98 lines
4.3 KiB
Rust
98 lines
4.3 KiB
Rust
//! Ephemeris sampling and interpolation.
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//!
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//! A propagator gives the state of a satellite at any instant, but calling
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//! it millions of times is wasteful when the result is only needed to draw a
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//! track or to search for a crossing. This crate records the state at a
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//! grid of times, called samples, and answers queries between them by
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//! interpolation.
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//!
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//! The two halves are deliberately independent:
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//!
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//! - [`Ephemeris`] is a table of times and states. It knows nothing about
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//! where the states came from, so a table propagated by SGP4, computed by
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//! two-body theory, or read from a file all work the same way.
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//! - [`Sampler`] fills a table by calling a function that produces a state
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//! from a time. In this workspace that function is normally
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//! `apsis_sgp4::Satellite::propagate_at`, but the sampler only requires
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//! a closure, so a test can use an analytic function.
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//!
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//! Interpolation is Hermite cubic, which uses both the position and the
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//! velocity at each end of an interval. Using the velocity is what makes it
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//! accurate: a cubic through two positions alone has no information about
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//! how fast the satellite is moving, while Hermite reconstruction matches
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//! the slope at both ends and so reproduces a smooth orbit far better for
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//! the same sample spacing. On a circular orbit the error is of order the
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//! fourth power of the step, so halving the step cuts the error about
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//! sixteen fold.
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//!
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//! Times are in seconds from an origin chosen by the caller, matching the
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//! rest of the orbit layer. Positions are in kilometers and velocities in
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//! kilometers per second.
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//!
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//! ```
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//! use apsis_ephemeris::{Sample, Sampler};
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//! use apsis_kepler::{GravityParameter, KeplerianElements};
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//!
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//! // A circular orbit at the Earth's equatorial radius.
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//! let elements = KeplerianElements {
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//! semi_major_axis: 7_000.0,
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//! eccentricity: 0.0,
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//! inclination: 0.9,
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//! right_ascension: 0.0,
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//! argument_of_perigee: 0.0,
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//! true_anomaly: 0.0,
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//! };
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//! let state_at = |seconds: f64| {
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//! let mean = 2.0 * core::f64::consts::PI * seconds
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//! / elements.period(GravityParameter::WGS84);
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//! let state = elements
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//! .with_mean_anomaly(mean)
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//! .to_state(GravityParameter::WGS84)
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//! .expect("the orbit is valid");
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//! Sample::new(seconds, state.position, state.velocity)
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//! };
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//!
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//! let sampler = Sampler::new(0.0, 600.0, 60.0);
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//! let ephemeris = sampler.sample(state_at).expect("the grid is usable");
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//! assert_eq!(ephemeris.len(), 11);
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//!
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//! // A query between two samples is interpolated.
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//! let state = ephemeris.state_at(30.0).expect("the time is covered");
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//! assert!(state.position.norm() > 6_900.0);
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//! ```
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//!
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//! 星历采样与插值。
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//!
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//! 传播器给出卫星在任意瞬时的状态，但当结果只用于绘制轨迹或搜索穿越时，调用
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//! 它数百万次是浪费的。本 crate 在一组时刻网格上记录状态（称为样本），并用
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//! 插值回答其间的查询。
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//!
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//! 两半是有意独立的：
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//!
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//! - [`Ephemeris`] 是时刻与状态的表。它对状态来自何处一无所知，故由 SGP4
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//! 传播、由二体理论计算，或从文件读取的表都以相同方式工作。
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//! - [`Sampler`] 通过调用一个由时刻产生状态的函数来填充表。在本工作区中该
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//! 函数通常是 `apsis_sgp4::Satellite::propagate_at`，但采样器只需要一个
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//! 闭包，故测试可用解析函数。
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//!
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//! 插值是 Hermite 三次插值，它同时使用区间两端的位与速度。使用速度正是它
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//! 准确的原因：只过两个位置的三次式没有卫星移动多快的信息，而 Hermite 重构
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//! 匹配两端的斜率，故在相同采样间距下能好得多地复现光滑轨道。在圆轨道上误差
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//! 是步长的四阶量，故步长减半使误差约减为十六分之一。
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//!
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//! 时间以距调用方所选原点的秒数计，与 orbit 层其余部分一致。位置以千米计，
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//! 速度以千米每秒计。
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#![forbid(unsafe_code)]
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#![deny(missing_docs)]
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mod ephemeris;
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mod error;
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mod sampler;
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pub use ephemeris::{Ephemeris, Sample, hermite_position, hermite_state, hermite_velocity};
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pub use error::{EphemerisError, EphemerisErrorKind};
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pub use sampler::Sampler;
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pub use apsis_math::Vec3;
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