224 lines
8.2 KiB
Rust
224 lines
8.2 KiB
Rust
//! Tests for the satellite geometry of a ground coverage calculation.
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//!
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//! The expected values are computed independently from the law of sines
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//! applied to the triangle formed by the satellite, the ground point, and
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//! the centre of the Earth.
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//!
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//! 地面覆盖计算中卫星几何的测试。
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//!
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//! 期望值由正弦定理独立计算，应用于卫星、地面点与地心构成的三角形。
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use apsis_coverage::{earth_central_angle, elevation_from_central_angle, nadir_angle, slant_range};
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use core::f64::consts::FRAC_PI_2;
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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 medium Earth orbit at 20 200 km altitude, near the navigation
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/// constellations.
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///
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/// 20 200 km 高度的中轨，接近导航星座。
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const MEDIUM_ORBIT: f64 = BODY_RADIUS + 20_200.0;
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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_angles_at_the_zenith_are_consistent() {
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// Directly below the satellite the elevation is a right angle, the
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// nadir angle is zero, and the central angle is zero.
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// 卫星正下方处仰角为直角，天底角为零，中心角为零。
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assert!(
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nadir_angle(LOW_ORBIT, BODY_RADIUS, FRAC_PI_2)
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.expect("valid")
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.abs()
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< TOLERANCE
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);
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assert!(
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earth_central_angle(LOW_ORBIT, BODY_RADIUS, FRAC_PI_2)
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.expect("valid")
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.abs()
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< TOLERANCE
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);
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// The slant range is the altitude.
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// 斜距即高度。
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assert!(
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(slant_range(LOW_ORBIT, BODY_RADIUS, FRAC_PI_2).expect("valid") - 550.0).abs() < TOLERANCE
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);
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}
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#[test]
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fn the_three_angles_are_complementary() {
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// elevation + nadir + central = 90 degrees, for every geometry.
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// 对每种几何，elevation + nadir + central = 90 度。
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for satellite_radius in [LOW_ORBIT, MEDIUM_ORBIT, GEOSTATIONARY] {
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for elevation_degrees in [0.0_f64, 5.0, 10.0, 30.0, 60.0, 89.0] {
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let elevation = elevation_degrees.to_radians();
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let nadir = nadir_angle(satellite_radius, BODY_RADIUS, elevation).expect("valid");
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let central =
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earth_central_angle(satellite_radius, BODY_RADIUS, elevation).expect("valid");
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let sum = elevation + nadir + central;
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assert!(
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(sum - FRAC_PI_2).abs() < 1e-9,
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"radius {satellite_radius}, elevation {elevation_degrees}: sum {sum}"
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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 the_geometry_matches_a_hand_computation() {
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// A 550 km satellite at a ten degree mask. The nadir angle is
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// asin(Re cos(el) / Rs) = 65.0434 degrees, the central angle is
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// 14.9566 degrees, and the slant range is 1815.652 km.
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// 十度遮蔽下的 550 km 卫星。天底角为 asin(Re cos(el) / Rs) = 65.0434 度，
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// 中心角为 14.9566 度，斜距为 1815.652 km。
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let elevation = 10.0_f64.to_radians();
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assert!(
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(nadir_angle(LOW_ORBIT, BODY_RADIUS, elevation)
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.expect("valid")
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.to_degrees()
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- 65.043_364_875_042_71)
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.abs()
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< 1e-9
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);
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assert!(
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(earth_central_angle(LOW_ORBIT, BODY_RADIUS, elevation)
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.expect("valid")
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.to_degrees()
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- 14.956_635_124_957_29)
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.abs()
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< 1e-9
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);
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assert!(
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(slant_range(LOW_ORBIT, BODY_RADIUS, elevation).expect("valid") - 1_815.652_169_368_375_8)
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.abs()
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< 1e-9
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);
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}
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#[test]
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fn a_higher_satellite_sees_further() {
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let elevation = 10.0_f64.to_radians();
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let low = earth_central_angle(LOW_ORBIT, BODY_RADIUS, elevation).expect("valid");
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let medium = earth_central_angle(MEDIUM_ORBIT, BODY_RADIUS, elevation).expect("valid");
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let high = earth_central_angle(GEOSTATIONARY, BODY_RADIUS, elevation).expect("valid");
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assert!(low < medium, "{low} against {medium}");
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assert!(medium < high, "{medium} against {high}");
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}
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#[test]
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fn a_lower_elevation_mask_sees_further() {
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// Relaxing the mask lets the satellite be seen closer to the horizon,
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// which increases the central angle.
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// 放宽遮蔽使卫星能被看到至更接近地平，这增大中心角。
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let mut previous = 0.0;
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for elevation_degrees in [30.0_f64, 20.0, 10.0, 5.0, 0.0] {
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let central = earth_central_angle(LOW_ORBIT, BODY_RADIUS, elevation_degrees.to_radians())
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.expect("valid");
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assert!(
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central > previous,
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"elevation {elevation_degrees}: {central} against {previous}"
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);
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previous = central;
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}
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}
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#[test]
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fn a_zero_degree_mask_is_the_horizon() {
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// At a zero degree mask the central angle is the horizon angle
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// acos(Re / Rs), which is where the line of sight is tangent to the
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// surface.
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// 零度遮蔽下中心角即地平角 acos(Re / Rs)，那里视线与地表相切。
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let central = earth_central_angle(LOW_ORBIT, BODY_RADIUS, 0.0).expect("valid");
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let horizon = (BODY_RADIUS / LOW_ORBIT).acos();
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assert!((central - horizon).abs() < 1e-9);
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}
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#[test]
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fn the_slant_range_grows_as_the_elevation_falls() {
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// A satellite near the horizon is further away than one overhead.
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// 接近地平的卫星比过顶的更远。
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let overhead = slant_range(LOW_ORBIT, BODY_RADIUS, FRAC_PI_2).expect("valid");
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let low = slant_range(LOW_ORBIT, BODY_RADIUS, 5.0_f64.to_radians()).expect("valid");
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assert!(low > overhead, "{low} against {overhead}");
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assert!(overhead < 600.0);
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assert!(low > 1_000.0);
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}
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#[test]
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fn the_elevation_inverts_the_central_angle() {
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for satellite_radius in [LOW_ORBIT, MEDIUM_ORBIT, GEOSTATIONARY] {
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for elevation_degrees in [0.0_f64, 10.0, 30.0, 70.0] {
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let elevation = elevation_degrees.to_radians();
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let central =
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earth_central_angle(satellite_radius, BODY_RADIUS, elevation).expect("valid");
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let recovered = elevation_from_central_angle(satellite_radius, BODY_RADIUS, central)
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.expect("valid");
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assert!(
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(recovered - elevation).abs() < 1e-9,
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"radius {satellite_radius}, elevation {elevation_degrees}: {recovered}"
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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 the_elevation_is_a_right_angle_when_the_central_angle_is_zero() {
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let elevation = elevation_from_central_angle(LOW_ORBIT, BODY_RADIUS, 0.0).expect("valid");
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assert!((elevation - FRAC_PI_2).abs() < TOLERANCE);
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}
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#[test]
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fn a_satellite_inside_the_body_is_rejected() {
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// A satellite below the surface has no geometry, so the functions
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// report nothing rather than a negative angle.
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// 地表以下的卫星没有几何，故这些函数报告空而非负角。
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assert_eq!(nadir_angle(BODY_RADIUS - 1.0, BODY_RADIUS, 0.0), None);
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assert_eq!(
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earth_central_angle(BODY_RADIUS - 1.0, BODY_RADIUS, 0.0),
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None
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);
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assert_eq!(slant_range(BODY_RADIUS - 1.0, BODY_RADIUS, 0.0), None);
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}
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#[test]
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fn non_finite_arguments_are_rejected() {
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assert_eq!(nadir_angle(f64::NAN, BODY_RADIUS, 0.0), None);
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assert_eq!(nadir_angle(LOW_ORBIT, f64::NAN, 0.0), None);
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assert_eq!(nadir_angle(LOW_ORBIT, BODY_RADIUS, f64::NAN), None);
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assert_eq!(
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earth_central_angle(LOW_ORBIT, BODY_RADIUS, f64::INFINITY),
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None
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);
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assert_eq!(slant_range(LOW_ORBIT, 0.0, 0.0), None);
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assert_eq!(
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elevation_from_central_angle(LOW_ORBIT, BODY_RADIUS, f64::NAN),
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None
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);
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}
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#[test]
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fn a_grazing_geometry_is_handled_at_the_horizon() {
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// At the horizon the nadir angle is the arc sine of the ratio of the
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// radii, which is exactly one when the satellite is at the surface and
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// less than one above it. The clamp keeps the arc sine defined.
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// 在地平处天底角是两半径之比的反正弦，卫星在地表时它恰为一，在其上方时小于一。
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// 该夹逼保持反正弦有定义。
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let nadir = nadir_angle(LOW_ORBIT, BODY_RADIUS, 0.0).expect("valid");
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assert!(nadir.is_finite());
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let expected = (BODY_RADIUS / LOW_ORBIT).asin();
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assert!((nadir - expected).abs() < 1e-9);
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}
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