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use super::{Cosm, Frame, LTCorr, State}; use std::cmp::{Eq, Ord, Ordering, PartialOrd}; use std::fmt; /// Stores the eclipse state #[derive(Clone, Copy, Debug, PartialEq)] pub enum EclipseState { Umbra, /// The f64 is between ]0; 1[ and corresponds to the percentage of penumbra: the closer to 1, the more light is seen. Penumbra(f64), Visibilis, } impl Eq for EclipseState {} impl Ord for EclipseState { /// Orders eclipse states to the greatest eclipse. /// /// *Examples* /// /// ``` /// extern crate nyx_space as nyx; /// use nyx::celestia::eclipse::EclipseState; /// assert!(EclipseState::Umbra == EclipseState::Umbra); /// assert!(EclipseState::Visibilis == EclipseState::Visibilis); /// assert!(EclipseState::Penumbra(0.5) == EclipseState::Penumbra(0.5)); /// assert!(EclipseState::Umbra > EclipseState::Penumbra(0.1)); /// assert!(EclipseState::Umbra > EclipseState::Penumbra(0.9)); /// assert!(EclipseState::Penumbra(0.1) < EclipseState::Umbra); /// assert!(EclipseState::Penumbra(0.9) < EclipseState::Umbra); /// assert!(EclipseState::Penumbra(0.9) > EclipseState::Visibilis); /// assert!(EclipseState::Visibilis < EclipseState::Penumbra(0.9)); /// ``` fn cmp(&self, other: &Self) -> Ordering { match *self { EclipseState::Umbra => { if *other == EclipseState::Umbra { Ordering::Equal } else { Ordering::Greater } } EclipseState::Visibilis => { if *other == EclipseState::Visibilis { Ordering::Equal } else { Ordering::Less } } EclipseState::Penumbra(s) => match *other { EclipseState::Penumbra(o) => { if s > o { Ordering::Greater } else { Ordering::Less } } EclipseState::Visibilis => Ordering::Greater, EclipseState::Umbra => Ordering::Less, }, } } } impl PartialOrd for EclipseState { fn partial_cmp(&self, other: &Self) -> Option<Ordering> { Some(self.cmp(other)) } } impl fmt::Display for EclipseState { fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result { match *self { Self::Umbra => write!(f, "Umbra"), Self::Visibilis => write!(f, "Visibilis"), Self::Penumbra(v) => write!(f, "Penumbra {}%", v * 100.0), } } } #[derive(Clone)] pub struct EclipseLocator<'a> { pub light_source: Frame, pub shadow_bodies: Vec<Frame>, pub cosm: &'a Cosm, pub correction: LTCorr, } impl<'a> EclipseLocator<'a> { /// Compute the visibility/eclipse between an observer and an observed state pub fn compute(&self, observer: &State) -> EclipseState { let mut state = EclipseState::Visibilis; for eclipsing_body in &self.shadow_bodies { let this_state = eclipse_state( observer, self.light_source, *eclipsing_body, self.cosm, self.correction, ); if this_state > state { state = this_state; } } state } } /// Computes the umbra/visibilis/penumbra state between between two states accounting for eclipsing of the providing geoid. pub fn eclipse_state( observer: &State, light_source: Frame, eclipsing_body: Frame, cosm: &Cosm, correction: LTCorr, ) -> EclipseState { // If the light source's radius is zero, just call the line of sight algorithm assert!(light_source.is_geoid() || light_source.is_celestial()); assert!(eclipsing_body.is_geoid()); if light_source.equatorial_radius() < std::f64::EPSILON { let observed = cosm.celestial_state( light_source.exb_id(), observer.dt, observer.frame, correction, ); return line_of_sight(observer, &observed, eclipsing_body, &cosm); } // All of the computations happen with the observer as the center. // `eb` stands for eclipsing body; `ls` stands for light source. // Vector from spacecraft to EB let r_eb = -cosm.frame_chg(observer, eclipsing_body).radius(); let r_eb_unit = r_eb / r_eb.norm(); // Vector from EB to LS let r_eb_ls = cosm .celestial_state( light_source.exb_id(), observer.dt, eclipsing_body, correction, ) .radius(); let r_eb_ls_unit = r_eb_ls / r_eb_ls.norm(); // Compute the angle between those vectors. If that angle is less than 90 degrees, then the light source // is in front of the eclipsing body, so we're visible. let beta2 = r_eb_unit.dot(&r_eb_ls_unit).acos(); if beta2 <= std::f64::consts::FRAC_PI_2 { return EclipseState::Visibilis; } // Get the state of the light source with respect to the spacecraft let r_ls = r_eb + r_eb_ls; let r_ls_unit = r_ls / r_ls.norm(); // Compute beta3, the angle between the spacecraft and the eclipsing body, and between the spacecraft and the light source. // We need this to project the radius of the light source onto the plane centered at the eclipsing geoid, and normal to // the direction to the spacecraft. let cos_beta3 = r_ls_unit.dot(&r_eb_unit); // Now compute r_ls_p, the vector from the eclipsing body to the center of the projected light source onto the plane. let r_ls_p = (r_eb.norm() / cos_beta3) * r_ls_unit; // Now let's compute the pseudo radius of the light source near the plane. // This is the pseudo radius because we're building a right triangle between the intersection point of r_ls with the plane, // the normal from r_ls at that point until intersection with r_eb_ls. let beta1 = (-r_ls_unit).dot(&-r_eb_ls_unit).acos(); // We can now compute the gamma angle let gamma = std::f64::consts::FRAC_PI_2 - beta2 - beta1; // Applying Thales theorem, we can compute the pseudo radius of the light source let pseudo_ls_radius = r_ls_p.norm() * light_source.equatorial_radius() / r_ls.norm(); // And then project that onto the plane to compute the actual project radius of the light source onto the plane let ls_radius = pseudo_ls_radius / gamma.cos(); // Compute the radius from the center of the eclipsing geoid to the intersection point let r_plane_ls = r_ls_p - r_eb; // Note that the eclipsing geoid's circle is centered at zero, so the norm of r_plane_ls is also the distance // between the center of the eclipsing body's shadow and the center of the light source's shadow. let d_plane_ls = r_plane_ls.norm(); let eb_radius = eclipsing_body.equatorial_radius(); if d_plane_ls - ls_radius > eb_radius { // If the closest point where the projected light source's circle _starts_ is further // away than the furthest point where the eclipsing body's shadow can reach, then the light // source is totally visible. return EclipseState::Visibilis; } else if eb_radius > d_plane_ls + ls_radius { // The light source is fully hidden by the eclipsing body, hence we're in total eclipse. // Note that because we test for the beta2 angle earlier, we know that the light source is behind the plane // from the vantage point of the spacecraft. return EclipseState::Umbra; } // If we have reached this point, we're in penumbra. // Both circles, which represent the light source projected onto the plane and the eclipsing geoid, // now overlap creating an asymmetrial lens. // The following math comes from http://mathworld.wolfram.com/Circle-CircleIntersection.html // and https://stackoverflow.com/questions/3349125/circle-circle-intersection-points . // Compute the distances between the center of the eclipsing geoid and the line crossing the intersection // points of both circles. let d1 = (d_plane_ls.powi(2) - ls_radius.powi(2) + eb_radius.powi(2)) / (2.0 * d_plane_ls); let d2 = (d_plane_ls.powi(2) + ls_radius.powi(2) - eb_radius.powi(2)) / (2.0 * d_plane_ls); let shadow_area = circ_seg_area(eb_radius, d1) + circ_seg_area(ls_radius, d2); if shadow_area.is_nan() { return EclipseState::Umbra; } // Compute the nominal area of the light source let nominal_area = std::f64::consts::PI * ls_radius.powi(2); // And return the percentage (between 0 and 1) of the eclipse. EclipseState::Penumbra((nominal_area - shadow_area) / nominal_area) } // Compute the area of the circular segment of radius r and chord length d fn circ_seg_area(r: f64, d: f64) -> f64 { r.powi(2) * (d / r).acos() - d * (r.powi(2) - d.powi(2)).sqrt() } /// Computes the light of sight the provided time between two states accounting for eclipsing of the providing geoid. /// This works for visibility between spacecraft and a ground station. For eclipsing, use `eclipse_state`. /// /// # Algorithm /// This function solves the [Line-Sphere intersection](https://en.wikipedia.org/wiki/Line%E2%80%93sphere_intersection) problem. /// 1. We create a line between the observer and observed. /// 2. We then check if the line will intersect the geoid, represented as a sphere. /// 3. We compute the discriminant from the quadratic formula which emanates from solving the distance at which the intersection of the line and the sphere will happen. /// 4. If the discriminant is less than 0.0, then the distance along the starting point of the line to the sphere is an complex number, i.e. no intersection. /// 5. If the discriminant is greater than 0.0, then there are exactly two intersection points between the line and the sphere. /// 6. If the discriminant is exactly zero, then the line "skims" the sphere. /// /// In practice, this code uses a tolerance of 1e-12 instead of 0.0 to account for rounding issues. pub fn line_of_sight( observer: &State, observed: &State, eclipsing_body: Frame, cosm: &Cosm, ) -> EclipseState { if observer == observed { return EclipseState::Visibilis; } // Convert the observed to the same frame as the origin (fok = frame OK) let observed_fok = &cosm.frame_chg(observed, eclipsing_body); let observer_fok = &cosm.frame_chg(observer, eclipsing_body); // Compute the unit direction between both let mut l = observed_fok.radius() - observer_fok.radius(); l /= l.norm(); // observer minus center point of the eclipsing body is already in the eclipsing body frame, so center is zero. let omc = observer_fok.radius(); let r = &eclipsing_body.equatorial_radius(); // l.dot(&l) should be 1.0, within rounding error. let discriminant_sq = (l.dot(&omc)).powi(2) - l.dot(&l) * (omc.dot(&omc) - (r.powi(2))); if discriminant_sq < -1e-12 { // No intersection between the direction of the origin and vis_chk objects and the sphere EclipseState::Visibilis } else { // Compute the distance from the origin to the intersection point. let intersect_dist = -(l.dot(&omc)) + discriminant_sq.sqrt(); // And the intersection point itself. let intersect_pt = observer_fok.radius() + intersect_dist * l; let dist_ori_inters = observer_fok.distance_to_point(&intersect_pt); let dist_oth_inters = observed_fok.distance_to_point(&intersect_pt); let dist_ori_oth = observer_fok.distance_to(&observed_fok); // If the intersection point is on the line between both, then it causes an eclipse. if (dist_ori_inters + dist_oth_inters - dist_ori_oth).abs() < 1e-15 { if discriminant_sq > 1e-12 { EclipseState::Umbra } else { EclipseState::Penumbra(0.5) } } else { EclipseState::Visibilis } } } #[cfg(test)] mod tests { use super::*; use hifitime::Epoch; #[test] fn los_trivial() { /* use crate::celestia::frames::*; let mut cosm = Cosm::from_xb("./de438s"); // Let's create a ficticious Geoid let gee = Frame { id: XbId { number: -1000, name: "Ficticious".to_owned(), }, exb_id: None, info: Frame::Geoid { axb_id: 0, exb_id: 0, gm: 1.0, flattening: 0.0, equatorial_radius: 1.0, semi_major_radius: 0.0, }, }; let ginfo = gee.info; cosm.mut_add_frame(gee); let dt = Epoch::from_gregorian_tai_at_midnight(2020, 1, 1); let x1 = State::cartesian(-1.0, -1.0, 0.0, 0.0, 0.0, 0.0, dt, ginfo); let x2 = State::cartesian(1.0, 1.0, 0.0, 0.0, 0.0, 0.0, dt, ginfo); let x3 = State::cartesian(-2.0, 1.0, 0.0, 0.0, 0.0, 0.0, dt, ginfo); let x4 = State::cartesian(-3.0, 2.0, 0.0, 0.0, 0.0, 0.0, dt, ginfo); let x5 = State::cartesian(1.0, -2.0, 0.0, 0.0, 0.0, 0.0, dt, ginfo); let earth_id = 399; assert_eq!( line_of_sight(&x1, &x2, earth_id, &cosm), EclipseState::Umbra ); assert_eq!( line_of_sight(&x1, &x3, earth_id, &cosm), EclipseState::Visibilis ); assert_eq!( line_of_sight(&x3, &x2, earth_id, &cosm), EclipseState::Penumbra(0.5) ); assert_eq!( line_of_sight(&x4, &x3, earth_id, &cosm), EclipseState::Visibilis ); assert_eq!( line_of_sight(&x3, &x4, earth_id, &cosm), EclipseState::Visibilis ); assert_eq!( line_of_sight(&x5, &x4, earth_id, &cosm), EclipseState::Umbra ); */ } #[test] fn los_earth_eclipse() { let cosm = Cosm::from_xb("./de438s"); let eme2k = cosm.frame("EME2000"); let dt = Epoch::from_gregorian_tai_at_midnight(2020, 1, 1); let sma = eme2k.equatorial_radius() + 300.0; let sc1 = State::keplerian(sma, 0.001, 0.1, 90.0, 75.0, 0.0, dt, eme2k); let sc2 = State::keplerian(sma + 1.0, 0.001, 0.1, 90.0, 75.0, 0.0, dt, eme2k); let sc3 = State::keplerian(sma, 0.001, 0.1, 90.0, 75.0, 180.0, dt, eme2k); // Out of phase by pi. assert_eq!(line_of_sight(&sc1, &sc3, eme2k, &cosm), EclipseState::Umbra); // Nearly identical orbits in the same phasing assert_eq!( line_of_sight(&sc1, &sc2, eme2k, &cosm), EclipseState::Visibilis ); } #[test] fn eclipse_sun_eclipse() { let cosm = Cosm::from_xb("./de438s"); let sun = cosm.frame("Sun J2000"); let eme2k = cosm.frame("EME2000"); let dt = Epoch::from_gregorian_tai_at_midnight(2020, 1, 1); let sma = eme2k.equatorial_radius() + 300.0; let sc1 = State::keplerian(sma, 0.001, 0.1, 90.0, 75.0, 25.0, dt, eme2k); let sc2 = State::keplerian(sma, 0.001, 0.1, 90.0, 75.0, 115.0, dt, eme2k); let sc3 = State::keplerian(sma, 0.001, 0.1, 90.0, 75.0, 77.2, dt, eme2k); let correction = LTCorr::None; assert_eq!( eclipse_state(&sc1, sun, eme2k, &cosm, correction), EclipseState::Visibilis ); assert_eq!( eclipse_state(&sc2, sun, eme2k, &cosm, correction), EclipseState::Umbra ); match eclipse_state(&sc3, sun, eme2k, &cosm, correction) { EclipseState::Penumbra(val) => assert!(val > 0.9), _ => panic!("should be in penumbra"), }; } }