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#[test]
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fn the_area_grows_with_the_central_angle() {
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let mut previous = 0.0;
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for mask_degrees in [30.0_f64, 20.0, 10.0, 5.0, 0.0] {
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let area =
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footprint_area(LOW_ORBIT, BODY_RADIUS, mask_degrees.to_radians()).expect("valid");
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assert!(
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area > previous,
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"mask {mask_degrees}: {area} against {previous}"
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);
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previous = area;
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}
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}
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#[test]
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fn a_footprint_can_never_cover_more_than_a_hemisphere() {
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// The limit is a satellite at the surface with no mask, which sees half
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// the sphere. Any real satellite sees less.
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// 极限是地表上、无遮蔽的卫星，它看到半个球面。任何真实卫星看到的都更少。
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for satellite_radius in [LOW_ORBIT, GEOSTATIONARY, 1.0e6] {
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for mask_degrees in [0.0_f64, 10.0, 45.0] {
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let fraction =
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footprint_fraction(satellite_radius, BODY_RADIUS, mask_degrees.to_radians())
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.expect("valid");
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assert!(
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fraction > 0.0 && fraction <= 0.5,
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"radius {satellite_radius}, mask {mask_degrees}: {fraction}"
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);
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}
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}
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}
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#[test]
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fn a_geostationary_satellite_sees_about_a_third_of_the_earth() {
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// A geostationary satellite at a zero degree mask sees to about 81.3
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// degrees of central angle, which is a fraction of about 0.42.
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// 零度遮蔽的地球静止卫星看到约 81.3 度的中心角，比例约为 0.42。
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let fraction = footprint_fraction(GEOSTATIONARY, BODY_RADIUS, 0.0).expect("valid");
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assert!(fraction > 0.40 && fraction < 0.43, "fraction {fraction}");
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}
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#[test]
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fn containment_is_inclusive_at_the_edge() {
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let footprint = Footprint::new(0.5, BODY_RADIUS);
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assert!(footprint.contains_central_angle(0.0));
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assert!(footprint.contains_central_angle(0.25));
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assert!(footprint.contains_central_angle(0.5));
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assert!(!footprint.contains_central_angle(0.500_001));
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assert!(!footprint.contains_central_angle(-0.1));
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assert!(!footprint.contains_central_angle(f64::NAN));
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}
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#[test]
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fn the_central_angle_between_two_surface_points_is_the_included_angle() {
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// Two points on the equator ninety degrees apart.
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// 赤道上相隔九十度的两个点。
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let first = Vec3::new(BODY_RADIUS, 0.0, 0.0);
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let second = Vec3::new(0.0, BODY_RADIUS, 0.0);
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let angle = central_angle_between(first, second).expect("valid");
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assert!((angle - FRAC_PI_2).abs() < TOLERANCE);
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// A point with itself gives zero.
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// 点与其自身给出零。
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assert!(central_angle_between(first, first).expect("valid").abs() < TOLERANCE);
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// Opposite points give a straight angle.
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// 相对的点给出平角。
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let opposite = Vec3::new(-BODY_RADIUS, 0.0, 0.0);
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assert!((central_angle_between(first, opposite).expect("valid") - PI).abs() < TOLERANCE);
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}
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#[test]
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fn the_central_angle_between_points_is_scale_invariant() {
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// The angle depends only on the directions, not on the radii.
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// 该角只依赖于方向，而不依赖于半径。
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let near = Vec3::new(1.0, 0.5, 0.25);
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let far = near * 1_000.0;
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let other = Vec3::new(0.0, 1.0, 0.0);
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let first = central_angle_between(near, other).expect("valid");
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let second = central_angle_between(far, other).expect("valid");
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assert!((first - second).abs() < 1e-12);
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}
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#[test]
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fn a_degenerate_vector_has_no_central_angle() {
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assert_eq!(central_angle_between(Vec3::ZERO, Vec3::X), None);
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assert_eq!(central_angle_between(Vec3::X, Vec3::ZERO), None);
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assert_eq!(central_angle_between(Vec3::splat(f64::NAN), Vec3::X), None);
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}
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#[test]
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fn point_in_footprint_uses_the_central_angle_from_the_sub_satellite_point() {
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let footprint = Footprint::new(0.1, BODY_RADIUS);
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// The sub-satellite point on the equator.
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// 赤道上的星下点。
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let sub_satellite = Vec3::new(BODY_RADIUS, 0.0, 0.0);
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// A point within the footprint, about 0.05 radians away.
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// 覆盖区内的一个点，约 0.05 弧度之外。
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let inside = Vec3::new(
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BODY_RADIUS * 0.05_f64.cos(),
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BODY_RADIUS * 0.05_f64.sin(),
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0.0,
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);
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assert_eq!(
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point_in_footprint(&footprint, inside, sub_satellite),
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Some(true)
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);
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// A point well outside it, about a quarter radian away.
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// 远在其外的一个点，约四分之一弧度之外。
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let outside = Vec3::new(
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BODY_RADIUS * 0.25_f64.cos(),
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BODY_RADIUS * 0.25_f64.sin(),
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0.0,
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);
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assert_eq!(
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point_in_footprint(&footprint, outside, sub_satellite),
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Some(false)
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);
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}
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#[test]
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fn the_edge_elevation_inverts_the_footprint_central_angle() {
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let mask = 12.0_f64.to_radians();
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let footprint = footprint(LOW_ORBIT, BODY_RADIUS, mask).expect("valid");
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let recovered = footprint_edge_elevation(LOW_ORBIT, &footprint).expect("valid");
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assert!(
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(recovered - mask).abs() < 1e-9,
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"{recovered} against {mask}"
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);
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}
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#[test]
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fn the_footprint_central_angle_helper_matches_the_constructor() {
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let mask = 15.0_f64.to_radians();
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let central = footprint_central_angle(LOW_ORBIT, BODY_RADIUS, mask).expect("valid");
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let footprint = footprint(LOW_ORBIT, BODY_RADIUS, mask).expect("valid");
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assert!((central - footprint.central_angle).abs() < TOLERANCE);
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}
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#[test]
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fn invalid_geometry_is_rejected() {
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assert_eq!(footprint(LOW_ORBIT, 0.0, 0.1), None);
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assert_eq!(footprint(BODY_RADIUS - 1.0, BODY_RADIUS, 0.1), None);
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assert_eq!(footprint(LOW_ORBIT, BODY_RADIUS, f64::NAN), None);
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assert_eq!(footprint_area(LOW_ORBIT, BODY_RADIUS, f64::INFINITY), None);
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assert_eq!(footprint_fraction(LOW_ORBIT, -1.0, 0.1), None);
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}
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