feat: 引入可切换星历模型并扩展天象观测链路
- 新增半解析、旧模型、自定义与多源堆叠星历实例，提供 Context、Instance、SPK 读取及状态与视位置计算 - 统一太阳、月球和行星实例接口，扩展黄经穿越、留、相位、最近角距、偕日可见、任意高度升落、轨道节点及凌日等天象查询 - 完善日月食、月掩与凌日的月缘剖面、有限盘面接触、站心修正、局地可见性、全球路径和地图输出 - 新增 SVG、GeoJSON、KML 天象输出及凌日、月掩和月缘地形相关缓存与几何求解 - 新增恒星星表导入与查询，支持 CSV、Hipparcos、BSC5、Stellarium 等格式及名称、交叉标识、锥面检索和星等过滤 - 补充 IAU 2006、地球定向、折射消光、大气观测、轨道传播及半解析行星/月球数据支持 - 将默认未来民用时标切换为 TimeScaleLeapHour，更新 2027–2400 农历速查表、中文日期解析和时区边界处理 - 增加事件基线、跨模型回归、几何边界、月缘地形和输出契约测试，完善中英文手册、示例资源、NOTICE 与忽略规则
This commit is contained in:
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package semianalytic
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import (
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"errors"
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"math"
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"sync"
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"b612.me/astro/internal/ephem"
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"b612.me/astro/planet/internal/semianalytic/lunar"
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"b612.me/astro/planet/internal/semianalytic/planets"
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)
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const (
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cKMPerDay = 299792.458 * 86400
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// 太阳史瓦西半径 2GM☉/c²，AU。
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srsAU = 1.97412574336e-8
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)
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var errInvalidObserver = errors.New("semianalytic: non-finite observer state")
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type observer struct {
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jd float64
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p, v [3]float64 // 地球日心位置 km、相对质心速度 km/日
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sunVel [3]float64 // 太阳相对质心速度 km/日
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}
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// 同一时刻常连续求多个天体，观测者状态缓存最近一次。
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var (
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observerMu sync.RWMutex
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observerCache observer
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observerSet bool
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)
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func observerAt(jd float64) (observer, error) {
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observerMu.RLock()
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c, set := observerCache, observerSet
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observerMu.RUnlock()
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if set && c.jd == jd {
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return c, nil
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}
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e, err := helio(ephem.Earth, jd)
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if err != nil {
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return observer{}, err
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}
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// 太阳质心速度只进光行差与光行时修正：快速档、只计四颗巨行星，内行星贡献 < 0.1 mas。
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var sv [3]float64
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_, total := planets.GM(1)
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for id := 1; id <= 4; id++ {
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gm, _ := planets.GM(id)
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total += gm
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}
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for id := 5; id <= 8; id++ {
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gm, _ := planets.GM(id)
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_, v, err := planets.Fast().HeliocentricState(id, jd)
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if err != nil {
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return observer{}, err
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}
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for i := range sv {
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sv[i] -= gm * v[i]
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}
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total += gm
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}
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o := observer{jd: jd, p: e.p}
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for i := range sv {
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sv[i] /= total
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o.sunVel[i] = sv[i]
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o.v[i] = e.v[i] + sv[i]
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// 坏表读出的非有限速度不得进缓存，否则同一时刻会一直返回 NaN 方向而 err 为 nil。
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if !finite(o.v[i]) || !finite(o.p[i]) {
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return observer{}, errInvalidObserver
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}
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}
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observerMu.Lock()
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observerCache, observerSet = o, true
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observerMu.Unlock()
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return o, nil
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}
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// targetHelio 目标日心位置；fast 用快速档，只作光行时初值与几何距离。
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func targetHelio(b ephem.Body, jd float64, fast bool) ([3]float64, error) {
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switch {
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case b == ephem.Sun:
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return [3]float64{}, nil
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case b == ephem.Moon:
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s, err := helio(ephem.Moon, jd)
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return s.p, err
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case b >= ephem.Mercury && b <= ephem.Neptune && b != ephem.EMB:
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if fast {
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return planets.Fast().Heliocentric(int(b), jd)
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}
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return planets.Default().Heliocentric(int(b), jd)
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}
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return [3]float64{}, ephem.ErrUnsupportedBody
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}
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type apparentEntry struct {
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jd float64
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dir [3]float64
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dist, tau float64
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set bool
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}
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var (
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apparentMu sync.RWMutex
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apparentCache [10]apparentEntry
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)
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func apparentStore(slot int, e apparentEntry) {
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e.set = true
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apparentMu.Lock()
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apparentCache[slot] = e
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apparentMu.Unlock()
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}
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// cacheSlot 天体对应的缓存槽；-1 表示不支持该天体。
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func cacheSlot(b ephem.Body) int {
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switch {
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case b == ephem.Sun:
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return 0
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case b == ephem.Moon:
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return 9
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case b >= ephem.Mercury && b <= ephem.Neptune && b != ephem.EMB:
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return int(b)
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}
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return -1
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}
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// Apparent 地心视方向（ICRF 单位矢量）、几何地心距 km、光行时 日 / geocentric apparent direction.
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func Apparent(target ephem.Body, jd float64) (dir [3]float64, distKM, tauDays float64, err error) {
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slot := cacheSlot(target)
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if slot < 0 {
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return dir, 0, 0, ephem.ErrUnsupportedBody
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}
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if !finite(jd) {
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return dir, 0, 0, ephem.ErrOutOfRange
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}
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apparentMu.RLock()
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c := apparentCache[slot]
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apparentMu.RUnlock()
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if c.set && c.jd == jd {
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return c.dir, c.dist, c.tau, nil
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}
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o, err := observerAt(jd)
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if err != nil {
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return dir, 0, 0, err
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}
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if target == ephem.Moon {
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e, err := apparentMoon(jd, o)
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if err != nil {
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return dir, 0, 0, err
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}
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apparentStore(slot, e)
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return e.dir, e.dist, e.tau, nil
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}
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now, err := targetHelio(target, jd, true)
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if err != nil {
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return dir, 0, 0, err
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}
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g := vsub(now, o.p)
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dist := vlen(g)
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tau := dist / cKMPerDay
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// 迭代光行时，每次误差缩小约 v/c 倍：先用快速档收敛 τ，末次用全表；太阳在 τ 内相对质心的位移按线性计入。
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var r [3]float64
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for k := 0; k < 2; k++ {
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if r, err = targetHelio(target, jd-tau, k == 0); err != nil {
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return dir, 0, 0, err
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}
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for i := range g {
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g[i] = r[i] - o.p[i] - o.sunVel[i]*tau
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}
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tau = vlen(g) / cKMPerDay
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}
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q := vscale(g, 1/vlen(g))
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if target != ephem.Sun && target != ephem.Moon {
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q = deflect(q, r, o.p)
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}
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q = aberrate(q, o.v)
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e := apparentEntry{jd: jd, dir: toICRF(q), dist: dist, tau: tau}
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apparentStore(slot, e)
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return e.dir, e.dist, e.tau, nil
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}
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// apparentMoon 月球地心视方向。光行时仅约 1.3 s，若像行星那样在 jd 与 jd−τ 各求一次地月质心
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// 日心位置（~1.5e8 km）再与地球相减，远历元表求值的舍入噪声（2981 年约 2e-4 km）会原样进入
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// 地心矢量，超过下游牛顿迭代的残差容差。这里全程用地心量：
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// 月球日心(jd−τ) − 地球日心(jd) = EMB(jd−τ) − EMB(jd) + f·m(jd−τ) + m(jd)/(1+μ)，
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// 其中 EMB 在 τ 内的位移按 jd 时刻速度线性外推，二阶项 ½aτ² < 1e-5 km。
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// 月球地心位置同样按 jd 时刻解析速度外推（½aτ² ≈ 2e-6 km）：直接求 m(jd−τ) 时，jd−τ 的舍入
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// （~4.7e-10 日）乘月球地心速度（~8.8e4 km/日）给出 ~1e-5 km 的逐点抖动，有限差分导数会把它放大。
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func apparentMoon(jd float64, o observer) (apparentEntry, error) {
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emb, err := planetHelio(int(ephem.EMB), jd)
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if err != nil {
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return apparentEntry{}, err
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}
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now, vel := lunar.Default().PositionVelocityJ2000(jd)
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dist := vlen(now)
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tau := dist / cKMPerDay
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f := emrat / (1 + emrat)
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g := now
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for k := 0; k < 2; k++ {
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for i := range g {
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g[i] = f*(now[i]-vel[i]*tau) + now[i]/(1+emrat) - (emb.v[i]+o.sunVel[i])*tau
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}
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tau = vlen(g) / cKMPerDay
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}
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q := aberrate(vscale(g, 1/vlen(g)), o.v)
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return apparentEntry{jd: jd, dir: toICRF(q), dist: dist, tau: tau}, nil
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}
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// deflect 太阳引力偏折；p 目标方向，t 目标日心位置，e 地球日心位置。
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func deflect(p, t, e [3]float64) [3]float64 {
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em := vlen(e) / auKM
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eu := vscale(e, 1/vlen(e))
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q := vscale(t, 1/vlen(t))
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qpe := vdot(q, eu) + 1
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if qpe < 1e-9 {
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return p
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}
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w := srsAU / em / qpe
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pe, pq := vdot(p, eu), vdot(p, q)
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// p × (e × q) = e(p·q) − q(p·e)
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for i := range p {
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p[i] += w * (eu[i]*pq - q[i]*pe)
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}
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return p
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}
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// aberrate 相对论光行差；v 观测者相对质心速度 km/日。
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func aberrate(p, v [3]float64) [3]float64 {
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b := vscale(v, 1/cKMPerDay)
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bm := 1 / math.Sqrt(1-vdot(b, b))
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pdv := vdot(p, b)
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w1 := 1 + pdv/(1+1/bm)
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w2 := 1 / (1 + pdv)
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var r [3]float64
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for i := range p {
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r[i] = (p[i]/bm + w1*b[i]) * w2
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}
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return vscale(r, 1/vlen(r))
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}
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func vdot(a, b [3]float64) float64 { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] }
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func vlen(a [3]float64) float64 { return math.Sqrt(vdot(a, a)) }
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func vsub(a, b [3]float64) [3]float64 {
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return [3]float64{a[0] - b[0], a[1] - b[1], a[2] - b[2]}
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}
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func vscale(a [3]float64, k float64) [3]float64 { return [3]float64{a[0] * k, a[1] * k, a[2] * k} }
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@@ -0,0 +1,45 @@
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package semianalytic
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import (
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"math"
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"testing"
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"b612.me/astro/internal/ephem"
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)
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// stateOnly 只暴露几何状态，迫使实例走通用矢量链。
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type stateOnly struct{ Ephemeris }
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func (e stateOnly) State(t, c ephem.Body, jd float64) ([3]float64, [3]float64, error) {
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return e.Ephemeris.State(t, c, jd)
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}
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func (e stateOnly) Coverage(t ephem.Body) (float64, float64, bool) { return e.Ephemeris.Coverage(t) }
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func TestGenericApparentMatchesNative(t *testing.T) {
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inst := ephem.NewInstance(stateOnly{})
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worst := 0.0
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for _, jd := range []float64{2451545.0, 2460409.25, 2433282.5, 2488069.5} {
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for _, b := range []ephem.Body{ephem.Sun, ephem.Moon, ephem.Mercury, ephem.Venus, ephem.Mars, ephem.Jupiter, ephem.Saturn, ephem.Uranus, ephem.Neptune} {
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want, wd, _, err := Ephemeris{}.Apparent(b, jd)
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if err != nil {
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t.Fatal(err)
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}
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got, gd, _, err := inst.Apparent(b, jd)
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if err != nil {
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t.Fatalf("body %d: %v", b, err)
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}
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cx := got[1]*want[2] - got[2]*want[1]
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cy := got[2]*want[0] - got[0]*want[2]
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cz := got[0]*want[1] - got[1]*want[0]
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c := got[0]*want[0] + got[1]*want[1] + got[2]*want[2]
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// acos 在 1 附近每 ulp 约 3 mas，用 atan2 避开这一噪声底。
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arcsec := math.Atan2(math.Sqrt(cx*cx+cy*cy+cz*cz), c) * 206264.806
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worst = math.Max(worst, arcsec)
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// 原生链的太阳质心速度只计四颗巨行星，与通用链差到数 mas。
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if arcsec > 0.005 || math.Abs(gd-wd)/wd > 1e-9 {
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t.Errorf("jd %.1f body %d: direction %.5f\" dist %.3f km", jd, b, arcsec, gd-wd)
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}
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}
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}
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t.Logf("worst %.6f\"", worst)
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}
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@@ -0,0 +1,76 @@
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package semianalytic
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import (
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"math"
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"testing"
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"b612.me/astro/internal/ephem"
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)
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// 视月球方向在远历元也必须是光滑函数：下游中心带牛顿迭代的残差容差约 2e-10，
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// 求值噪声需留出一个量级。二阶差分 RMS 按月地距折算成 km，h=1e-7 日时真实曲率项可忽略。
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func TestApparentMoonSmoothAtDistantEpochs(t *testing.T) {
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const h, n, limitKM = 1e-7, 200, 6e-5
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for _, jd0 := range []float64{2451545.0, 2460680.5, 2288000.5, 2810139.6097} {
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var prev [2][3]float64
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var sum float64
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for i := 0; i < n; i++ {
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d, _, _, err := Apparent(ephem.Moon, jd0+float64(i)*h)
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if err != nil {
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t.Fatal(err)
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}
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p := [3]float64{d[0] * 3.844e5, d[1] * 3.844e5, d[2] * 3.844e5}
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if i >= 2 {
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for k := range p {
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dd := p[k] - 2*prev[1][k] + prev[0][k]
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sum += dd * dd
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}
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}
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prev[0], prev[1] = prev[1], p
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}
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if rms := math.Sqrt(sum / (n - 2)); rms > limitKM {
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t.Errorf("jd %.1f: apparent Moon second-difference rms %.2e km, want <= %.0e", jd0, rms, limitKM)
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}
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}
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}
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// 地心化的光行时链与"两次日心相减"的旧链在数学上等价，只差 EMB 的二阶外推项（< 0.01 mas）。
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// 旧链自身带有 jd−τ 的舍入（~1e-10 日）乘地月质心速度（2.6e6 km/日）的误差，最大约 0.35 mas，
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// 因此容差取 0.5 mas；两者差值反映的是旧链误差，不是新链误差。
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func TestApparentMoonMatchesHeliocentricChain(t *testing.T) {
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for _, jd := range []float64{2451545.0, 2460409.25, 2433282.5, 2810139.6097, 2086000.5} {
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got, gd, gt, err := Apparent(ephem.Moon, jd)
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if err != nil {
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t.Fatal(err)
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}
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o, err := observerAt(jd)
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if err != nil {
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t.Fatal(err)
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}
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tau := gt
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r, err := targetHelio(ephem.Moon, jd-tau, false)
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if err != nil {
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t.Fatal(err)
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}
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var g [3]float64
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for i := range g {
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g[i] = r[i] - o.p[i] - o.sunVel[i]*tau
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}
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want := toICRF(aberrate(vscale(g, 1/vlen(g)), o.v))
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cx := got[1]*want[2] - got[2]*want[1]
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cy := got[2]*want[0] - got[0]*want[2]
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cz := got[0]*want[1] - got[1]*want[0]
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c := got[0]*want[0] + got[1]*want[1] + got[2]*want[2]
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mas := math.Atan2(math.Sqrt(cx*cx+cy*cy+cz*cz), c) * 206264806.2
|
||||
if mas > 0.5 {
|
||||
t.Errorf("jd %.1f: geocentric chain differs by %.4f mas", jd, mas)
|
||||
}
|
||||
now, err := targetHelio(ephem.Moon, jd, true)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
if wd := vlen(vsub(now, o.p)); math.Abs(gd-wd) > 1 {
|
||||
t.Errorf("jd %.1f: geometric distance %.3f km, heliocentric chain %.3f km", jd, gd, wd)
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,45 @@
|
||||
// 被测契约：非法 Body 与非有限历元必须报错而不是 panic 或静默返回 NaN；缓存槽不得跨天体串用。
|
||||
package semianalytic
|
||||
|
||||
import (
|
||||
"math"
|
||||
"testing"
|
||||
|
||||
"b612.me/astro/internal/ephem"
|
||||
)
|
||||
|
||||
func TestApparentRejectsUnsupportedBody(t *testing.T) {
|
||||
for _, body := range []ephem.Body{ephem.SSB, ephem.EMB, ephem.Earth, ephem.Body(-1), ephem.Body(2000001)} {
|
||||
if _, _, _, err := Apparent(body, 2451545); err != ephem.ErrUnsupportedBody {
|
||||
t.Errorf("Apparent(%d) err = %v, want %v", body, err, ephem.ErrUnsupportedBody)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestApparentCacheSlotsAreDistinct(t *testing.T) {
|
||||
const jd = 2451545.0
|
||||
sunDir, sunDist, _, err := Apparent(ephem.Sun, jd)
|
||||
if err != nil {
|
||||
t.Fatalf("Apparent(Sun) err = %v", err)
|
||||
}
|
||||
for _, body := range []ephem.Body{ephem.Mercury, ephem.Mars, ephem.Neptune, ephem.Moon} {
|
||||
dir, dist, _, err := Apparent(body, jd)
|
||||
if err != nil {
|
||||
t.Fatalf("Apparent(%d) err = %v", body, err)
|
||||
}
|
||||
if dir == sunDir && dist == sunDist {
|
||||
t.Errorf("Apparent(%d) returned the Sun entry", body)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestNonFiniteEpochIsOutOfRange(t *testing.T) {
|
||||
for _, jd := range []float64{math.NaN(), math.Inf(1), math.Inf(-1)} {
|
||||
if _, _, err := (Ephemeris{}).State(ephem.Mars, ephem.Sun, jd); err != ephem.ErrOutOfRange {
|
||||
t.Errorf("State(%v) err = %v, want %v", jd, err, ephem.ErrOutOfRange)
|
||||
}
|
||||
if _, _, _, err := (Ephemeris{}).Apparent(ephem.Mars, jd); err != ephem.ErrOutOfRange {
|
||||
t.Errorf("Apparent(%v) err = %v, want %v", jd, err, ephem.ErrOutOfRange)
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,46 @@
|
||||
package lunar
|
||||
|
||||
import (
|
||||
_ "embed"
|
||||
"sync"
|
||||
)
|
||||
|
||||
//go:embed lunar.bin
|
||||
var defaultTable []byte
|
||||
|
||||
var (
|
||||
defaultOnce sync.Once
|
||||
defaultModel *Model
|
||||
)
|
||||
|
||||
// Default 内置表，首次调用时解析 / the built-in table, parsed on first use.
|
||||
func Default() *Model {
|
||||
defaultOnce.Do(func() {
|
||||
m, err := Parse(defaultTable)
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
defaultModel = m
|
||||
})
|
||||
return defaultModel
|
||||
}
|
||||
|
||||
//go:embed fast.bin
|
||||
var fastTable []byte
|
||||
|
||||
var (
|
||||
fastOnce sync.Once
|
||||
fastModel *Model
|
||||
)
|
||||
|
||||
// Fast 快速档表（n ≥ 0 用），首次调用时解析 / the fast-tier table used for n ≥ 0, parsed on first use.
|
||||
func Fast() *Model {
|
||||
fastOnce.Do(func() {
|
||||
m, err := Parse(fastTable)
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
fastModel = m
|
||||
})
|
||||
return fastModel
|
||||
}
|
||||
Binary file not shown.
Binary file not shown.
@@ -0,0 +1,513 @@
|
||||
// Package lunar 月球半解析级数运行时（地心，J2000 平黄道）。
|
||||
package lunar
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"errors"
|
||||
"math"
|
||||
"sync"
|
||||
)
|
||||
|
||||
const (
|
||||
j2000 = 2451545.0
|
||||
century = 36525.0
|
||||
arcsec = math.Pi / 648000.0
|
||||
fundCount = 13
|
||||
maxEnvelope = 8
|
||||
)
|
||||
|
||||
type coordinate struct {
|
||||
args []uint16
|
||||
nodes []int32
|
||||
// 包络阶数为 0 的项单独成段：flat0 为 [cos,sin] 交错
|
||||
nodes0 []int32
|
||||
flat0 []float32
|
||||
// 其余项（阶数 ≥1）
|
||||
nodesH []int32
|
||||
envH []uint8
|
||||
coefH []float32
|
||||
env []uint8
|
||||
secular []float64
|
||||
coef []float32
|
||||
}
|
||||
|
||||
// Model 已解析的月球级数表 / parsed lunar series table.
|
||||
type Model struct {
|
||||
s2 [5][]float64
|
||||
args [fundCount][5]float64
|
||||
lonPoly [5]float64
|
||||
p, q [5]float64
|
||||
maxMult [fundCount]int
|
||||
powOff [fundCount]int
|
||||
coords [3]coordinate
|
||||
maxEnv int
|
||||
// 前缀树：节点 i 的复相位 = 节点 parent[i] × pow[factor[i]]，parent 恒小于 i（-1 为根）
|
||||
nodeParent []int32
|
||||
nodeFactor []int32
|
||||
argNode []int32
|
||||
// pow 槽位 → (基本幅角, 乘数)，用于速度计算中的相位变化率
|
||||
slotFund []int8
|
||||
slotMult []float64
|
||||
powLen int
|
||||
legLen int
|
||||
// Parse 之后 Model 只读；每次求值的缓冲从池中取，可并发调用
|
||||
pool sync.Pool
|
||||
}
|
||||
|
||||
// scratch 单次求值的工作区。
|
||||
type scratch struct {
|
||||
pow []complex128
|
||||
node []complex128
|
||||
nodeRate []float64
|
||||
leg []float64
|
||||
dleg []float64
|
||||
env [maxEnvelope + 1]float64
|
||||
denv [maxEnvelope + 1]float64
|
||||
}
|
||||
|
||||
func (m *Model) getScratch() *scratch {
|
||||
if s, ok := m.pool.Get().(*scratch); ok {
|
||||
return s
|
||||
}
|
||||
return &scratch{
|
||||
pow: make([]complex128, m.powLen),
|
||||
node: make([]complex128, len(m.nodeParent)),
|
||||
nodeRate: make([]float64, len(m.nodeParent)),
|
||||
leg: make([]float64, m.legLen),
|
||||
dleg: make([]float64, m.legLen),
|
||||
}
|
||||
}
|
||||
|
||||
type reader struct {
|
||||
b []byte
|
||||
off int
|
||||
err error
|
||||
}
|
||||
|
||||
func (r *reader) take(n int) []byte {
|
||||
if r.err != nil || r.off+n > len(r.b) {
|
||||
r.err = errors.New("lunar: truncated table")
|
||||
return make([]byte, n)
|
||||
}
|
||||
s := r.b[r.off : r.off+n]
|
||||
r.off += n
|
||||
return s
|
||||
}
|
||||
|
||||
func (r *reader) u8() uint8 { return r.take(1)[0] }
|
||||
func (r *reader) u16() uint16 { return binary.LittleEndian.Uint16(r.take(2)) }
|
||||
func (r *reader) f64() float64 { return math.Float64frombits(binary.LittleEndian.Uint64(r.take(8))) }
|
||||
func (r *reader) f32() float32 { return math.Float32frombits(binary.LittleEndian.Uint32(r.take(4))) }
|
||||
|
||||
// Parse 解析 LM7 v2 二进制表 / parse an LM7 v2 table.
|
||||
func Parse(b []byte) (*Model, error) {
|
||||
r := &reader{b: b}
|
||||
if string(r.take(4)) != "LM7\x02" {
|
||||
return nil, errors.New("lunar: bad magic")
|
||||
}
|
||||
m := &Model{}
|
||||
nargs := int(r.u16())
|
||||
s2n := int(r.u16())
|
||||
secDeg := int(r.u8())
|
||||
for j := 0; j < 5; j++ {
|
||||
m.s2[j] = make([]float64, s2n)
|
||||
for k := range m.s2[j] {
|
||||
m.s2[j][k] = r.f64()
|
||||
}
|
||||
}
|
||||
for i := 0; i < fundCount; i++ {
|
||||
for k := 0; k < 5; k++ {
|
||||
m.args[i][k] = r.f64()
|
||||
}
|
||||
}
|
||||
for k := range m.lonPoly {
|
||||
m.lonPoly[k] = r.f64()
|
||||
}
|
||||
for k := range m.p {
|
||||
m.p[k] = r.f64()
|
||||
}
|
||||
for k := range m.q {
|
||||
m.q[k] = r.f64()
|
||||
}
|
||||
r.f64() // 距离比例已折入拟合系数
|
||||
mults := make([][fundCount]int8, nargs)
|
||||
for a := range mults {
|
||||
mask := r.u16()
|
||||
for i := 0; i < 16; i++ {
|
||||
if mask&(1<<uint(i)) == 0 {
|
||||
continue
|
||||
}
|
||||
if i >= fundCount {
|
||||
return nil, errors.New("lunar: multiplier index out of range")
|
||||
}
|
||||
k := int8(r.u8())
|
||||
mults[a][i] = k
|
||||
if v := int(math.Abs(float64(k))); v > m.maxMult[i] {
|
||||
m.maxMult[i] = v
|
||||
}
|
||||
}
|
||||
}
|
||||
m.buildTrie(mults)
|
||||
for c := 0; c < 3; c++ {
|
||||
n := int(r.u16())
|
||||
co := &m.coords[c]
|
||||
co.args = make([]uint16, n)
|
||||
for j := range co.args {
|
||||
co.args[j] = r.u16()
|
||||
if int(co.args[j]) >= nargs {
|
||||
return nil, errors.New("lunar: argument index out of range")
|
||||
}
|
||||
}
|
||||
co.env = r.take(n)
|
||||
ncoef := 0
|
||||
for _, e := range co.env {
|
||||
if int(e) > maxEnvelope {
|
||||
return nil, errors.New("lunar: envelope degree too high")
|
||||
}
|
||||
if int(e) > m.maxEnv {
|
||||
m.maxEnv = int(e)
|
||||
}
|
||||
ncoef += 2 * (int(e) + 1)
|
||||
}
|
||||
co.secular = make([]float64, secDeg+1)
|
||||
for k := range co.secular {
|
||||
co.secular[k] = r.f64()
|
||||
}
|
||||
raw := make([]float32, ncoef)
|
||||
for k := range raw {
|
||||
raw[k] = r.f32()
|
||||
}
|
||||
co.coef = interleave(co.env, raw)
|
||||
}
|
||||
if r.err != nil {
|
||||
return nil, r.err
|
||||
}
|
||||
if r.off != len(b) {
|
||||
return nil, errors.New("lunar: trailing bytes")
|
||||
}
|
||||
for c := range m.coords {
|
||||
co := &m.coords[c]
|
||||
co.nodes = make([]int32, len(co.args))
|
||||
pos := 0
|
||||
for j, a := range co.args {
|
||||
co.nodes[j] = m.argNode[a]
|
||||
e := int(co.env[j])
|
||||
if e == 0 {
|
||||
co.nodes0 = append(co.nodes0, co.nodes[j])
|
||||
co.flat0 = append(co.flat0, co.coef[pos], co.coef[pos+1])
|
||||
} else {
|
||||
co.nodesH = append(co.nodesH, co.nodes[j])
|
||||
co.envH = append(co.envH, co.env[j])
|
||||
co.coefH = append(co.coefH, co.coef[pos:pos+2*(e+1)]...)
|
||||
}
|
||||
pos += 2 * (e + 1)
|
||||
}
|
||||
}
|
||||
m.legLen = max3(s2n, secDeg+1, m.maxEnv+1)
|
||||
return m, nil
|
||||
}
|
||||
|
||||
func (m *Model) buildTrie(mults [][fundCount]int8) {
|
||||
total := 0
|
||||
for i := 0; i < fundCount; i++ {
|
||||
m.powOff[i] = total + m.maxMult[i]
|
||||
total += 2*m.maxMult[i] + 1
|
||||
}
|
||||
m.powLen = total
|
||||
m.slotFund = make([]int8, total)
|
||||
m.slotMult = make([]float64, total)
|
||||
for i := 0; i < fundCount; i++ {
|
||||
for k := -m.maxMult[i]; k <= m.maxMult[i]; k++ {
|
||||
m.slotFund[m.powOff[i]+k] = int8(i)
|
||||
m.slotMult[m.powOff[i]+k] = float64(k)
|
||||
}
|
||||
}
|
||||
type edge struct{ parent, factor int32 }
|
||||
index := map[edge]int32{}
|
||||
m.argNode = make([]int32, len(mults))
|
||||
for a, mv := range mults {
|
||||
cur := int32(-1)
|
||||
for i := 0; i < fundCount; i++ {
|
||||
if mv[i] == 0 {
|
||||
continue
|
||||
}
|
||||
e := edge{cur, int32(m.powOff[i] + int(mv[i]))}
|
||||
n, ok := index[e]
|
||||
if !ok {
|
||||
n = int32(len(m.nodeParent))
|
||||
index[e] = n
|
||||
m.nodeParent = append(m.nodeParent, e.parent)
|
||||
m.nodeFactor = append(m.nodeFactor, e.factor)
|
||||
}
|
||||
cur = n
|
||||
}
|
||||
m.argNode[a] = cur
|
||||
}
|
||||
}
|
||||
|
||||
// cmul 绕开内建复数乘法的 Inf/NaN 分支。
|
||||
func cmul(a, b complex128) complex128 {
|
||||
ar, ai, br, bi := real(a), imag(a), real(b), imag(b)
|
||||
return complex(ar*br-ai*bi, ar*bi+ai*br)
|
||||
}
|
||||
|
||||
func max3(a, b, c int) int {
|
||||
if b > a {
|
||||
a = b
|
||||
}
|
||||
if c > a {
|
||||
a = c
|
||||
}
|
||||
return a
|
||||
}
|
||||
|
||||
func poly(c *[5]float64, t float64) float64 {
|
||||
return c[0] + t*(c[1]+t*(c[2]+t*(c[3]+t*c[4])))
|
||||
}
|
||||
|
||||
// phase 与 poly 同值，但线性项单独做补偿归约：c1·t 在 ±1 万年达 1e6 rad，直接相加会丢掉约 1e-10 rad。
|
||||
func phase(c *[5]float64, t, tLow float64) float64 {
|
||||
const twoPiLow = 2.4492935982947064e-16
|
||||
product := c[1] * t
|
||||
roundoff := math.FMA(c[1], t, -product) + c[1]*tLow
|
||||
turns := math.Round(product / (2 * math.Pi))
|
||||
lin := math.FMA(-turns, 2*math.Pi, product) + (roundoff - turns*twoPiLow)
|
||||
return lin + (c[0] + t*t*(c[2]+t*(c[3]+t*c[4])))
|
||||
}
|
||||
|
||||
// dpoly 返回 poly 的一阶导数。
|
||||
func dpoly(c *[5]float64, t float64) float64 {
|
||||
return c[1] + t*(2*c[2]+t*(3*c[3]+t*4*c[4]))
|
||||
}
|
||||
|
||||
// legendreD 写入 P0..P(n-1)(x)；withD 时同时写入导数 P'k(x) 到 d。
|
||||
func legendreD(x float64, out, d []float64, withD bool) {
|
||||
out[0] = 1
|
||||
if len(out) > 1 {
|
||||
out[1] = x
|
||||
}
|
||||
for k := 2; k < len(out); k++ {
|
||||
out[k] = ((2*float64(k)-1)*x*out[k-1] - (float64(k)-1)*out[k-2]) / float64(k)
|
||||
}
|
||||
if !withD {
|
||||
return
|
||||
}
|
||||
d[0] = 0
|
||||
if len(d) > 1 {
|
||||
d[1] = 1
|
||||
}
|
||||
// P'k = P'(k-2) + (2k-1)·P(k-1)
|
||||
for k := 2; k < len(d); k++ {
|
||||
d[k] = d[k-2] + (2*float64(k)-1)*out[k-1]
|
||||
}
|
||||
}
|
||||
|
||||
func dot(c []float64, l []float64) float64 {
|
||||
s := 0.0
|
||||
for k, v := range c {
|
||||
s += v * l[k]
|
||||
}
|
||||
return s
|
||||
}
|
||||
|
||||
// PositionJ2000 地心月球 J2000 平黄道几何位置（km）/ geocentric Moon, J2000 mean ecliptic, km.
|
||||
// 可并发调用。
|
||||
func (m *Model) PositionJ2000(jdTT float64) [3]float64 {
|
||||
p, _ := m.eval(jdTT, false)
|
||||
return p
|
||||
}
|
||||
|
||||
// PositionVelocityJ2000 位置（km）与解析速度（km/日，对 TT）/ position (km) and analytic velocity (km/day).
|
||||
// 可并发调用。
|
||||
func (m *Model) PositionVelocityJ2000(jdTT float64) (pos, vel [3]float64) {
|
||||
return m.eval(jdTT, true)
|
||||
}
|
||||
|
||||
// eval 所有量先对 t（儒略世纪）求导，最后换算到每日。
|
||||
func (m *Model) eval(jdTT float64, wantVel bool) (pos, vel [3]float64) {
|
||||
s := m.getScratch()
|
||||
defer m.pool.Put(s)
|
||||
days := jdTT - j2000
|
||||
origin := days - jdTT
|
||||
daysLow := (jdTT - (days - origin)) - (j2000 + origin)
|
||||
t := days / century
|
||||
// tLow 保留历元相减与世纪除法的舍入，远离 J2000 时线性相位才不丢精度。
|
||||
tLow := (math.FMA(-t, century, days) + daysLow) / century
|
||||
x := (t + 20) / 100
|
||||
const dxdt = 0.01
|
||||
leg, dleg := s.leg, s.dleg
|
||||
// 递推前缀稳定，一次算到最长，S2 修正与各坐标长期项共用。
|
||||
legendreD(x, leg[:m.legLen], dleg[:m.legLen], wantVel)
|
||||
var dc, ddc [5]float64
|
||||
for j := range dc {
|
||||
dc[j] = dot(m.s2[j], leg)
|
||||
if wantVel {
|
||||
ddc[j] = dot(m.s2[j], dleg) * dxdt
|
||||
}
|
||||
}
|
||||
// ζ 随 W1 修正，D/F/l/l′ 各自修正
|
||||
var corr, dcorr, rate [fundCount]float64
|
||||
corr[0], corr[1], corr[2], corr[3], corr[12] = dc[1], dc[2], dc[3], dc[4], dc[0]
|
||||
dcorr[0], dcorr[1], dcorr[2], dcorr[3], dcorr[12] = ddc[1], ddc[2], ddc[3], ddc[4], ddc[0]
|
||||
for i := 0; i < fundCount; i++ {
|
||||
k := m.maxMult[i]
|
||||
if k == 0 {
|
||||
continue
|
||||
}
|
||||
rate[i] = dpoly(&m.args[i], t) + dcorr[i]
|
||||
sn, cs := math.Sincos(phase(&m.args[i], t, tLow) + corr[i])
|
||||
e := complex(cs, sn)
|
||||
p := s.pow[m.powOff[i]-k : m.powOff[i]+k+1]
|
||||
p[k] = 1
|
||||
for n := 1; n <= k; n++ {
|
||||
p[k+n] = cmul(p[k+n-1], e)
|
||||
p[k-n] = complex(real(p[k+n]), -imag(p[k+n]))
|
||||
}
|
||||
}
|
||||
// 热循环按 wantVel 拆开，纯位置路径不写 nodeRate
|
||||
node, factor := s.node, m.nodeFactor
|
||||
if wantVel {
|
||||
nr := s.nodeRate
|
||||
for n, parent := range m.nodeParent {
|
||||
fac := factor[n]
|
||||
f := s.pow[fac]
|
||||
r := m.slotMult[fac] * rate[m.slotFund[fac]]
|
||||
if parent >= 0 {
|
||||
f = cmul(node[parent], f)
|
||||
r += nr[parent]
|
||||
}
|
||||
node[n] = f
|
||||
nr[n] = r
|
||||
}
|
||||
} else {
|
||||
for n, parent := range m.nodeParent {
|
||||
f := s.pow[factor[n]]
|
||||
if parent >= 0 {
|
||||
f = cmul(node[parent], f)
|
||||
}
|
||||
node[n] = f
|
||||
}
|
||||
}
|
||||
env, denv := s.env[:m.maxEnv+1], s.denv[:m.maxEnv+1]
|
||||
legendreD(x, env, denv, wantVel)
|
||||
var v, dv [3]float64
|
||||
for c := 0; c < 3; c++ {
|
||||
co := &m.coords[c]
|
||||
sum := dot(co.secular, leg)
|
||||
dsum := 0.0
|
||||
if wantVel {
|
||||
dsum = dot(co.secular, dleg) * dxdt
|
||||
}
|
||||
f0 := co.flat0
|
||||
if wantVel {
|
||||
nr := s.nodeRate
|
||||
for j, n := range co.nodes0 {
|
||||
z := node[n]
|
||||
a, b := float64(f0[2*j]), float64(f0[2*j+1])
|
||||
sum += a*real(z) + b*imag(z)
|
||||
dsum += nr[n] * (b*real(z) - a*imag(z))
|
||||
}
|
||||
pos := 0
|
||||
for j, e := range co.envH {
|
||||
n := co.nodesH[j]
|
||||
z := node[n]
|
||||
var ac, as, dac, das float64
|
||||
for d := 0; d <= int(e); d++ {
|
||||
cc, cn := float64(co.coefH[pos]), float64(co.coefH[pos+1])
|
||||
ac += env[d] * cc
|
||||
as += env[d] * cn
|
||||
dac += denv[d] * cc
|
||||
das += denv[d] * cn
|
||||
pos += 2
|
||||
}
|
||||
sum += ac*real(z) + as*imag(z)
|
||||
dsum += dxdt*(dac*real(z)+das*imag(z)) + nr[n]*(as*real(z)-ac*imag(z))
|
||||
}
|
||||
} else {
|
||||
for j, n := range co.nodes0 {
|
||||
z := node[n]
|
||||
sum += float64(f0[2*j])*real(z) + float64(f0[2*j+1])*imag(z)
|
||||
}
|
||||
pos := 0
|
||||
for j, e := range co.envH {
|
||||
z := node[co.nodesH[j]]
|
||||
var ac, as float64
|
||||
for d := 0; d <= int(e); d++ {
|
||||
ac += env[d] * float64(co.coefH[pos])
|
||||
as += env[d] * float64(co.coefH[pos+1])
|
||||
pos += 2
|
||||
}
|
||||
sum += ac*real(z) + as*imag(z)
|
||||
}
|
||||
}
|
||||
v[c], dv[c] = sum, dsum
|
||||
}
|
||||
lon := v[0]*arcsec + phase(&m.lonPoly, t, tLow) + dc[0]
|
||||
lat := v[1] * arcsec
|
||||
rad := v[2]
|
||||
sl, cl := math.Sincos(lon)
|
||||
sb, cb := math.Sincos(lat)
|
||||
x0, y0, z0 := rad*cb*cl, rad*cb*sl, rad*sb
|
||||
p := poly(&m.p, t) * t
|
||||
q := poly(&m.q, t) * t
|
||||
ra := 2 * math.Sqrt(1-p*p-q*q)
|
||||
pos = [3]float64{
|
||||
(1-2*p*p)*x0 + 2*p*q*y0 + p*ra*z0,
|
||||
2*p*q*x0 + (1-2*q*q)*y0 - q*ra*z0,
|
||||
-p*ra*x0 + q*ra*y0 + (1-2*p*p-2*q*q)*z0,
|
||||
}
|
||||
if !wantVel {
|
||||
return pos, vel
|
||||
}
|
||||
dlon := dv[0]*arcsec + dpoly(&m.lonPoly, t) + ddc[0]
|
||||
dlat := dv[1] * arcsec
|
||||
drad := dv[2]
|
||||
// 球坐标 → 直角坐标的时间导数
|
||||
dx0 := drad*cb*cl - rad*sb*cl*dlat - rad*cb*sl*dlon
|
||||
dy0 := drad*cb*sl - rad*sb*sl*dlat + rad*cb*cl*dlon
|
||||
dz0 := drad*sb + rad*cb*dlat
|
||||
// 历元黄道 → J2000 旋转矩阵本身随 P、Q 变化
|
||||
dp := dpoly(&m.p, t)*t + poly(&m.p, t)
|
||||
dq := dpoly(&m.q, t)*t + poly(&m.q, t)
|
||||
dra := -4 * (p*dp + q*dq) / ra
|
||||
dpq := 2 * (dp*q + p*dq)
|
||||
vel = [3]float64{
|
||||
(1-2*p*p)*dx0 + 2*p*q*dy0 + p*ra*dz0 +
|
||||
-4*p*dp*x0 + dpq*y0 + (dp*ra+p*dra)*z0,
|
||||
2*p*q*dx0 + (1-2*q*q)*dy0 - q*ra*dz0 +
|
||||
dpq*x0 - 4*q*dq*y0 - (dq*ra+q*dra)*z0,
|
||||
-p*ra*dx0 + q*ra*dy0 + (1-2*p*p-2*q*q)*dz0 +
|
||||
-(dp*ra+p*dra)*x0 + (dq*ra+q*dra)*y0 - 4*(p*dp+q*dq)*z0,
|
||||
}
|
||||
for i := range vel {
|
||||
vel[i] /= century
|
||||
}
|
||||
return pos, vel
|
||||
}
|
||||
|
||||
// interleave 把按阶数分块（每阶先 cos 块后 sin 块）的系数重排为逐项 [d0cos,d0sin,d1cos,…]。
|
||||
func interleave(env []uint8, raw []float32) []float32 {
|
||||
out := make([]float32, len(raw))
|
||||
start := make([]int, len(env))
|
||||
for j := 1; j < len(env); j++ {
|
||||
start[j] = start[j-1] + 2*(int(env[j-1])+1)
|
||||
}
|
||||
pos := 0
|
||||
for d := 0; ; d++ {
|
||||
var idx []int
|
||||
for j, e := range env {
|
||||
if int(e) >= d {
|
||||
idx = append(idx, j)
|
||||
}
|
||||
}
|
||||
if len(idx) == 0 {
|
||||
break
|
||||
}
|
||||
for n, j := range idx {
|
||||
out[start[j]+2*d] = raw[pos+n]
|
||||
out[start[j]+2*d+1] = raw[pos+len(idx)+n]
|
||||
}
|
||||
pos += 2 * len(idx)
|
||||
}
|
||||
return out
|
||||
}
|
||||
@@ -0,0 +1,115 @@
|
||||
// 被测契约：内置表与参考向量一致（< 0.1 m），解析速度与差分一致，可并发求值。
|
||||
package lunar
|
||||
|
||||
import (
|
||||
"bufio"
|
||||
"math"
|
||||
"os"
|
||||
"strconv"
|
||||
"strings"
|
||||
"sync"
|
||||
"testing"
|
||||
)
|
||||
|
||||
func sq(x float64) float64 { return x * x }
|
||||
|
||||
func TestMatchesReferenceVectors(t *testing.T) { checkVectors(t, Default(), "testdata/vectors.csv") }
|
||||
|
||||
func TestFastMatchesReferenceVectors(t *testing.T) { checkVectors(t, Fast(), "testdata/fast.csv") }
|
||||
|
||||
func checkVectors(t *testing.T, m *Model, path string) {
|
||||
f, err := os.Open(path)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
defer f.Close()
|
||||
sc := bufio.NewScanner(f)
|
||||
n, worst := 0, 0.0
|
||||
for sc.Scan() {
|
||||
parts := strings.Split(sc.Text(), ",")
|
||||
var v [4]float64
|
||||
for i := range v {
|
||||
if v[i], err = strconv.ParseFloat(parts[i], 64); err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
}
|
||||
got := m.PositionJ2000(v[0])
|
||||
if d := math.Sqrt(sq(got[0]-v[1]) + sq(got[1]-v[2]) + sq(got[2]-v[3])); d > worst {
|
||||
worst = d
|
||||
}
|
||||
n++
|
||||
}
|
||||
if n < 40 {
|
||||
t.Fatalf("only %d vectors", n)
|
||||
}
|
||||
if worst > 1e-4 {
|
||||
t.Fatalf("max diff %.3e km over %d vectors", worst, n)
|
||||
}
|
||||
}
|
||||
|
||||
func TestVelocityMatchesFiniteDifference(t *testing.T) {
|
||||
m := Default()
|
||||
const h = 0.05
|
||||
worst := 0.0
|
||||
for _, jd := range []float64{990545.5, 1500000.25, 2299160.5, 2451545.0, 2460676.5, 2816787.5, 3912545.0} {
|
||||
p, v := m.PositionVelocityJ2000(jd)
|
||||
if q := m.PositionJ2000(jd); q != p {
|
||||
t.Fatalf("jd=%.1f position mismatch", jd)
|
||||
}
|
||||
a, b := m.PositionJ2000(jd+h), m.PositionJ2000(jd-h)
|
||||
a2, b2 := m.PositionJ2000(jd+2*h), m.PositionJ2000(jd-2*h)
|
||||
for i := range v {
|
||||
fd := (8*(a[i]-b[i]) - (a2[i] - b2[i])) / (12 * h)
|
||||
if d := math.Abs(fd - v[i]); d > worst {
|
||||
worst = d
|
||||
}
|
||||
}
|
||||
}
|
||||
if worst > 2e-3 {
|
||||
t.Fatalf("max velocity diff %.3e km/day", worst)
|
||||
}
|
||||
}
|
||||
|
||||
func TestParseRejectsTruncated(t *testing.T) {
|
||||
for _, n := range []int{0, 3, 5, 40, len(defaultTable) / 2, len(defaultTable) - 1} {
|
||||
if _, err := Parse(defaultTable[:n]); err == nil {
|
||||
t.Errorf("len %d: expected error", n)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestConcurrentEvaluation(t *testing.T) {
|
||||
m := Default()
|
||||
const n = 64
|
||||
var want [n][3]float64
|
||||
for i := range want {
|
||||
want[i] = m.PositionJ2000(2451545.0 + float64(i)*13.7)
|
||||
}
|
||||
var wg sync.WaitGroup
|
||||
var bad [8]bool
|
||||
for g := 0; g < 8; g++ {
|
||||
wg.Add(1)
|
||||
go func(g int) {
|
||||
defer wg.Done()
|
||||
for k := 0; k < n; k++ {
|
||||
i := (k + g*7) % n
|
||||
if m.PositionJ2000(2451545.0+float64(i)*13.7) != want[i] {
|
||||
bad[g] = true
|
||||
}
|
||||
}
|
||||
}(g)
|
||||
}
|
||||
wg.Wait()
|
||||
for g, b := range bad {
|
||||
if b {
|
||||
t.Fatalf("goroutine %d saw a mismatch", g)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkPositionJ2000(b *testing.B) {
|
||||
m := Default()
|
||||
for i := 0; i < b.N; i++ {
|
||||
_ = m.PositionJ2000(2460000.5 + float64(i%10000)*0.37)
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,51 @@
|
||||
-1931455,-263046.57528520969,297684.18718319025,-24345.864066160168
|
||||
-1785355,24378.534686367391,-400825.36392118747,-44672.568525917093
|
||||
-1639255,221175.99144970218,325206.96587989992,-14472.844556519216
|
||||
-1493155,-319978.52720147866,-179819.4818149425,-7729.6582925465245
|
||||
-1347055,362622.46972198499,20286.814075592443,4137.3575503146285
|
||||
-1200955,-346235.18691354321,185914.73322113504,30174.27456151383
|
||||
-1054855,171052.68131930399,-366289.65810158779,26232.886379638556
|
||||
-908755,98623.637690714822,376297.77810421737,40802.587272379009
|
||||
-762655,-253665.11515733672,-272838.23852057324,19911.166048921259
|
||||
-616555,335485.16883375292,146456.59956479297,14870.504114287725
|
||||
-470455,-383645.40573639271,65997.21790989369,-826.92611041679697
|
||||
-324355,276927.4702533714,-295829.19680496032,-30322.013752343068
|
||||
-178255,-26435.785915690412,386079.73800098576,-28015.326875332928
|
||||
-32155,-173562.98376470321,-327340.8539868113,-37468.408479997677
|
||||
113945,284098.82846766489,239256.46597111417,-25343.748850755001
|
||||
260045,-385157.83176014025,-49369.527013191553,-15281.761574469898
|
||||
406145,345160.97807879257,-214636.8383361497,3414.5771813550259
|
||||
552245,-134108.10483846199,361980.9990905014,29968.389469456466
|
||||
698345,-83984.239959958926,-355799.14247223095,28817.078112816904
|
||||
844445,223226.00566205085,299354.17357796693,36909.979945451472
|
||||
990545,-362607.45994305814,-147502.75304507115,28081.953043893249
|
||||
1136645,383606.60880971845,-132531.90493783797,8832.002235690501
|
||||
1282745,-216360.67463345666,321769.59784516064,-8957.0037364521304
|
||||
1428845,7433.8731166889338,-359577.9208704764,-27286.722728085369
|
||||
1574945,157042.40898349817,338967.54339773324,-30844.406074648126
|
||||
1721045,-328371.10510008538,-221529.93877308263,-36739.865212875557
|
||||
1867145,400234.08615918033,-57984.149689135251,-23513.254374541601
|
||||
2013245,-274021.09564645251,273929.27390877635,-2133.8352285152291
|
||||
2159345,92791.766991493409,-345234.67832922813,12342.071461675338
|
||||
2305445,88338.286030037401,363169.93015197461,26462.650120618968
|
||||
2451545,-291607.24183591013,-274978.62186731066,36267.30787189916
|
||||
2597645,401391.47803711233,3266.8554273079903,31443.354743021413
|
||||
2743745,-312245.28483573761,223268.80530781401,14449.195688692611
|
||||
2889845,167261.68852763134,-317547.01628260425,854.67113282198795
|
||||
3035945,22710.051466743793,377536.27831278293,-18254.778814458063
|
||||
3182045,-258568.79979545044,-310953.08002426871,-31511.794215090176
|
||||
3328145,391597.73715416581,50492.738155701489,-35663.250569429547
|
||||
3474245,-336640.78667349386,169381.01759883287,-24138.799220522917
|
||||
3620345,229894.62683911348,-283245.2596621954,-10124.478719948
|
||||
3766445,-30725.076385326527,386554.31412064168,4630.937622600225
|
||||
3912545,-232347.00044598628,-331529.30967142241,31692.736681196671
|
||||
4058645,373153.27734119527,88709.654120304229,33189.966274715975
|
||||
4204745,-352665.5780016224,110675.94346091514,29168.298060724752
|
||||
4350845,279862.12418001605,-250761.84026383076,22491.093918623097
|
||||
4496945,-63300.801294757643,393827.49900787073,-4549.380602734378
|
||||
4643045,-211639.87281130059,-339806.65624159103,-18216.154066961921
|
||||
4789145,345869.06789046078,125142.00856319141,-35847.90651925862
|
||||
4935245,-365917.02341126435,47072.64876266574,-31135.795917215175
|
||||
5081345,313235.01489341311,-233557.38203767358,-25005.730334995031
|
||||
5227445,-71563.036314018507,398823.35837659024,-9633.2749911986139
|
||||
5373545,-186164.91514019907,-338423.50248531549,24637.566759055353
|
||||
|
@@ -0,0 +1,51 @@
|
||||
-1931455,-263012.14372776932,297721.55430688168,-24324.987254599062
|
||||
-1785355,24414.613429926769,-400822.30277713871,-44670.197726442522
|
||||
-1639255,221200.37674641001,325184.92725227826,-14474.943560636351
|
||||
-1493155,-319973.35559277143,-179836.67922932078,-7722.0931910639329
|
||||
-1347055,362620.6275818554,20261.340424064758,4158.7475902214901
|
||||
-1200955,-346245.11238489667,185898.25815803016,30163.905893696552
|
||||
-1054855,171029.90424524632,-366296.60906562442,26231.502494924491
|
||||
-908755,98585.018472548079,376301.83738717507,40804.120474682692
|
||||
-762655,-253673.35964539216,-272828.69776402361,19905.706493336733
|
||||
-616555,335481.25258198346,146459.68939852307,14858.106694331284
|
||||
-470455,-383647.05975822004,66013.008896738858,-829.53397079068804
|
||||
-324355,276926.62049089983,-295829.60577838111,-30320.482347503283
|
||||
-178255,-26445.54739251201,386080.83489992673,-28013.881581822534
|
||||
-32155,-173564.14468521808,-327344.00872558804,-37468.46077107366
|
||||
113945,284090.35252503335,239265.58618684916,-25343.650846110519
|
||||
260045,-385159.51631046517,-49348.816915762458,-15277.391684530896
|
||||
406145,345165.46504725312,-214639.96530993938,3409.4271382105871
|
||||
552245,-134100.72888107621,361985.48449367564,29978.850367708317
|
||||
698345,-83982.342926013938,-355811.46501246258,28808.215852912752
|
||||
844445,223235.08660139333,299351.08166803332,36915.189665281585
|
||||
990545,-362602.7882248871,-147511.51703076772,28082.07356267815
|
||||
1136645,383604.91929247783,-132547.95810837013,8838.4387429826493
|
||||
1282745,-216364.57090490102,321764.38059364131,-8961.5757619206961
|
||||
1428845,7411.8790805348717,-359585.32555476134,-27293.192427568905
|
||||
1574945,157039.98810843128,338969.64958912093,-30843.917066599242
|
||||
1721045,-328370.6008870838,-221528.04782516821,-36744.16639076647
|
||||
1867145,400234.16277750907,-57976.122899650822,-23521.520092170747
|
||||
2013245,-274016.4330496171,273934.67297238286,-2129.3720209763578
|
||||
2159345,92794.113822126208,-345233.42375816189,12336.461166121979
|
||||
2305445,88335.023380869083,363166.75449031434,26461.650624866372
|
||||
2451545,-291608.37627978966,-274979.69324404577,36271.128877822775
|
||||
2597645,401391.20135964605,3263.1459841862388,31451.825037924391
|
||||
2743745,-312251.31017224718,223260.77557797215,14444.457253400202
|
||||
2889845,167249.48724887962,-317556.36523747904,861.57897404768664
|
||||
3035945,22695.663788870559,377539.04920572782,-18246.340165569305
|
||||
3182045,-258575.29689052334,-310947.48117673211,-31511.022415741383
|
||||
3328145,391596.12233842851,50493.68541584225,-35666.970403817082
|
||||
3474245,-336640.9610806547,169391.52518719292,-24128.503619066782
|
||||
3620345,229900.52348247898,-283241.08259236073,-10118.936107852864
|
||||
3766445,-30703.555025148959,386554.4143357625,4624.3092540068592
|
||||
3912545,-232340.39127966101,-331532.73305540072,31692.97586258821
|
||||
4058645,373158.78561370028,88690.555206671619,33189.3675445954
|
||||
4204745,-352676.95412928553,110654.5265917302,29168.430885959289
|
||||
4350845,279850.74386479775,-250759.61582796593,22465.457479309545
|
||||
4496945,-63304.248176228684,393828.06630098209,-4545.7108401102751
|
||||
4643045,-211635.86742416851,-339798.65198398969,-18217.631416908665
|
||||
4789145,345881.5840039468,125117.11976231023,-35854.923632790691
|
||||
4935245,-365925.61155116902,47053.327116662622,-31140.397995070532
|
||||
5081345,313238.78055125696,-233551.4275320005,-25002.984985012321
|
||||
5227445,-71571.816487501972,398827.95987496921,-9638.4140099458273
|
||||
5373545,-186177.32558991387,-338413.93355647428,24655.523094058852
|
||||
|
@@ -0,0 +1,154 @@
|
||||
package semianalytic
|
||||
|
||||
import (
|
||||
"math"
|
||||
"sync"
|
||||
|
||||
"b612.me/astro/internal/ltp"
|
||||
"b612.me/astro/planet/internal/semianalytic/lunar"
|
||||
"b612.me/astro/planet/internal/semianalytic/planets"
|
||||
"b612.me/astro/tools"
|
||||
)
|
||||
|
||||
const (
|
||||
auKM = 149597870.7
|
||||
earthSlot = 0
|
||||
moonSlot = 8
|
||||
fastBase = 9
|
||||
)
|
||||
|
||||
var sinEps0, cosEps0 = math.Sincos(eps0)
|
||||
|
||||
// xt 1..7 对应的表内天体号。
|
||||
var bodyID = [8]int{0, planets.Mercury, planets.Venus, planets.Mars, planets.Jupiter, planets.Saturn, planets.Uranus, planets.Neptune}
|
||||
|
||||
type lbr struct{ jd, l, b, r float64 }
|
||||
|
||||
type lbrSlot struct {
|
||||
v lbr
|
||||
set bool
|
||||
}
|
||||
|
||||
// L、B、R 通常在同一时刻连续取用，每个天体每档缓存最近一次的结果；0..8 全表，9..17 快速档。
|
||||
var (
|
||||
cacheMu sync.RWMutex
|
||||
cache [18]lbrSlot
|
||||
)
|
||||
|
||||
// tier n < 0 用全表，n ≥ 0 用快速档；新模型的快速档不随 n 细分。
|
||||
func tier(n int) (*planets.Model, *lunar.Model, int) {
|
||||
if n < 0 {
|
||||
return planets.Default(), lunar.Default(), 0
|
||||
}
|
||||
return planets.Fast(), lunar.Fast(), fastBase
|
||||
}
|
||||
|
||||
func cached(slot int, jd float64) (lbr, bool) {
|
||||
cacheMu.RLock()
|
||||
c := cache[slot]
|
||||
cacheMu.RUnlock()
|
||||
if c.set && c.v.jd == jd {
|
||||
return c.v, true
|
||||
}
|
||||
return lbr{}, false
|
||||
}
|
||||
|
||||
func store(slot int, jd float64, v [3]float64) lbr {
|
||||
l, b, r := ofDate(v, jd)
|
||||
c := lbr{jd, l, b, r}
|
||||
cacheMu.Lock()
|
||||
cache[slot] = lbrSlot{v: c, set: true}
|
||||
cacheMu.Unlock()
|
||||
return c
|
||||
}
|
||||
|
||||
type moonVec struct {
|
||||
jd float64
|
||||
p [3]float64
|
||||
set bool
|
||||
}
|
||||
|
||||
// 地球合成与月球本身在同一时刻都要月球向量，按档缓存最近一次。
|
||||
var (
|
||||
moonVecMu sync.RWMutex
|
||||
moonVecCache [2]moonVec
|
||||
)
|
||||
|
||||
func moonJ2000(lm *lunar.Model, slot int, jde float64) [3]float64 {
|
||||
moonVecMu.RLock()
|
||||
c := moonVecCache[slot]
|
||||
moonVecMu.RUnlock()
|
||||
if c.set && c.jd == jde {
|
||||
return c.p
|
||||
}
|
||||
p := lm.PositionJ2000(jde)
|
||||
moonVecMu.Lock()
|
||||
moonVecCache[slot] = moonVec{jd: jde, p: p, set: true}
|
||||
moonVecMu.Unlock()
|
||||
return p
|
||||
}
|
||||
|
||||
// ofDate J2000 平黄道向量 → 历元平黄道经纬（弧度，经度在 [0, 2π)）与模长。
|
||||
func ofDate(v [3]float64, jde float64) (l, b, r float64) {
|
||||
q0, q1, q2 := v[0], v[1]*cosEps0-v[2]*sinEps0, v[1]*sinEps0+v[2]*cosEps0
|
||||
x, y, z := ltp.EclipticBasis(2000 + (jde-2451545)/365.25)
|
||||
ex := x[0]*q0 + x[1]*q1 + x[2]*q2
|
||||
ey := y[0]*q0 + y[1]*q1 + y[2]*q2
|
||||
ez := z[0]*q0 + z[1]*q1 + z[2]*q2
|
||||
l = math.Atan2(ey, ex)
|
||||
if l < 0 {
|
||||
l += 2 * math.Pi
|
||||
}
|
||||
return l, math.Atan2(ez, math.Hypot(ex, ey)), math.Sqrt(ex*ex + ey*ey + ez*ez)
|
||||
}
|
||||
|
||||
// Planet 与 planet.WherePlanetN 同语义（xt 取 -1..7，zn 取 0..2），调用方负责越界检查 / same contract as planet.WherePlanetN.
|
||||
func Planet(xt, zn int, jde float64, n int) float64 {
|
||||
pm, lm, base := tier(n)
|
||||
slot := base + earthSlot
|
||||
if xt > 0 {
|
||||
slot = base + xt
|
||||
}
|
||||
c, ok := cached(slot, jde)
|
||||
if !ok {
|
||||
var p [3]float64
|
||||
if xt <= 0 {
|
||||
emb, _ := pm.Heliocentric(planets.EMB, jde)
|
||||
p = planets.EarthFromEMB(emb, moonJ2000(lm, base/fastBase, jde))
|
||||
} else {
|
||||
p, _ = pm.Heliocentric(bodyID[xt], jde)
|
||||
}
|
||||
c = store(slot, jde, p)
|
||||
}
|
||||
switch zn {
|
||||
case 0:
|
||||
l := c.l * 180 / math.Pi
|
||||
if xt == 0 {
|
||||
l += 180
|
||||
}
|
||||
return tools.Limit360(l)
|
||||
case 1:
|
||||
if xt == 0 {
|
||||
return -c.b * 180 / math.Pi
|
||||
}
|
||||
return c.b * 180 / math.Pi
|
||||
}
|
||||
return c.r / auKM
|
||||
}
|
||||
|
||||
// Moon 地心月球历元平黄道：coord 0 黄经、1 黄纬（弧度）、2 距离（km），n ≥ 0 用快速档，调用方负责越界检查 / geocentric Moon of date.
|
||||
func Moon(coord int, jde float64, n int) float64 {
|
||||
_, lm, base := tier(n)
|
||||
slot := base + moonSlot
|
||||
c, ok := cached(slot, jde)
|
||||
if !ok {
|
||||
c = store(slot, jde, moonJ2000(lm, base/fastBase, jde))
|
||||
}
|
||||
switch coord {
|
||||
case 0:
|
||||
return c.l
|
||||
case 1:
|
||||
return c.b
|
||||
}
|
||||
return c.r
|
||||
}
|
||||
@@ -0,0 +1,67 @@
|
||||
package planets
|
||||
|
||||
import (
|
||||
_ "embed"
|
||||
"sync"
|
||||
)
|
||||
|
||||
// 现代段为 J2000 ± 1000 儒略年。
|
||||
const (
|
||||
ModernStart = 2086295.0
|
||||
ModernEnd = 2816795.0
|
||||
)
|
||||
|
||||
var (
|
||||
//go:embed long.bin
|
||||
longTable []byte
|
||||
//go:embed modern.bin
|
||||
modernTable []byte
|
||||
)
|
||||
|
||||
var (
|
||||
defaultOnce sync.Once
|
||||
defaultModel *Model
|
||||
)
|
||||
|
||||
// Default 内置长时段表叠加现代段，首次调用时解析 / built-in long-range plus modern tables, parsed on first use.
|
||||
func Default() *Model {
|
||||
defaultOnce.Do(func() {
|
||||
m, err := Parse(longTable)
|
||||
if err == nil {
|
||||
err = m.WithModernSegment(modernTable, ModernStart, ModernEnd)
|
||||
}
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
defaultModel = m
|
||||
})
|
||||
return defaultModel
|
||||
}
|
||||
|
||||
// GM 天体号 1..8 的 GM 与太阳 GM，au³/日²；EMB 为地月合计，越界返回 0 / GM of body id and of the Sun, au³/day².
|
||||
func GM(id int) (body, sun float64) {
|
||||
if id < 1 || id > 8 {
|
||||
return 0, gmSol
|
||||
}
|
||||
return gmp[id-1], gmSol
|
||||
}
|
||||
|
||||
//go:embed fast.bin
|
||||
var fastTable []byte
|
||||
|
||||
var (
|
||||
fastOnce sync.Once
|
||||
fastModel *Model
|
||||
)
|
||||
|
||||
// Fast 快速档表（n ≥ 0 用），首次调用时解析 / the fast-tier table used for n ≥ 0, parsed on first use.
|
||||
func Fast() *Model {
|
||||
fastOnce.Do(func() {
|
||||
m, err := Parse(fastTable)
|
||||
if err != nil {
|
||||
panic(err)
|
||||
}
|
||||
fastModel = m
|
||||
})
|
||||
return fastModel
|
||||
}
|
||||
Binary file not shown.
Binary file not shown.
Binary file not shown.
@@ -0,0 +1,610 @@
|
||||
// Package planets 行星半解析级数运行时（PLN1/PLN2/PLN3 表，日心，J2000 平黄道）。
|
||||
package planets
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"errors"
|
||||
"math"
|
||||
"sync"
|
||||
)
|
||||
|
||||
const (
|
||||
j2000 = 2451545.0
|
||||
millennium = 365250.0
|
||||
blendDays = 36525.0
|
||||
auKM = 149597870.691
|
||||
tMid = -2.0
|
||||
tHalf = 10.0
|
||||
emrat = 81.3005682214972
|
||||
gmSol = 2.9591220836841438269e-04
|
||||
maxDeg = 24
|
||||
)
|
||||
|
||||
// Body 编号 / body id；3 为地月质心。
|
||||
const (
|
||||
Mercury = 1
|
||||
Venus = 2
|
||||
EMB = 3
|
||||
Mars = 4
|
||||
Jupiter = 5
|
||||
Saturn = 6
|
||||
Uranus = 7
|
||||
Neptune = 8
|
||||
)
|
||||
|
||||
var ci0 = [17]float64{4.402608631669, 3.176134461576, 1.753470369433, 6.203500014141, 4.091360003050,
|
||||
1.713740719173, 5.598641292287, 2.805136360408, 2.326989734620, 0.5995461070350,
|
||||
0.8740185101070, 5.481225395663, 5.311897933164, 0.0, 5.19846640063,
|
||||
1.62790513602, 2.35555563875}
|
||||
|
||||
var ci1 = [17]float64{26087.90314068555, 10213.28554743445, 6283.075850353215, 3340.612434145457,
|
||||
1731.170452721855, 1704.450855027201, 1428.948917844273, 1364.756513629990,
|
||||
1361.923207632842, 529.6909615623250, 213.2990861084880, 74.78165903077800,
|
||||
38.13297222612500, 0.3595362285049309, 77713.7714481804, 84334.6615717837,
|
||||
83286.9142477147}
|
||||
|
||||
var gmp = [8]float64{4.9125474514508118699e-11, 7.2434524861627027000e-10, 8.9970116036316091182e-10,
|
||||
9.5495351057792580598e-11, 2.8253458420837780000e-07, 8.4597151856806587398e-08,
|
||||
1.2920249167819693900e-08, 1.5243589007842762800e-08}
|
||||
|
||||
// topDMu 必须逐步按 float64 舍入（与 Python 参考求值一致），不能写成常量表达式。
|
||||
var topDMu = func() float64 {
|
||||
f0, f1, d := 529.6909622785881, 213.2990811942489, 880.0
|
||||
return (f0 - f1) / d
|
||||
}()
|
||||
|
||||
// skyToVSOP skyfield ecliptic_J2000 → VSOP2013 动力学黄道；求值时用其转置。
|
||||
var skyToVSOP = func() [3][3]float64 {
|
||||
as := 180 / math.Pi * 3600
|
||||
return mul(transpose(mul(rz(-0.05188/as), rx(84381.41136/as))), rx(84381.448/as))
|
||||
}()
|
||||
|
||||
// element 的项按包络阶降序排列，第 d 阶只覆盖前 cnt[d] 项。
|
||||
type element struct {
|
||||
secular []float64
|
||||
arg []int32
|
||||
cnt []int
|
||||
c, s [][]float64
|
||||
}
|
||||
|
||||
const (
|
||||
maxKeys = 8192
|
||||
maxTab = 512
|
||||
topBits = 6
|
||||
// 超出此值的幅角乘数必然撑破幂表，先在 int64 下拒绝，保证转 int 不溢出。
|
||||
maxKeyAbs = maxTab << (2 * topBits)
|
||||
)
|
||||
|
||||
var errBadKey = errors.New("planets: argument multiplier out of range")
|
||||
|
||||
// factor 幂表槽位；neg 表示取共轭。
|
||||
type factor struct {
|
||||
slot int32
|
||||
neg bool
|
||||
}
|
||||
|
||||
type body struct {
|
||||
top bool
|
||||
f, l0 float64
|
||||
rgm float64
|
||||
// 幂表：VSOP 每个基本幅角一段，TOP 每个 6 位数字层一段
|
||||
tabMax [17]int
|
||||
tabOff [17]int
|
||||
keyOff []int32
|
||||
factors []factor
|
||||
keyNeg []bool
|
||||
el [6]element
|
||||
// legDeg 长期项与包络用到的最高 Legendre 阶。
|
||||
legDeg int
|
||||
}
|
||||
|
||||
// Model 已解析的 PLN1 表，只读、可并发求值 / parsed PLN1 table, safe for concurrent use.
|
||||
type Model struct {
|
||||
bodies [9]*body
|
||||
modernBodies [9]*body
|
||||
modernStart float64
|
||||
modernEnd float64
|
||||
}
|
||||
|
||||
type reader struct {
|
||||
b []byte
|
||||
p int
|
||||
err error
|
||||
}
|
||||
|
||||
func (r *reader) take(n int) []byte {
|
||||
if r.err != nil || r.p+n > len(r.b) {
|
||||
r.err = errors.New("planets: truncated table")
|
||||
return make([]byte, n)
|
||||
}
|
||||
s := r.b[r.p : r.p+n]
|
||||
r.p += n
|
||||
return s
|
||||
}
|
||||
|
||||
func (r *reader) u8() uint8 { return r.take(1)[0] }
|
||||
func (r *reader) f64() float64 { return math.Float64frombits(binary.LittleEndian.Uint64(r.take(8))) }
|
||||
func (r *reader) f32() float32 { return math.Float32frombits(binary.LittleEndian.Uint32(r.take(4))) }
|
||||
|
||||
func (r *reader) uvar() uint64 {
|
||||
n, shift := uint64(0), uint(0)
|
||||
for {
|
||||
c := r.u8()
|
||||
n |= uint64(c&0x7F) << shift
|
||||
shift += 7
|
||||
if c < 0x80 || r.err != nil || shift > 56 {
|
||||
return n
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func (r *reader) zvar() int64 {
|
||||
z := r.uvar()
|
||||
if z%2 == 0 {
|
||||
return int64(z >> 1)
|
||||
}
|
||||
return -int64(z>>1) - 1
|
||||
}
|
||||
|
||||
// Parse 解析 PLN1 表 / parse a PLN1 table.
|
||||
func Parse(b []byte) (*Model, error) {
|
||||
bodies, err := parseBodies(b)
|
||||
if err != nil {
|
||||
return nil, err
|
||||
}
|
||||
return &Model{bodies: bodies}, nil
|
||||
}
|
||||
|
||||
// WithModernSegment 为长时段表叠加现代段表，[jdStart, jdEnd] 内优先使用 / add a modern-era segment used inside [jdStart, jdEnd].
|
||||
func (m *Model) WithModernSegment(b []byte, jdStart, jdEnd float64) error {
|
||||
bodies, err := parseBodies(b)
|
||||
if err != nil {
|
||||
return err
|
||||
}
|
||||
m.modernBodies, m.modernStart, m.modernEnd = bodies, jdStart, jdEnd
|
||||
return nil
|
||||
}
|
||||
|
||||
func parseBodies(b []byte) (bodies [9]*body, err error) {
|
||||
r := &reader{b: b}
|
||||
magic := string(r.take(4))
|
||||
if magic != "PLN1" && magic != "PLN2" && magic != "PLN3" {
|
||||
return bodies, errors.New("planets: bad magic")
|
||||
}
|
||||
quant, packed := magic == "PLN2", magic == "PLN3"
|
||||
for n := int(r.u8()); n > 0 && r.err == nil; n-- {
|
||||
id := int(r.u8())
|
||||
if id < 1 || id > 8 {
|
||||
return bodies, errors.New("planets: bad body id")
|
||||
}
|
||||
bd := &body{top: r.u8() != 0}
|
||||
secDeg := int(r.u8())
|
||||
bd.f, bd.l0 = r.f64(), r.f64()
|
||||
bd.rgm = math.Sqrt(gmp[id-1] + gmSol)
|
||||
nk := r.uvar()
|
||||
if nk > maxKeys {
|
||||
return bodies, errors.New("planets: too many arguments")
|
||||
}
|
||||
if err := readKeys(r, bd, int(nk)); err != nil {
|
||||
return bodies, err
|
||||
}
|
||||
bd.legDeg = secDeg
|
||||
sortedArgs := packed && r.u8() != 0
|
||||
for v := range bd.el {
|
||||
var err error
|
||||
if packed {
|
||||
err = readElement3(r, &bd.el[v], secDeg, int(nk), sortedArgs)
|
||||
} else {
|
||||
err = readElement(r, &bd.el[v], secDeg, int(nk), quant)
|
||||
}
|
||||
if err != nil {
|
||||
return bodies, err
|
||||
}
|
||||
if d := len(bd.el[v].cnt) - 1; d > bd.legDeg {
|
||||
bd.legDeg = d
|
||||
}
|
||||
}
|
||||
bodies[id] = bd
|
||||
}
|
||||
if r.err != nil {
|
||||
return bodies, r.err
|
||||
}
|
||||
if r.p != len(b) {
|
||||
return bodies, errors.New("planets: trailing bytes")
|
||||
}
|
||||
return bodies, nil
|
||||
}
|
||||
|
||||
// readKeys 把整数幅角拆成幂表槽位：VSOP 按基本幅角升序，TOP 按 6 位数字层由低到高。
|
||||
func readKeys(r *reader, bd *body, nk int) error {
|
||||
type raw struct{ fund, k int }
|
||||
keys := make([][]raw, nk)
|
||||
bd.keyNeg = make([]bool, nk)
|
||||
for j := 0; j < nk && r.err == nil; j++ {
|
||||
if bd.top {
|
||||
k := r.zvar()
|
||||
if k > maxKeyAbs || k < -maxKeyAbs {
|
||||
return errBadKey
|
||||
}
|
||||
a := int(k)
|
||||
if a < 0 {
|
||||
a, bd.keyNeg[j] = -a, true
|
||||
}
|
||||
for lvl := 0; lvl < 3; lvl++ {
|
||||
d := a >> uint(topBits*lvl)
|
||||
if lvl < 2 {
|
||||
d &= 1<<topBits - 1
|
||||
}
|
||||
keys[j] = append(keys[j], raw{lvl, d})
|
||||
}
|
||||
continue
|
||||
}
|
||||
mb := r.take(3)
|
||||
mask := int(mb[0]) | int(mb[1])<<8 | int(mb[2])<<16
|
||||
for i := 0; i < 17; i++ {
|
||||
if mask>>uint(i)&1 != 0 {
|
||||
k := r.zvar()
|
||||
if k > maxKeyAbs || k < -maxKeyAbs {
|
||||
return errBadKey
|
||||
}
|
||||
keys[j] = append(keys[j], raw{i, int(k)})
|
||||
}
|
||||
}
|
||||
}
|
||||
if r.err != nil {
|
||||
return r.err
|
||||
}
|
||||
for _, ks := range keys {
|
||||
for _, f := range ks {
|
||||
a := f.k
|
||||
if a < 0 {
|
||||
a = -a
|
||||
}
|
||||
if a > bd.tabMax[f.fund] {
|
||||
bd.tabMax[f.fund] = a
|
||||
}
|
||||
}
|
||||
}
|
||||
n := 0
|
||||
for i := range bd.tabMax {
|
||||
bd.tabOff[i] = n
|
||||
if bd.tabMax[i] > 0 || (bd.top && i < 3) {
|
||||
n += bd.tabMax[i] + 1
|
||||
}
|
||||
}
|
||||
if n > maxTab {
|
||||
return errors.New("planets: power table too large")
|
||||
}
|
||||
bd.keyOff = make([]int32, nk+1)
|
||||
for j, ks := range keys {
|
||||
for _, f := range ks {
|
||||
a, neg := f.k, false
|
||||
if a < 0 {
|
||||
a, neg = -a, true
|
||||
}
|
||||
if !bd.top && a == 0 {
|
||||
continue
|
||||
}
|
||||
bd.factors = append(bd.factors, factor{int32(bd.tabOff[f.fund] + a), neg})
|
||||
}
|
||||
bd.keyOff[j+1] = int32(len(bd.factors))
|
||||
}
|
||||
return nil
|
||||
}
|
||||
|
||||
// readElement 把文件里按包络阶分块的列序重排为逐项连续；quant 为 PLN2 整数量化系数。
|
||||
func readElement(r *reader, e *element, secDeg, nk int, quant bool) error {
|
||||
if secDeg > maxDeg {
|
||||
return errors.New("planets: secular degree too high")
|
||||
}
|
||||
n64 := r.uvar()
|
||||
if n64 > uint64(nk) {
|
||||
return errors.New("planets: too many terms")
|
||||
}
|
||||
nint := int(n64)
|
||||
e.secular = make([]float64, secDeg+1)
|
||||
for i := range e.secular {
|
||||
e.secular[i] = r.f64()
|
||||
}
|
||||
args, env := make([]int32, nint), make([]int, nint)
|
||||
top := 0
|
||||
for j := 0; j < nint; j++ {
|
||||
a := r.uvar()
|
||||
if a >= uint64(nk) {
|
||||
return errors.New("planets: argument index out of range")
|
||||
}
|
||||
args[j], env[j] = int32(a), int(r.u8())
|
||||
if env[j] > maxDeg {
|
||||
return errors.New("planets: envelope degree too high")
|
||||
}
|
||||
if env[j] > top {
|
||||
top = env[j]
|
||||
}
|
||||
}
|
||||
// 按包络阶降序的稳定排序：pos[j] 为文件第 j 项的新位置
|
||||
pos := make([]int, nint)
|
||||
e.arg = make([]int32, nint)
|
||||
k := 0
|
||||
for d := top; d >= 0; d-- {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] == d {
|
||||
pos[j], e.arg[k] = k, args[j]
|
||||
k++
|
||||
}
|
||||
}
|
||||
}
|
||||
coef := func() float64 { return float64(r.f32()) }
|
||||
if quant {
|
||||
step := r.f64()
|
||||
coef = func() float64 { return float64(r.zvar()) * step }
|
||||
}
|
||||
if nint == 0 {
|
||||
return r.err
|
||||
}
|
||||
e.cnt = make([]int, top+1)
|
||||
e.c, e.s = make([][]float64, top+1), make([][]float64, top+1)
|
||||
for d := 0; d <= top; d++ {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] >= d {
|
||||
e.cnt[d]++
|
||||
}
|
||||
}
|
||||
e.c[d], e.s[d] = make([]float64, e.cnt[d]), make([]float64, e.cnt[d])
|
||||
for _, dst := range [][]float64{e.c[d], e.s[d]} {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] >= d {
|
||||
dst[pos[j]] = coef()
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
return r.err
|
||||
}
|
||||
|
||||
// Heliocentric 日心位置，km，J2000 平黄道 / heliocentric position, km, mean ecliptic J2000.
|
||||
func (m *Model) Heliocentric(id int, jdTDB float64) ([3]float64, error) {
|
||||
pos, _, err := m.state(id, jdTDB, false)
|
||||
return pos, err
|
||||
}
|
||||
|
||||
// HeliocentricState 日心位置（km）与密切速度（km/日），J2000 平黄道 / heliocentric position and osculating velocity.
|
||||
func (m *Model) HeliocentricState(id int, jdTDB float64) (pos, vel [3]float64, err error) {
|
||||
return m.state(id, jdTDB, true)
|
||||
}
|
||||
|
||||
// state wantVel 为 false 时 vel 不计算、恒为零。
|
||||
func (m *Model) state(id int, jdTDB float64, wantVel bool) (pos, vel [3]float64, err error) {
|
||||
if id < 1 || id > 8 {
|
||||
return pos, vel, errors.New("planets: body not in table")
|
||||
}
|
||||
bd := m.bodies[id]
|
||||
if bd == nil {
|
||||
return pos, vel, errors.New("planets: body not in table")
|
||||
}
|
||||
t := (jdTDB - j2000) / millennium
|
||||
md := m.modernBodies[id]
|
||||
sky := func(p, v [3]float64) ([3]float64, [3]float64, error) {
|
||||
if !wantVel {
|
||||
return toSky(p), v, nil
|
||||
}
|
||||
return toSky(p), toSky(v), nil
|
||||
}
|
||||
if md == nil || jdTDB <= m.modernStart || jdTDB >= m.modernEnd {
|
||||
p, v := bd.ellxyz(bd.elements(t), wantVel)
|
||||
return sky(p, v)
|
||||
}
|
||||
w, dw := m.modernWeight(jdTDB)
|
||||
pm, vm := md.ellxyz(md.elements(t), wantVel)
|
||||
if w == 1 {
|
||||
return sky(pm, vm)
|
||||
}
|
||||
pl, vl := bd.ellxyz(bd.elements(t), wantVel)
|
||||
for i := range pos {
|
||||
pos[i] = pl[i] + w*(pm[i]-pl[i])
|
||||
if wantVel {
|
||||
vel[i] = vl[i] + w*(vm[i]-vl[i]) + dw*(pm[i]-pl[i])
|
||||
}
|
||||
}
|
||||
return sky(pos, vel)
|
||||
}
|
||||
|
||||
// modernWeight 现代段权重及其对 JD 的导数；两端各 blendDays 内用 smoothstep 过渡，位置与速度均连续。
|
||||
func (m *Model) modernWeight(jd float64) (w, dw float64) {
|
||||
u, sign := (jd-m.modernStart)/blendDays, 1.0
|
||||
if e := (m.modernEnd - jd) / blendDays; e < u {
|
||||
u, sign = e, -1
|
||||
}
|
||||
if u >= 1 {
|
||||
return 1, 0
|
||||
}
|
||||
return u * u * (3 - 2*u), sign * 6 * u * (1 - u) / blendDays
|
||||
}
|
||||
|
||||
// toSky 动力学黄道 au → skyfield ecliptic_J2000 km。
|
||||
func toSky(p [3]float64) (out [3]float64) {
|
||||
for i := range out {
|
||||
out[i] = (skyToVSOP[0][i]*p[0] + skyToVSOP[1][i]*p[1] + skyToVSOP[2][i]*p[2]) * auKM
|
||||
}
|
||||
return out
|
||||
}
|
||||
|
||||
// cmul 显式转换阻止编译器融合乘加，保证与 Python 参考求值逐位一致。
|
||||
func cmul(ar, ai, br, bi float64) (float64, float64) {
|
||||
return float64(ar*br) - float64(ai*bi), float64(ar*bi) + float64(ai*br)
|
||||
}
|
||||
|
||||
// phasors 填充每个幅角的 (cos, sin)。
|
||||
// tc、ts 为倍角表工作区，只读取本次写入的槽位，复用时不必清零。
|
||||
func (bd *body) phasors(t float64, pc, ps, tc, ts []float64) {
|
||||
for i := range bd.tabMax {
|
||||
if bd.tabMax[i] == 0 && !(bd.top && i < 3) {
|
||||
continue
|
||||
}
|
||||
var s, c float64
|
||||
if bd.top {
|
||||
s, c = math.Sincos(topDMu * t * float64(int(1)<<uint(topBits*i)))
|
||||
} else {
|
||||
s, c = math.Sincos(ci0[i] + ci1[i]*t)
|
||||
}
|
||||
o := bd.tabOff[i]
|
||||
tc[o], ts[o] = 1, 0
|
||||
for j := 1; j <= bd.tabMax[i]; j++ {
|
||||
tc[o+j], ts[o+j] = cmul(tc[o+j-1], ts[o+j-1], c, s)
|
||||
}
|
||||
if bd.top && i == 2 {
|
||||
break
|
||||
}
|
||||
}
|
||||
for j := 0; j+1 < len(bd.keyOff); j++ {
|
||||
fs := bd.factors[bd.keyOff[j]:bd.keyOff[j+1]]
|
||||
r, im := 1.0, 0.0
|
||||
if len(fs) > 0 {
|
||||
r, im = tc[fs[0].slot], ts[fs[0].slot]
|
||||
if fs[0].neg {
|
||||
im = -im
|
||||
}
|
||||
fs = fs[1:]
|
||||
}
|
||||
for _, f := range fs {
|
||||
br, bi := tc[f.slot], ts[f.slot]
|
||||
if f.neg {
|
||||
bi = -bi
|
||||
}
|
||||
r, im = cmul(r, im, br, bi)
|
||||
}
|
||||
if bd.keyNeg[j] {
|
||||
im = -im
|
||||
}
|
||||
pc[j], ps[j] = r, im
|
||||
}
|
||||
}
|
||||
|
||||
type scratch struct{ buf []float64 }
|
||||
|
||||
var scratchPool = sync.Pool{New: func() interface{} { return new(scratch) }}
|
||||
|
||||
// elements t 为 TDB 千年（J2000 起算）。
|
||||
func (bd *body) elements(t float64) [6]float64 {
|
||||
x := (t - tMid) / tHalf
|
||||
var leg [maxDeg + 1]float64
|
||||
leg[0], leg[1] = 1, x
|
||||
for k := 2; k <= bd.legDeg; k++ {
|
||||
leg[k] = (leg[k-1]*x*float64(2*k-1) - leg[k-2]*float64(k-1)) / float64(k)
|
||||
}
|
||||
nk := len(bd.keyNeg)
|
||||
sc := scratchPool.Get().(*scratch)
|
||||
defer scratchPool.Put(sc)
|
||||
if cap(sc.buf) < 2*nk+2*maxTab {
|
||||
sc.buf = make([]float64, 2*nk+2*maxTab)
|
||||
}
|
||||
// 各段在读取前都会被完整写入，复用时不必清零。
|
||||
buf := sc.buf[:2*nk+2*maxTab]
|
||||
pc, ps := buf[:nk], buf[nk:2*nk]
|
||||
bd.phasors(t, pc, ps, buf[2*nk:2*nk+maxTab], buf[2*nk+maxTab:])
|
||||
var el [6]float64
|
||||
for v := range bd.el {
|
||||
e := &bd.el[v]
|
||||
sum := 0.0
|
||||
for i, c := range e.secular {
|
||||
sum += c * leg[i]
|
||||
}
|
||||
// 逐阶做点积再乘 Legendre 值，避免逐项累加包络系数的读改写。
|
||||
for d := range e.cnt {
|
||||
cd, sd := e.c[d], e.s[d]
|
||||
arg := e.arg[:len(cd)]
|
||||
s0, s1 := 0.0, 0.0
|
||||
for i, a := range arg {
|
||||
s0 += cd[i] * pc[a]
|
||||
s1 += sd[i] * ps[a]
|
||||
}
|
||||
sum += leg[d] * (s0 + s1)
|
||||
}
|
||||
el[v] = sum
|
||||
}
|
||||
// 先归约平经度再加周期和，与 Python 参考求值一致。
|
||||
lm := math.Mod(bd.l0+bd.f*t, 2*math.Pi)
|
||||
if lm < 0 {
|
||||
lm += 2 * math.Pi
|
||||
}
|
||||
el[1] += lm
|
||||
return el
|
||||
}
|
||||
|
||||
// EarthFromEMB 由地月质心与地心月球合成物理地心 / Earth centre from EMB and geocentric Moon.
|
||||
func EarthFromEMB(emb, moon [3]float64) [3]float64 {
|
||||
k := 1 / (1 + emrat)
|
||||
return [3]float64{emb[0] - moon[0]*k, emb[1] - moon[1]*k, emb[2] - moon[2]*k}
|
||||
}
|
||||
|
||||
// ellxyz VSOP2013 椭圆元件 (a,l,k,h,q,p) → 动力学黄道位置（au）与速度（au/日）。
|
||||
func (bd *body) ellxyz(el [6]float64, wantVel bool) (pos, vel [3]float64) {
|
||||
a, l, k, h, q, p := el[0], el[1], el[2], el[3], el[4], el[5]
|
||||
fi := math.Sqrt(1 - k*k - h*h)
|
||||
ki := math.Sqrt(1 - q*q - p*p)
|
||||
u := 1 / (1 + fi)
|
||||
ex := math.Hypot(k, h)
|
||||
gl := math.Mod(l, 2*math.Pi)
|
||||
if gl < 0 {
|
||||
gl += 2 * math.Pi
|
||||
}
|
||||
gm := gl - math.Atan2(h, k)
|
||||
e := gl + (ex-0.125*ex*ex*ex)*math.Sin(gm) + 0.5*ex*ex*math.Sin(2*gm) + 0.375*ex*ex*ex*math.Sin(3*gm)
|
||||
var zs, zc float64
|
||||
for it := 0; it < 20; it++ {
|
||||
zs, zc = math.Sincos(e)
|
||||
z3r, z3i := k*zc+h*zs, k*zs-h*zc
|
||||
dl := gl - e + z3i
|
||||
e += dl / (1 - z3r)
|
||||
if math.Abs(dl) < 1e-15 {
|
||||
break
|
||||
}
|
||||
}
|
||||
zs, zc = math.Sincos(e)
|
||||
z3r, z3i := k*zc+h*zs, k*zs-h*zc
|
||||
rsa := 1 - z3r
|
||||
z1r, z1i := u*k*z3i, u*h*z3i
|
||||
z2r, z2i := z1i, -z1r
|
||||
xcw := (-k + zc + z2r) / rsa
|
||||
xsw := (-h + zs + z2i) / rsa
|
||||
xm := p*xcw - q*xsw
|
||||
xr := a * rsa
|
||||
pos = [3]float64{xr * (xcw - 2*p*xm), xr * (xsw + 2*q*xm), -2 * xr * ki * xm}
|
||||
if !wantVel {
|
||||
return pos, vel
|
||||
}
|
||||
xms := a * (h + xsw) / fi
|
||||
xmc := a * (k + xcw) / fi
|
||||
xn := bd.rgm / math.Pow(a, 1.5)
|
||||
vel = [3]float64{xn * ((2*p*p-1)*xms + 2*p*q*xmc), xn * ((1-2*q*q)*xmc - 2*p*q*xms), 2 * xn * ki * (p*xms + q*xmc)}
|
||||
return pos, vel
|
||||
}
|
||||
|
||||
func rx(a float64) [3][3]float64 {
|
||||
s, c := math.Sincos(a)
|
||||
return [3][3]float64{{1, 0, 0}, {0, c, -s}, {0, s, c}}
|
||||
}
|
||||
|
||||
func rz(a float64) [3][3]float64 {
|
||||
s, c := math.Sincos(a)
|
||||
return [3][3]float64{{c, -s, 0}, {s, c, 0}, {0, 0, 1}}
|
||||
}
|
||||
|
||||
func mul(a, b [3][3]float64) (out [3][3]float64) {
|
||||
for i := 0; i < 3; i++ {
|
||||
for j := 0; j < 3; j++ {
|
||||
for k := 0; k < 3; k++ {
|
||||
out[i][j] += a[i][k] * b[k][j]
|
||||
}
|
||||
}
|
||||
}
|
||||
return out
|
||||
}
|
||||
|
||||
func transpose(a [3][3]float64) (out [3][3]float64) {
|
||||
for i := 0; i < 3; i++ {
|
||||
for j := 0; j < 3; j++ {
|
||||
out[i][j] = a[j][i]
|
||||
}
|
||||
}
|
||||
return out
|
||||
}
|
||||
@@ -0,0 +1,166 @@
|
||||
// 被测契约：内置表与参考向量一致（< 10 cm），现代段区间外回落长时段表，接缝连续，可并发求值。
|
||||
package planets
|
||||
|
||||
import (
|
||||
"bufio"
|
||||
"math"
|
||||
"os"
|
||||
"strconv"
|
||||
"strings"
|
||||
"sync"
|
||||
"testing"
|
||||
)
|
||||
|
||||
func sq(x float64) float64 { return x * x }
|
||||
|
||||
func longOnly(t *testing.T) *Model {
|
||||
m, err := Parse(longTable)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
return m
|
||||
}
|
||||
|
||||
func checkVectors(t *testing.T, m *Model, path string) {
|
||||
f, err := os.Open(path)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
defer f.Close()
|
||||
n := 0
|
||||
sc := bufio.NewScanner(f)
|
||||
for sc.Scan() {
|
||||
parts := strings.Split(sc.Text(), ",")
|
||||
var v [8]float64
|
||||
for i := range v {
|
||||
if v[i], err = strconv.ParseFloat(parts[i], 64); err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
}
|
||||
id := int(v[0])
|
||||
p, vel, err := m.HeliocentricState(id, v[1])
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
d := math.Sqrt(sq(p[0]-v[2]) + sq(p[1]-v[3]) + sq(p[2]-v[4]))
|
||||
dv := math.Sqrt(sq(vel[0]-v[5]) + sq(vel[1]-v[6]) + sq(vel[2]-v[7]))
|
||||
if !(d <= 1e-4 && dv <= 1e-6) {
|
||||
t.Errorf("body %d jd %.1f: %.3e km, %.3e km/day", id, v[1], d, dv)
|
||||
}
|
||||
n++
|
||||
}
|
||||
if n < 100 {
|
||||
t.Fatalf("only %d vectors", n)
|
||||
}
|
||||
}
|
||||
|
||||
func TestLongTableMatchesReference(t *testing.T) {
|
||||
checkVectors(t, longOnly(t), "testdata/long.csv")
|
||||
}
|
||||
|
||||
func TestModernSegmentMatchesReference(t *testing.T) {
|
||||
checkVectors(t, Default(), "testdata/modern.csv")
|
||||
}
|
||||
|
||||
func TestFastTableMatchesReference(t *testing.T) {
|
||||
checkVectors(t, Fast(), "testdata/fast.csv")
|
||||
}
|
||||
|
||||
func TestFallsBackOutsideModern(t *testing.T) {
|
||||
long, dual := longOnly(t), Default()
|
||||
for _, jd := range []float64{ModernStart, ModernEnd, ModernStart - 1, ModernEnd + 1, 625000.5, 5000000.5} {
|
||||
for id := 1; id <= 8; id++ {
|
||||
a, _ := long.Heliocentric(id, jd)
|
||||
b, _ := dual.Heliocentric(id, jd)
|
||||
if a != b {
|
||||
t.Errorf("body %d jd %.1f: did not fall back to long table", id, jd)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestSeamContinuous(t *testing.T) {
|
||||
m := Default()
|
||||
const h = 0.5
|
||||
for _, jd := range []float64{ModernStart, ModernEnd, ModernStart + blendDays/2, ModernEnd - blendDays/2} {
|
||||
for id := 1; id <= 8; id++ {
|
||||
a, _ := m.Heliocentric(id, jd-h)
|
||||
b, _ := m.Heliocentric(id, jd+h)
|
||||
_, v, _ := m.HeliocentricState(id, jd)
|
||||
var d, vn float64
|
||||
for i := range v {
|
||||
d += sq((b[i]-a[i])/(2*h) - v[i])
|
||||
vn += sq(v[i])
|
||||
}
|
||||
if d, vn = math.Sqrt(d), math.Sqrt(vn); d > 1e-3*vn {
|
||||
t.Errorf("body %d jd %.1f: velocity differs from finite difference by %.3f of %.0f km/day", id, jd, d, vn)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestParseRejectsTruncated(t *testing.T) {
|
||||
for _, b := range [][]byte{longTable, modernTable} {
|
||||
for _, n := range []int{0, 3, 5, 40, len(b) / 2, len(b) - 1} {
|
||||
if _, err := Parse(b[:n]); err == nil {
|
||||
t.Errorf("len %d: expected error", n)
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestConcurrentMatchesSerial(t *testing.T) {
|
||||
m := Default()
|
||||
const n = 64
|
||||
var want [n][3]float64
|
||||
for i := range want {
|
||||
want[i], _ = m.Heliocentric(1+i%8, 2451545.0+float64(i)*977.3)
|
||||
}
|
||||
var wg sync.WaitGroup
|
||||
var bad [8]bool
|
||||
for g := 0; g < 8; g++ {
|
||||
wg.Add(1)
|
||||
go func(g int) {
|
||||
defer wg.Done()
|
||||
for i := 0; i < n; i++ {
|
||||
if got, _ := m.Heliocentric(1+i%8, 2451545.0+float64(i)*977.3); got != want[i] {
|
||||
bad[g] = true
|
||||
}
|
||||
}
|
||||
}(g)
|
||||
}
|
||||
wg.Wait()
|
||||
for g, b := range bad {
|
||||
if b {
|
||||
t.Fatalf("goroutine %d saw a mismatch", g)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkHeliocentricState(b *testing.B) {
|
||||
m := Default()
|
||||
for id := 1; id <= 8; id++ {
|
||||
id := id
|
||||
b.Run(strconv.Itoa(id), func(b *testing.B) {
|
||||
for i := 0; i < b.N; i++ {
|
||||
m.HeliocentricState(id, 2378496.0+float64(i%14610)*10)
|
||||
}
|
||||
})
|
||||
}
|
||||
}
|
||||
|
||||
func TestZigzagDecodeBeyond32Bits(t *testing.T) {
|
||||
for _, want := range []int64{0, -1, 1, 1<<31 - 1, -1 << 31, 1 << 40, -(1 << 40) - 7, 1<<55 + 3} {
|
||||
z := uint64(want<<1) ^ uint64(want>>63)
|
||||
var b []byte
|
||||
for z >= 0x80 {
|
||||
b = append(b, byte(z)|0x80)
|
||||
z >>= 7
|
||||
}
|
||||
b = append(b, byte(z))
|
||||
r := &reader{b: b}
|
||||
if got := r.zvar(); got != want || r.err != nil || r.p != len(b) {
|
||||
t.Errorf("zvar(%d) = %d, err %v, read %d/%d", want, got, r.err, r.p, len(b))
|
||||
}
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,193 @@
|
||||
package planets
|
||||
|
||||
import (
|
||||
"encoding/binary"
|
||||
"errors"
|
||||
"math/bits"
|
||||
)
|
||||
|
||||
// bitReader 按位读取，字节内高位在前。
|
||||
type bitReader struct {
|
||||
b []byte
|
||||
p int // 位位置
|
||||
err error
|
||||
}
|
||||
|
||||
// window 返回从当前位开始的 64 位窗口（高位对齐，越界补零），有效位至少 57 位。
|
||||
func (br *bitReader) window() uint64 {
|
||||
i := br.p >> 3
|
||||
var w uint64
|
||||
if i+8 <= len(br.b) {
|
||||
w = binary.BigEndian.Uint64(br.b[i:])
|
||||
} else {
|
||||
for k := 0; k < 8; k++ {
|
||||
w <<= 8
|
||||
if i+k < len(br.b) {
|
||||
w |= uint64(br.b[i+k])
|
||||
}
|
||||
}
|
||||
}
|
||||
return w << uint(br.p&7)
|
||||
}
|
||||
|
||||
func (br *bitReader) skip(n int) {
|
||||
br.p += n
|
||||
if br.p > 8*len(br.b) {
|
||||
br.err = errors.New("planets: truncated bit stream")
|
||||
}
|
||||
}
|
||||
|
||||
func (br *bitReader) get(n int) uint64 {
|
||||
if n == 0 || br.err != nil {
|
||||
return 0
|
||||
}
|
||||
if n > 56 {
|
||||
hi := br.get(n - 32)
|
||||
return hi<<32 | br.get(32)
|
||||
}
|
||||
v := br.window() >> uint(64-n)
|
||||
br.skip(n)
|
||||
return v
|
||||
}
|
||||
|
||||
// gamma Elias-gamma，编码值为 n+1。
|
||||
func (br *bitReader) gamma() int {
|
||||
if br.err != nil {
|
||||
return 0
|
||||
}
|
||||
z := bits.LeadingZeros64(br.window())
|
||||
if z > 28 {
|
||||
br.err = errors.New("planets: bad gamma code")
|
||||
return 0
|
||||
}
|
||||
v := br.get(2*z + 1)
|
||||
return int(v) - 1
|
||||
}
|
||||
|
||||
func unzigzag(z int) int {
|
||||
if z&1 == 0 {
|
||||
return z >> 1
|
||||
}
|
||||
return -(z >> 1) - 1
|
||||
}
|
||||
|
||||
// readElement3 读取 PLN3 元件位流：包络游程、幅角号（定长或同阶升序间隔）、成对共享位宽的量化系数。
|
||||
func readElement3(r *reader, e *element, secDeg, nk int, sortedArgs bool) error {
|
||||
if secDeg > maxDeg {
|
||||
return errors.New("planets: secular degree too high")
|
||||
}
|
||||
n64 := r.uvar()
|
||||
if n64 > uint64(nk) {
|
||||
return errors.New("planets: too many terms")
|
||||
}
|
||||
nint := int(n64)
|
||||
e.secular = make([]float64, secDeg+1)
|
||||
for i := range e.secular {
|
||||
e.secular[i] = r.f64()
|
||||
}
|
||||
step := r.f64()
|
||||
size := r.uvar()
|
||||
if r.err != nil {
|
||||
return r.err
|
||||
}
|
||||
if size > uint64(len(r.b)-r.p) {
|
||||
return errors.New("planets: truncated table")
|
||||
}
|
||||
br := &bitReader{b: r.take(int(size))}
|
||||
if r.err != nil {
|
||||
return r.err
|
||||
}
|
||||
env := make([]int, 0, nint)
|
||||
for runs := br.gamma(); runs > 0 && br.err == nil; runs-- {
|
||||
d := int(br.get(4))
|
||||
cnt := br.gamma() + 1
|
||||
if d > maxDeg || len(env)+cnt > nint {
|
||||
return errors.New("planets: bad envelope runs")
|
||||
}
|
||||
for ; cnt > 0; cnt-- {
|
||||
env = append(env, d)
|
||||
}
|
||||
}
|
||||
if br.err != nil {
|
||||
return br.err
|
||||
}
|
||||
if len(env) != nint {
|
||||
return errors.New("planets: envelope count mismatch")
|
||||
}
|
||||
args := make([]int32, nint)
|
||||
nbits := bits.Len(uint(nk - 1))
|
||||
if nbits == 0 {
|
||||
nbits = 1
|
||||
}
|
||||
prev, cur := -1, -1
|
||||
for j := 0; j < nint; j++ {
|
||||
a := 0
|
||||
if sortedArgs {
|
||||
if env[j] != cur {
|
||||
prev, cur = -1, env[j]
|
||||
}
|
||||
a = prev + 1 + br.gamma()
|
||||
prev = a
|
||||
} else {
|
||||
a = int(br.get(nbits))
|
||||
}
|
||||
if a >= nk {
|
||||
return errors.New("planets: argument index out of range")
|
||||
}
|
||||
args[j] = int32(a)
|
||||
}
|
||||
top := 0
|
||||
for _, d := range env {
|
||||
if d > top {
|
||||
top = d
|
||||
}
|
||||
}
|
||||
// 按包络阶降序的稳定排序：pos[j] 为位流第 j 项的新位置
|
||||
pos := make([]int, nint)
|
||||
e.arg = make([]int32, nint)
|
||||
k := 0
|
||||
for d := top; d >= 0; d-- {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] == d {
|
||||
pos[j], e.arg[k] = k, args[j]
|
||||
k++
|
||||
}
|
||||
}
|
||||
}
|
||||
if nint == 0 {
|
||||
return br.err
|
||||
}
|
||||
e.cnt = make([]int, top+1)
|
||||
e.c, e.s = make([][]float64, top+1), make([][]float64, top+1)
|
||||
for d := 0; d <= top; d++ {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] >= d {
|
||||
e.cnt[d]++
|
||||
}
|
||||
}
|
||||
e.c[d], e.s[d] = make([]float64, e.cnt[d]), make([]float64, e.cnt[d])
|
||||
}
|
||||
width := 0
|
||||
coef := func() float64 {
|
||||
neg := br.get(1) != 0
|
||||
v := float64(br.get(width))
|
||||
if neg {
|
||||
v = -v
|
||||
}
|
||||
return v * step
|
||||
}
|
||||
for d := 0; d <= top; d++ {
|
||||
for j := 0; j < nint; j++ {
|
||||
if env[j] < d {
|
||||
continue
|
||||
}
|
||||
width += unzigzag(br.gamma())
|
||||
if width < 0 || width > 63 {
|
||||
return errors.New("planets: bad coefficient width")
|
||||
}
|
||||
e.c[d][pos[j]] = coef()
|
||||
e.s[d][pos[j]] = coef()
|
||||
}
|
||||
}
|
||||
return br.err
|
||||
}
|
||||
@@ -0,0 +1,108 @@
|
||||
1,-1931455,-62833473.893474385,-11738779.389872823,6761826.5210533086,14582.743821870408,-3696554.6520415167,-230752.33664395515
|
||||
1,-982346.61040627258,-54594365.924901746,-40249361.98021353,3524624.2650957904,1711348.2495792741,-2996593.1799513367,-395982.00376442779
|
||||
1,-664723.78605570132,19568697.79645298,41744274.883307591,670482.25088474201,-4562923.694390011,2147128.8468987569,659053.82913683238
|
||||
1,421526.7353404928,-8560427.7447433379,46317092.227732658,4314797.4566545757,-4930648.2616276676,-487278.75317214674,484118.99164901557
|
||||
1,613717.16879534395,50633858.869895719,-23956414.024757061,-7062273.6544543374,1013728.6378109402,4113246.5162761854,200754.98254079727
|
||||
1,1204502.931725678,12176372.939927423,-66239425.365220524,-6319067.7063551536,3316934.4824261386,1057323.5527012271,-251499.67586286186
|
||||
1,2332037.5255191391,21884339.865066517,40755036.895314112,1284676.9193076652,-4545596.9765684316,2165482.7567381081,597004.52219926508
|
||||
1,2469806.8315679757,-23900066.995238971,41442929.584906727,5578718.794936697,-4493684.7198801376,-1942325.6042346412,253081.92401840785
|
||||
1,3655932.6525249016,-15625619.077793298,-67848691.682821631,-4521720.6778781908,3243436.5201193294,-809742.86308659229,-339015.81050683191
|
||||
1,3836523.2060893951,-44660371.648988307,-49451083.941693358,-618447.01226177043,2254980.1946469825,-2714128.8424649457,-418801.59788438171
|
||||
1,4285288.7909884127,52518688.948609084,-29805567.862637836,-6735289.4021467147,1232776.764282319,3732096.7001830083,230849.22404800789
|
||||
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8,2257195.4500466366,-3346551542.7509909,-3057371207.8180952,139938586.00300646,312648.59912843094,-343836.68198063067,-111.95093670548243
|
||||
8,2260911.4868015177,-1966079746.8493695,-4083473592.2128506,129311044.57189198,419359.36570602335,-200507.88523263048,-5504.2028925456198
|
||||
8,2264337.206939836,-434743777.59809506,-4507285145.2369576,102778706.23543219,465412.70853146043,-41866.575934101762,-9837.1751075919765
|
||||
8,2266530.1337492219,585422109.10781682,-4483380298.9961071,78821428.491007224,462127.25470633816,62719.829204599846,-11940.048534724378
|
||||
8,2271408.2113666162,2672715813.3493323,-3625476059.2911377,13132769.028181078,374894.77702834539,280112.80400628818,-14408.573235334174
|
||||
8,2276097.4006803907,4047916876.4911733,-1933666687.5247586,-53356550.207526475,200011.04325969331,425707.77992662182,-13383.416223740498
|
||||
8,2276914.8015547134,4196583170.3500242,-1578607319.1409891,-64093787.955680564,163304.39986170919,442617.53613383882,-12867.864562194542
|
||||
8,2278679.8090668465,4409359865.7767172,-773706745.32482636,-85536633.433175027,76944.139409186973,465730.78392303508,-11351.588640384334
|
||||
8,2278761.4153937893,4415474775.6360035,-735678340.65861213,-86459746.075593293,72929.794657590086,466260.62214132393,-11273.148669869164
|
||||
8,2279222.2136139097,4443888462.2875118,-520216670.74786848,-91549819.307950243,50444.753555813899,468729.07167573716,-10817.294473361
|
||||
8,2289079.1836576555,2671761391.1978607,3568267338.1966453,-134964223.47402656,-378241.74844598171,283606.9932980985,2852.3365495062899
|
||||
8,2291213.3288700399,1803406361.0536544,4080443257.7449069,-125504318.00257933,-433226.87270752288,193618.456444073,6003.4753854280998
|
||||
8,2291770.2140345257,1559008962.405709,4180919045.5314898,-121940945.10737747,-444130.38697466045,167070.13267813422,6787.6263381931449
|
||||
8,2292752.6251051375,1115357065.1206529,4321547334.0028877,-114631724.3851361,-457961.93508348049,119180.80702402951,8071.2278249770307
|
||||
8,2293000.3730586977,1001573933.7189749,4349584204.791234,-112594025.02787597,-460521.63705392834,107155.4021690909,8376.7810273077412
|
||||
8,2300175.1073118928,-2267971136.0712938,3871475988.4665818,-27502283.611518424,-408965.94606763555,-233788.80813500052,14237.401796646656
|
||||
8,2310762.2702826909,-4516090486.1480684,-271742174.13249499,109522338.11635686,25999.285576563627,-466617.40561864112,8996.449741810693
|
||||
8,2330636.7151068226,2305456684.4753156,-3874233944.1169686,26683797.740969542,399674.53258948843,243244.34984594988,-14205.700707459519
|
||||
8,2343298.7898191474,4270494527.1071978,1300866594.552392,-125103878.08110164,-140688.90196373887,452994.70296084089,-6071.7207631993733
|
||||
8,2346262.8809786653,3654148250.8896966,2554348267.2944241,-136731686.86531192,-271154.56164190272,387728.42742878624,-1732.2869858583313
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||||
8,2354615.1618713546,332214156.47192317,4454752607.2148018,-99383866.368734792,-470193.60813758464,37857.011358560521,10047.815817929695
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||||
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|
||||
8,2373948.8806485189,-4224820150.6474094,-1635043759.5635223,130953258.13884374,165839.31318433117,-434572.00430445519,5133.3024040441896
|
||||
8,2382631.3812187007,-1379423888.4731245,-4315809799.3283195,120629162.81425929,443534.411658308,-140092.50458552709,-7327.6991063650576
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||||
8,2389208.1926018596,1628648490.9802358,-4210325697.1456652,49162253.020578735,435772.39800444187,171637.77063136251,-13572.306846573802
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||||
8,2397904.0036513801,4288144616.3471293,-1297181804.5078053,-72084037.725864843,133641.79052362451,452148.60538932553,-12388.556425509323
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||||
8,2403501.2887358326,4267101470.2635121,1308685388.4139054,-125236952.59539004,-140596.22279635596,452730.23249205545,-6068.7840266945832
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||||
8,2423314.1935228184,-3291878829.2709017,3067926304.0416193,12665526.208394626,-322386.5759443079,-341633.76348100282,14446.374246720876
|
||||
8,2426810.3250820599,-4179453672.7549562,1702756035.5504658,61227489.499345794,-180270.17671690611,-432683.0709301359,13045.769297855006
|
||||
8,2428427.2917341487,-4409306943.97229,982713972.67666709,81327959.522674903,-103748.51162613487,-455169.78545350494,11763.841546263511
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||||
8,2429597.5699358359,-4498652367.817977,444966147.10073686,94476157.059761062,-49143.590831672162,-463089.57136807055,10688.753203276292
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||||
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||||
8,2442512.3685318003,-1516326857.6480813,-4270101253.3896389,122860928.54620628,439263.04339446081,-153526.29543944821,-6936.3882966851243
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||||
8,2442915.2675501364,-1338214505.204284,-4328292188.5330458,119963817.44731553,444790.1639103904,-135365.89335221157,-7442.5904775154204
|
||||
8,2445054.0861903615,-361531153.25943577,-4513224942.2772532,101256413.97691917,465805.27568941715,-35912.392506577555,-10008.100557651382
|
||||
8,2451545,2515045869.8652868,-3738714470.7545485,19032309.156529054,385853.97308510658,265820.57228461537,-14347.876408079434
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||||
8,2455075.6939767599,3680414368.5302563,-2575349176.1164789,-31783278.368950848,266719.08935843216,388272.9668955424,-14126.148241228591
|
||||
8,2458180.9034184003,4298490336.6490717,-1258434104.0063851,-73156208.668618634,129660.59873150715,452826.06108211773,-12328.0223920054
|
||||
8,2460000.5,4454447819.2631941,-414301361.3401581,-94125146.201658666,40157.663656568962,471692.34042991709,-10622.495096099408
|
||||
8,2467275.3446910325,3470558196.6603708,2796242995.4203486,-137573803.69929424,-296383.46676020452,368143.77478957037,-757.85748724977361
|
||||
8,2472665.5748623828,1404991101.6551394,4235876085.7290063,-119620616.60249272,-448391.74644502142,152121.80389413188,7221.4317392731145
|
||||
8,2474522.5806957306,548854769.79629242,4433790046.6489677,-103950466.04341871,-469585.40337640792,59990.44198402678,9575.7541189377534
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||||
8,2486527.0242732824,-4089757830.9311767,1906601971.4410529,55013609.543197669,-202111.0252654379,-422307.1448584079,13365.632971924106
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||||
8,2501867.9424220412,-1880993619.4784524,-4126155231.5187559,128311453.53743042,425541.93097477249,-192297.52179298186,-5855.8267754312583
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||||
8,2509740.3647796647,1689952247.6726317,-4185152788.8884659,47237244.64315068,432678.070238685,177398.38282870001,-13645.796171820346
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||||
8,2510600.060933358,2055155801.5661516,-4015854389.1994753,35320385.96019458,416203.80575289414,216382.20045396325,-14056.154512466597
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||||
8,2511909.952754871,2579164881.7492838,-3694850204.440309,16639305.089781553,382099.55688178906,272631.58556416596,-14408.89904528933
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||||
8,2518576.4147364241,4322265371.3809443,-1167129033.1705673,-75608573.925866604,119479.27076904512,455158.75156173494,-12141.878624282013
|
||||
8,2525370.0137001472,4006023624.5630937,1961059799.3569775,-132745745.6428504,-210323.65765957677,425669.44641188363,-3906.8506845631155
|
||||
8,2531672.3758322261,1922577177.1636333,4023148357.2664075,-127192947.69382137,-425791.59123174765,204590.17862355805,5585.5176083378865
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||||
8,2534824.4901680332,498342052.38547146,4439559320.4422646,-102929006.29032543,-470218.20302579255,55286.30410685423,9691.4013827729468
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8,2541816.7498776624,-2625110446.2304316,3645850779.0536532,-14569461.322786739,-383244.59409862768,-270442.28547872737,14422.021980817239
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8,2543036.073701357,-3070895417.5873909,3287331238.6740317,3107415.3627009355,-346723.68394888594,-317325.94990057556,14529.774582291235
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8,2546994.5257124593,-4142883219.4360399,1790607428.6862524,58642836.720905818,-189692.62707493181,-426957.08091778134,13181.667299294337
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8,2551052.7434542929,-4526193433.9997454,-51573718.972142957,105436927.26526648,2150.5357920604706,-465599.16471895081,9559.6966650015784
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8,2558314.4581084568,-3295761155.2466497,-3118266248.2066631,140204014.56534061,320764.81585671741,-338087.78936397546,-431.91082854534318
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8,2561890.4046752327,-1958100725.8851564,-4090751860.6025405,129409771.15190539,420877.40047634736,-200987.72102560525,-5578.9986223014475
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8,2564589.685945244,-760914840.92699397,-4465291790.1114178,109531758.72521909,459080.90627958684,-75863.104390858934,-9021.4875984333194
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8,2565365.3985973313,-402705260.04360342,-4510173189.0474281,102190270.21002667,464204.289063123,-39701.366105638313,-9901.9634829219503
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||||
8,2577128.7351568425,4063158326.450985,-1899046528.6230195,-54582189.461109929,195324.14397010318,429416.14201630664,-13338.337280032993
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||||
8,2577639.2677030656,4156848887.0918455,-1677337974.2934921,-61306355.070811465,171705.71896734723,438844.23145891394,-12998.860875238814
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||||
8,2590334.2671391643,2551568660.1077352,3655932137.800746,-134153558.93984658,-388890.16345552931,272864.08933394216,3360.640120554986
|
||||
8,2595997.4277934292,37773325.03103219,4469555495.9632492,-92935556.987670049,-472655.42525418487,6209.7956580738428,10754.201784382836
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||||
8,2596685.4703123774,-286895917.49701768,4462098033.6312971,-85307382.119633496,-470697.19817468972,-27739.298698894698,11409.702362744896
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||||
8,2596902.4767300789,-388928940.05981785,4454940494.0463638,-82810114.572604403,-469648.39004792296,-38233.341019808875,11605.007660958332
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8,2599958.6811479013,-1782169056.1175373,4115713526.8735213,-43680559.438126236,-434429.57460043562,-183751.83576328747,13792.792755929899
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8,2607461.5385275586,-4193230528.7213321,1674681138.3096232,62225813.142429605,-177260.09163831593,-432059.0036235493,13001.539905357038
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8,2618665.2202832801,-3250023335.285738,-3168971013.4188023,140236923.48816052,325919.40749394702,-333797.546804482,-652.59817942365294
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||||
8,2622969.6595060355,-1582570981.3352432,-4249876080.7904916,124034955.79179592,437769.22545015934,-161344.2189749362,-6780.1116099869841
|
||||
8,2636101.3604303026,3786803574.9413924,-2411196370.8757682,-37687369.190034173,249711.19062637916,398625.37203822302,-13974.815244520825
|
||||
8,2641305.6078180475,4468798320.0026255,-85895304.933750868,-101328004.63431399,6596.7738907046041,473413.23014396202,-9893.9751535678788
|
||||
8,2646186.7395561016,3915312960.5546041,2132161751.9031265,-134240821.67659056,-228126.16996093906,416630.56287164864,-3298.3681064604652
|
||||
8,2652672.8788275202,1663881276.0043931,4136756606.8938818,-123611043.02195102,-438270.92664133152,177630.39391310574,6431.2100302141353
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8,2655817.3911270499,219785749.22791481,4463263509.9894085,-97010220.425259113,-473179.29779453663,26586.317384063539,10369.654307483805
|
||||
8,2657675.7904352564,-656630609.61434937,4425518715.3262663,-76029772.428152174,-466737.09407372319,-66085.82882942626,12124.966785228149
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8,2660712.9689958571,-2019547932.2566075,4006991703.4158711,-35945852.310723387,-422853.19846211537,-208898.02393021624,14043.04767638558
|
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8,2673114.1483041537,-4457711275.731514,-821251442.49612474,119776838.96361506,81388.889813181144,-458516.1448204632,7564.4191923903936
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||||
8,2690567.3579719397,1779461093.5289602,-4147398168.7292647,44401164.328235,427115.64410711214,187754.00468843628,-13722.99411462197
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|
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8,2699249.9134048764,4328807272.1854143,-1142596776.8940125,-76333170.184159264,115350.11566701748,456995.56269231607,-12077.248946626141
|
||||
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|
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|
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|
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|
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|
||||
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|
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|
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|
||||
8,2742359.3750335346,-2020929810.8783176,-4062298751.94416,130333809.57045616,415873.15691872191,-205802.18714607431,-5353.064139407973
|
||||
8,2745002.8418905083,-857629252.40640724,-4452227774.6234665,111505708.18844627,458683.30284085334,-85617.601805857557,-8812.9795582470269
|
||||
8,2747657.219437053,373558148.4211542,-4510901256.8479471,84307866.610288709,464538.66325567727,40683.65653023425,-11578.860241889808
|
||||
8,2749649.840763649,1286739996.4421947,-4333380391.6026087,59558083.143449381,447752.89189448353,137546.06094952556,-13155.309086603038
|
||||
8,2752433.6495864699,2459078917.6055379,-3778101942.0373502,21065693.248819966,390401.14398965676,258384.44563385475,-14345.105804929401
|
||||
8,2761257.4085423201,4459503277.0635357,-308325355.11825836,-96585992.921304777,29516.137033078154,470814.36001048546,-10395.582251357788
|
||||
|
@@ -0,0 +1,126 @@
|
||||
// Package semianalytic 内置半解析模型：VSOP2013/TOP2013 与 MPP02 结构、按 DE441 重拟的表，提供历元 L/B/R 与 ICRF 几何状态。
|
||||
package semianalytic
|
||||
|
||||
import (
|
||||
"math"
|
||||
|
||||
"b612.me/astro/internal/ephem"
|
||||
"b612.me/astro/planet/internal/semianalytic/lunar"
|
||||
"b612.me/astro/planet/internal/semianalytic/planets"
|
||||
)
|
||||
|
||||
// 表以 TT 为自变量拟合；TDB−TT 小于 1.7 ms，直接当作 TDB 使用。
|
||||
const (
|
||||
coverStart = -1931455.0
|
||||
coverEnd = 5373545.0
|
||||
eps0 = 84381.448 / 3600 * math.Pi / 180
|
||||
emrat = 81.3005682214972
|
||||
)
|
||||
|
||||
// Ephemeris 内置表；越过覆盖范围仍外推求值，只在 Coverage 中报告范围 / built-in tables; extrapolates beyond coverage.
|
||||
type Ephemeris struct{}
|
||||
|
||||
var _ ephem.Engine = Ephemeris{}
|
||||
|
||||
// Apparent 地心视方向（ICRF 单位矢量）、几何地心距 km、光行时日 / apparent geocentric direction.
|
||||
func (Ephemeris) Apparent(target ephem.Body, jdTT float64) (dir [3]float64, distKM, tauDays float64, err error) {
|
||||
return Apparent(target, jdTT)
|
||||
}
|
||||
|
||||
func finite(x float64) bool { return !math.IsNaN(x) && !math.IsInf(x, 0) }
|
||||
|
||||
type state struct{ p, v [3]float64 }
|
||||
|
||||
func (a state) sub(b state) state {
|
||||
for i := range a.p {
|
||||
a.p[i] -= b.p[i]
|
||||
a.v[i] -= b.v[i]
|
||||
}
|
||||
return a
|
||||
}
|
||||
|
||||
// State 目标相对中心的 ICRF 几何状态 / geometric ICRF state of target relative to center.
|
||||
func (Ephemeris) State(target, center ephem.Body, jdTDB float64) (pos, vel [3]float64, err error) {
|
||||
if !finite(jdTDB) {
|
||||
return pos, vel, ephem.ErrOutOfRange
|
||||
}
|
||||
t, err := helio(target, jdTDB)
|
||||
if err != nil {
|
||||
return pos, vel, err
|
||||
}
|
||||
c, err := helio(center, jdTDB)
|
||||
if err != nil {
|
||||
return pos, vel, err
|
||||
}
|
||||
d := t.sub(c)
|
||||
return toICRF(d.p), toICRF(d.v), nil
|
||||
}
|
||||
|
||||
// Coverage 可信区间 / trusted time span.
|
||||
func (Ephemeris) Coverage(target ephem.Body) (start, end float64, ok bool) {
|
||||
if _, err := helio(target, 2451545); err != nil {
|
||||
return 0, 0, false
|
||||
}
|
||||
return coverStart, coverEnd, true
|
||||
}
|
||||
|
||||
// helio 日心 J2000 平黄道状态（km、km/日）。
|
||||
func helio(b ephem.Body, jd float64) (state, error) {
|
||||
switch b {
|
||||
case ephem.Sun:
|
||||
return state{}, nil
|
||||
case ephem.SSB:
|
||||
return ssbHelio(jd), nil
|
||||
case ephem.Earth, ephem.Moon:
|
||||
emb, err := planetHelio(int(ephem.EMB), jd)
|
||||
if err != nil {
|
||||
return state{}, err
|
||||
}
|
||||
mp, mv := lunar.Default().PositionVelocityJ2000(jd)
|
||||
k := 1.0 / (1 + emrat)
|
||||
if b == ephem.Moon {
|
||||
k -= 1
|
||||
}
|
||||
for i := range mp {
|
||||
emb.p[i] -= mp[i] * k
|
||||
emb.v[i] -= mv[i] * k
|
||||
}
|
||||
return emb, nil
|
||||
}
|
||||
if b >= ephem.Mercury && b <= ephem.Neptune {
|
||||
return planetHelio(int(b), jd)
|
||||
}
|
||||
return state{}, ephem.ErrUnsupportedBody
|
||||
}
|
||||
|
||||
func planetHelio(id int, jd float64) (state, error) {
|
||||
p, v, err := planets.Default().HeliocentricState(id, jd)
|
||||
return state{p, v}, err
|
||||
}
|
||||
|
||||
// ssbHelio 太阳系质心的日心状态：Σ GMᵢ·rᵢ / (GM☉ + Σ GMᵢ)，冥王星等小天体不计。
|
||||
func ssbHelio(jd float64) state {
|
||||
var s state
|
||||
_, gmSun := planets.GM(1)
|
||||
total := gmSun
|
||||
for id := 1; id <= 8; id++ {
|
||||
gm, _ := planets.GM(id)
|
||||
h, _ := planetHelio(id, jd)
|
||||
for i := range s.p {
|
||||
s.p[i] += gm * h.p[i]
|
||||
s.v[i] += gm * h.v[i]
|
||||
}
|
||||
total += gm
|
||||
}
|
||||
for i := range s.p {
|
||||
s.p[i] /= total
|
||||
s.v[i] /= total
|
||||
}
|
||||
return s
|
||||
}
|
||||
|
||||
// toICRF J2000 平黄道 → ICRF 赤道（绕 x 轴转 −ε0）。
|
||||
func toICRF(e [3]float64) [3]float64 {
|
||||
s, c := math.Sincos(eps0)
|
||||
return [3]float64{e[0], e[1]*c - e[2]*s, e[1]*s + e[2]*c}
|
||||
}
|
||||
@@ -0,0 +1,153 @@
|
||||
// 被测契约：内置表经 ICRF 适配后与 DE441 几何状态一致到表本身的精度；质心推算误差不影响光行差。
|
||||
package semianalytic
|
||||
|
||||
import (
|
||||
"bufio"
|
||||
"math"
|
||||
"os"
|
||||
"strconv"
|
||||
"strings"
|
||||
"testing"
|
||||
|
||||
"b612.me/astro/internal/ephem"
|
||||
)
|
||||
|
||||
type sample struct {
|
||||
target, center ephem.Body
|
||||
jd float64
|
||||
p, v [3]float64
|
||||
}
|
||||
|
||||
func loadSamples(t *testing.T) []sample {
|
||||
f, err := os.Open("testdata/de441-states.csv")
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
defer f.Close()
|
||||
var out []sample
|
||||
sc := bufio.NewScanner(f)
|
||||
for sc.Scan() {
|
||||
parts := strings.Split(sc.Text(), ",")
|
||||
var v [9]float64
|
||||
for i := range v {
|
||||
if v[i], err = strconv.ParseFloat(parts[i], 64); err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
}
|
||||
out = append(out, sample{ephem.Body(v[0]), ephem.Body(v[1]), v[2], [3]float64{v[3], v[4], v[5]}, [3]float64{v[6], v[7], v[8]}})
|
||||
}
|
||||
if len(out) < 500 {
|
||||
t.Fatalf("only %d samples", len(out))
|
||||
}
|
||||
return out
|
||||
}
|
||||
|
||||
func norm(a, b [3]float64) float64 {
|
||||
return math.Sqrt((a[0]-b[0])*(a[0]-b[0]) + (a[1]-b[1])*(a[1]-b[1]) + (a[2]-b[2])*(a[2]-b[2]))
|
||||
}
|
||||
|
||||
func modern(jd float64) bool { return jd >= 2086302.5 && jd <= 2816787.5 }
|
||||
|
||||
func TestStatesMatchDE441(t *testing.T) {
|
||||
type key struct {
|
||||
target, center ephem.Body
|
||||
modern bool
|
||||
}
|
||||
type acc struct{ n, dp, dv, maxDp, maxDv, maxAng float64 }
|
||||
stats := map[key]*acc{}
|
||||
e := Ephemeris{}
|
||||
for _, s := range loadSamples(t) {
|
||||
p, v, err := e.State(s.target, s.center, s.jd)
|
||||
if err != nil {
|
||||
t.Fatal(err)
|
||||
}
|
||||
k := key{s.target, s.center, modern(s.jd)}
|
||||
if stats[k] == nil {
|
||||
stats[k] = &acc{}
|
||||
}
|
||||
a := stats[k]
|
||||
dp, dv := norm(p, s.p), norm(v, s.v)/86.4
|
||||
r := math.Sqrt(s.p[0]*s.p[0] + s.p[1]*s.p[1] + s.p[2]*s.p[2])
|
||||
a.n++
|
||||
a.dp += dp * dp
|
||||
a.dv += dv * dv
|
||||
a.maxDp = math.Max(a.maxDp, dp)
|
||||
a.maxDv = math.Max(a.maxDv, dv)
|
||||
a.maxAng = math.Max(a.maxAng, dp/r*206264.806)
|
||||
}
|
||||
// 上限：最大位置差 km、最大速度差 m/s；太阳相对质心的残差来自表外天体（冥王星、阋神星等）。
|
||||
type limit struct{ km, ms float64 }
|
||||
limits := map[key]limit{
|
||||
{ephem.Sun, ephem.SSB, true}: {300, 1e-3}, {ephem.Sun, ephem.SSB, false}: {300, 1e-3},
|
||||
{ephem.Earth, ephem.SSB, true}: {300, 0.01}, {ephem.Earth, ephem.SSB, false}: {500, 0.05},
|
||||
{ephem.Earth, ephem.Sun, true}: {40, 0.01}, {ephem.Earth, ephem.Sun, false}: {250, 0.05},
|
||||
{ephem.Moon, ephem.Earth, true}: {0.6, 0.005}, {ephem.Moon, ephem.Earth, false}: {1.2, 0.008},
|
||||
{ephem.Mars, ephem.SSB, true}: {400, 0.04}, {ephem.Mars, ephem.SSB, false}: {1200, 0.1},
|
||||
{ephem.Jupiter, ephem.SSB, true}: {2000, 0.03}, {ephem.Jupiter, ephem.SSB, false}: {4000, 0.05},
|
||||
{ephem.Saturn, ephem.SSB, true}: {2500, 0.02}, {ephem.Saturn, ephem.SSB, false}: {7000, 0.04},
|
||||
}
|
||||
for k, a := range stats {
|
||||
t.Logf("%3d-%3d modern=%-5v n=%2.0f pos rms %.3g km max %.3g km (%.4f″) vel rms %.3g m/s max %.3g m/s",
|
||||
k.target, k.center, k.modern, a.n, math.Sqrt(a.dp/a.n), a.maxDp, a.maxAng, math.Sqrt(a.dv/a.n), a.maxDv)
|
||||
l, ok := limits[k]
|
||||
if !ok {
|
||||
t.Errorf("%d-%d modern=%v: no limit defined", k.target, k.center, k.modern)
|
||||
continue
|
||||
}
|
||||
if a.maxDp > l.km || a.maxDv > l.ms {
|
||||
t.Errorf("%d-%d modern=%v: max %.3g km / %.3g m/s exceeds %.3g km / %.3g m/s",
|
||||
k.target, k.center, k.modern, a.maxDp, a.maxDv, l.km, l.ms)
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestStateAntisymmetricAndComposable(t *testing.T) {
|
||||
e := Ephemeris{}
|
||||
bodies := []ephem.Body{ephem.SSB, ephem.Sun, ephem.Mercury, ephem.EMB, ephem.Earth, ephem.Moon, ephem.Neptune}
|
||||
for _, jd := range []float64{2451545.0, 2460000.5, 1000000.5} {
|
||||
for _, a := range bodies {
|
||||
for _, b := range bodies {
|
||||
p1, v1, err1 := e.State(a, b, jd)
|
||||
p2, v2, err2 := e.State(b, a, jd)
|
||||
if err1 != nil || err2 != nil {
|
||||
t.Fatal(err1, err2)
|
||||
}
|
||||
for i := range p1 {
|
||||
if math.Abs(p1[i]+p2[i]) > 1e-6 || math.Abs(v1[i]+v2[i]) > 1e-9 {
|
||||
t.Fatalf("%d-%d jd %.1f: not antisymmetric", a, b, jd)
|
||||
}
|
||||
}
|
||||
}
|
||||
// 经质心中转与直接求差一致
|
||||
ps, _, _ := e.State(a, ephem.SSB, jd)
|
||||
pe, _, _ := e.State(ephem.Earth, ephem.SSB, jd)
|
||||
pd, _, _ := e.State(a, ephem.Earth, jd)
|
||||
for i := range pd {
|
||||
if math.Abs(ps[i]-pe[i]-pd[i]) > 1e-4 {
|
||||
t.Fatalf("%d via SSB differs from direct by %.3g km", a, ps[i]-pe[i]-pd[i])
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
func TestUnsupportedBodyAndCoverage(t *testing.T) {
|
||||
e := Ephemeris{}
|
||||
if _, _, err := e.State(ephem.Body(999), ephem.Sun, 2451545); err != ephem.ErrUnsupportedBody {
|
||||
t.Fatalf("want ErrUnsupportedBody, got %v", err)
|
||||
}
|
||||
if _, _, ok := e.Coverage(ephem.Body(999)); ok {
|
||||
t.Fatal("unsupported body reported coverage")
|
||||
}
|
||||
s, end, ok := e.Coverage(ephem.Moon)
|
||||
if !ok || s >= 2086302.5 || end <= 2816787.5 {
|
||||
t.Fatalf("coverage %v..%v ok=%v", s, end, ok)
|
||||
}
|
||||
}
|
||||
|
||||
func BenchmarkEarthBarycentric(b *testing.B) {
|
||||
e := Ephemeris{}
|
||||
for i := 0; i < b.N; i++ {
|
||||
e.State(ephem.Earth, ephem.SSB, 2451545.0+float64(i%7300)*10)
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,560 @@
|
||||
10,0,-453760.43827763933,627503.58386753942,-124230.69050468586,-70199.078707220062,26.76776105652425,765.92648268149367,334.66502282017069
|
||||
399,0,-453760.43827763933,107103581.39105695,92605789.262403503,41615993.840190336,-1825853.499460791,1701479.4253012564,784308.67706974538
|
||||
301,399,-453760.43827763933,-378705.73482052982,-28103.816160514951,-4017.4131024926901,3342.9625418581395,-77819.182821935115,-44213.971528624854
|
||||
399,10,-453760.43827763933,106476077.80718942,92730019.952908188,41686192.918897554,-1825880.2672218478,1700713.4988185749,783974.01204692514
|
||||
4,0,-453760.43827763933,169899735.16094986,-110355741.70409171,-56951329.050765976,1390624.903042719,1643145.9958309424,681686.37711209245
|
||||
5,0,-453760.43827763933,-795152443.37427366,-114721004.00195973,-25286023.797442842,159314.46442211611,-988964.39427058503,-431497.11358438112
|
||||
6,0,-453760.43827763933,1018743245.1316302,782191583.20550311,289192256.68771762,-579827.2059701574,633218.12694378977,273048.03342590691
|
||||
10,0,-423678.70671046677,179909.8780418032,-63616.807055276884,-40950.160518573954,83.110891028374496,742.67766260582778,323.1304096576477
|
||||
399,0,-423678.70671046677,-149343645.39114499,9355483.6249353141,4992417.8648941768,-231365.52615053259,-2326441.6302622342,-1057956.1165324459
|
||||
301,399,-423678.70671046677,-362497.12572547793,-18989.414561057463,-26273.515087980777,9050.9046067815598,-87472.242646161438,-31950.617127462578
|
||||
399,10,-423678.70671046677,-149523555.26918679,9419100.4319905918,5033368.0254127504,-231448.63704156096,-2327184.3079248401,-1058279.2469421034
|
||||
4,0,-423678.70671046677,-124479878.0323623,-165270415.92394394,-69258047.861014932,1871669.9375692941,-978522.93242947722,-520494.3005525489
|
||||
5,0,-423678.70671046677,-789098416.28881919,127609049.23493271,79009712.306077182,-211886.21464492343,-986005.85410317755,-418932.84563305299
|
||||
6,0,-423678.70671046677,1055647465.7742503,-875380582.46072364,-384706841.81956458,509714.64545812609,617854.61940350023,236530.72638943736
|
||||
10,0,-341426.16644567705,1262769.5920344677,-12843.113056088087,-44673.111321944591,192.05195299485459,1122.6787803388454,472.82069914201332
|
||||
399,0,-341426.16644567705,-67420712.2168971,-123924288.49601531,-56057011.641266786,2249658.9569060388,-1043850.8712911939,-484948.76346071513
|
||||
301,399,-341426.16644567705,353508.68930772692,81476.007399842143,27496.600809656084,-25016.476000322597,84701.806706080868,29842.278451677859
|
||||
399,10,-341426.16644567705,-68683481.808931574,-123911445.38295922,-56012338.529944845,2249466.9049530439,-1044973.5500715327,-485421.58415985713
|
||||
4,0,-341426.16644567705,-194700914.1804221,132111452.73911095,67805538.859190211,-1106469.9289963758,-1453285.0502874847,-609306.52568247006
|
||||
5,0,-341426.16644567705,-772362855.05181193,190373590.34130129,105414962.08175862,-306762.49500183394,-965002.72271918959,-407101.11956292926
|
||||
6,0,-341426.16644567705,-1398022432.4734106,-562786993.05195999,-188571905.17817026,275356.2760138099,-674855.90839133295,-281669.90831381845
|
||||
10,0,-324796.10496353707,70937.878713973201,-693144.55331471935,-300420.81453991978,1158.1163208507717,119.39272746038905,22.442442342931706
|
||||
399,0,-324796.10496353707,42742866.585810877,127221490.89314052,57641128.49656865,-2510762.2874431824,685382.01387348806,323035.27252551523
|
||||
301,399,-324796.10496353707,-66186.945268243551,-351223.13583222032,-193947.72853952646,82731.122926523749,-10694.849705449889,-9210.9054652472169
|
||||
399,10,-324796.10496353707,42671928.707096905,127914635.44645524,57941549.311108567,-2511920.4037640332,685262.6211460277,323012.8300831723
|
||||
4,0,-324796.10496353707,-192197639.67468974,-111839819.18567654,-42395532.288457409,1253199.6871998506,-1518782.3089291244,-737951.33603576955
|
||||
5,0,-324796.10496353707,-250476891.47148129,678697469.34220517,300365365.55205262,-1071758.3956206813,-306557.97302640002,-100009.46333471482
|
||||
6,0,-324796.10496353707,1120314399.2619877,667410859.63375628,238772380.73121825,-496473.62316226226,685255.79174112098,292228.49759181245
|
||||
10,0,-240920.88948244418,-75454.751970275684,596690.9036632292,252642.55203370831,-955.3831380591871,375.06841084704524,194.94239957869917
|
||||
399,0,-240920.88948244418,76011539.575863644,-118842251.59630252,-54283713.502295278,2176925.0884052352,1187286.3231776035,529551.13488172321
|
||||
301,399,-240920.88948244418,-240195.25513634086,-291111.43127427995,-145459.04963837564,66462.133179508732,-48564.774128241814,-14620.894423581543
|
||||
399,10,-240920.88948244418,76086994.327833921,-119438942.49996576,-54536356.054328986,2177880.4715432944,1186911.2547667564,529356.19248214446
|
||||
4,0,-240920.88948244418,-83915284.901893944,-181679091.85636759,-78575043.891084388,2078302.2405602112,-621887.10568215535,-367304.18231882545
|
||||
5,0,-240920.88948244418,-506666036.12325954,-570435363.11525273,-230983463.82616255,866177.87226951157,-612820.75171545194,-290335.85495241586
|
||||
6,0,-240920.88948244418,1003176300.2264693,-936133043.14471006,-408882641.44364846,547291.55888138711,584496.16270809667,221230.75135872042
|
||||
10,0,-136305.25725227379,143094.43903393406,1167331.2967486593,489165.05573821237,-1227.9900662357579,-95.239974211215539,-7.8524917579509879
|
||||
399,0,-136305.25725227379,-5115705.7768299906,134794008.3806335,61059780.776681036,-2622807.104624155,-80473.118247179853,-26205.829805254147
|
||||
301,399,-136305.25725227379,-135071.25769134518,-321196.27134543657,-121554.68873813003,84752.537477942387,-29880.855052582217,-20935.866063526304
|
||||
399,10,-136305.25725227379,-5258800.2158639245,133626677.08388485,60570615.720942825,-2621579.1145579191,-80377.878272968635,-26197.977313496194
|
||||
4,0,-136305.25725227379,216383601.43630025,23271023.442273706,1580481.4558775835,-48056.937799281521,1988673.2289311781,900792.58517917059
|
||||
5,0,-136305.25725227379,164213995.9978635,-691617404.07310879,-303285467.8200323,1098572.9234916801,267409.22831109242,82755.005996207547
|
||||
6,0,-136305.25725227379,-1094650719.3921556,-1009686290.7719079,-377293906.60044181,534084.27739309974,-510907.40708203777,-223116.28406723318
|
||||
10,0,30779.849641129607,325285.19509265444,-622658.9547295532,-274866.49127055617,972.13826311861328,502.27178429537702,190.66368771312477
|
||||
399,0,30779.849641129607,-45218113.618455507,-133198911.02380063,-60038082.129406638,2409954.832107571,-692040.73699167243,-320568.28503903653
|
||||
301,399,30779.849641129607,199094.05585694313,270804.87592631578,132343.87062557787,-79923.592886510713,48124.246877130056,12789.008542954869
|
||||
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399,0,3220882.2318521156,-131600426.273826,-63714222.365568921,-27181987.919335734,1171390.0323369175,-2100744.7657913165,-900361.64265116374
|
||||
301,399,3220882.2318521156,287190.25853562355,204623.0590602383,88096.893050741404,-58679.44702403916,63242.674760293587,36499.494879429825
|
||||
399,10,3220882.2318521156,-132305843.12259188,-64826981.841611832,-27628549.854511973,1172471.8276860581,-2101373.2896668483,-900657.4704568726
|
||||
4,0,3220882.2318521156,127145929.47647579,-150416860.94788399,-71880153.395914376,1721679.9195421906,1335376.4408867529,575377.78740930685
|
||||
5,0,3220882.2318521156,-456373166.14974523,-616980280.776636,-252714114.49773023,912826.91283776076,-528810.26906156889,-247163.07552614264
|
||||
6,0,3220882.2318521156,-807066814.99702883,-1149338172.0408068,-443060640.4493888,657331.49981390988,-420322.85171357793,-205244.77834561619
|
||||
10,0,3522038.5148897273,110056.50484767664,-16613.006591152425,-19447.686801002634,787.88873079710515,-286.48651847621261,-137.19824613784144
|
||||
399,0,3522038.5148897273,133370206.05783606,62183357.141661592,26278764.118446916,-1200103.2453972441,2097299.0520725865,895123.93705909874
|
||||
301,399,3522038.5148897273,-17986.898892328143,-362193.04711612314,-161391.26644778624,84665.290674686039,-10145.092773908584,3519.1984598343424
|
||||
399,10,3522038.5148897273,133260149.55298838,62199970.148252748,26298211.805247918,-1200891.1341280411,2097585.5385910627,895261.13530523656
|
||||
4,0,3522038.5148897273,-39243030.689604692,209140429.64275125,96750182.783643201,-2024869.7930933982,-156551.4218204731,-31834.887610838785
|
||||
5,0,3522038.5148897273,293802376.47452813,635561851.78699481,264033414.70368987,-1060401.0486543966,450508.7366668178,216627.58475300754
|
||||
6,0,3522038.5148897273,-870310584.33829212,-1096696388.618474,-419762219.56776369,633792.15333532926,-459073.05057237478,-221580.23992920638
|
||||
10,0,3559348.6398703274,-548790.68918734929,286262.45392846817,146291.80013305493,-888.91812682720854,-372.71458541429809,-139.95395225597872
|
||||
399,0,3559348.6398703274,22784175.547997218,134430140.36742711,57221032.469525471,-2577702.5437567816,358732.66890176706,156701.31035158594
|
||||
301,399,3559348.6398703274,-179549.35987118632,325993.16425362229,149832.28890164942,-76535.775792740926,-35811.31441832093,-6914.8322999860638
|
||||
399,10,3559348.6398703274,23332966.237184566,134143877.91349864,57074740.669392414,-2576813.6256299545,359105.38348718133,156841.26430384192
|
||||
4,0,3559348.6398703274,-238430127.76609886,-62182142.675967455,-23884235.127862602,602288.64283137128,-1648839.0980139873,-768416.8006487767
|
||||
5,0,3559348.6398703274,93810257.110855103,-717385317.4362396,-307843204.99194074,1099259.7751216677,183831.95541153956,52832.085259415224
|
||||
6,0,3559348.6398703274,1182609672.4668341,722421180.54068661,248569149.56536657,-486909.41428985522,628044.16177704884,285831.20012196462
|
||||
10,0,3646878.6329298224,-749698.73736538005,22932.115104886343,27282.345596787658,93.692316364403382,-1065.5398277262204,-462.3818418687257
|
||||
399,0,3646878.6329298224,100089905.20911871,-104278072.45385405,-44497069.720660977,1887596.754755832,1558470.1129182847,659350.66471412824
|
||||
301,399,3646878.6329298224,362817.0748629272,30083.633481830359,-11490.14750187844,-3344.3878684526567,88014.438177131742,30138.084702202203
|
||||
399,10,3646878.6329298224,100839603.94648409,-104301004.56895894,-44524352.066257767,1887503.0624394675,1559535.6527460108,659813.04655599699
|
||||
4,0,3646878.6329298224,201623010.72873473,-33318180.405505005,-19091381.770639636,422803.35758950189,2053333.5251773715,934225.30486937752
|
||||
5,0,3646878.6329298224,735502629.55407512,-75308693.02887772,-49112512.037197709,113012.78495476655,1083356.4840918905,458786.67616147263
|
||||
6,0,3646878.6329298224,157037376.96542469,1257651465.2747264,520879183.92768192,-863104.83766322699,61024.265517823391,65417.880292777198
|
||||
10,0,3685691.7969500911,-861300.68953968037,351869.11709532182,174039.09387760653,-557.13603267194731,-1101.4842451308225,-451.4108318655139
|
||||
399,0,3685691.7969500911,104006229.83662674,97522347.68894279,41268466.139579229,-1862154.5735088601,1653700.0251794613,706085.1583323126
|
||||
301,399,3685691.7969500911,-332502.78835575283,-194372.69736206532,-103434.5827480033,49121.873954649163,-66799.957533849403,-21188.888950975143
|
||||
399,10,3685691.7969500911,104867530.52616642,97170478.571847469,41094427.045701623,-1861597.4374761879,1654801.5094245921,706536.5691641781
|
||||
4,0,3685691.7969500911,-246297246.48052597,41101818.998038232,23436025.872868404,-360263.37872430758,-1692749.607083021,-769914.00774753653
|
||||
5,0,3685691.7969500911,687174047.86679399,-262914130.87896961,-127856526.14426911,419271.66748449643,1011129.3816468153,420829.09163305222
|
||||
6,0,3685691.7969500911,814629057.17884731,-1136012401.2208102,-514945980.95201999,663726.4006903281,418249.04894464283,145133.12098811727
|
||||
10,0,3834580.5701606283,272121.94564087683,-56.618389920962727,-14677.089291653141,718.20269088086309,482.92855738713718,193.61096311684383
|
||||
399,0,3834580.5701606283,9677326.1669106279,-139358633.26135755,-59117744.375900045,2535317.7431928939,133500.90947394067,50983.194704818176
|
||||
301,399,3834580.5701606283,322472.32114823349,151287.07283136249,97818.239416882396,-43695.888397809264,75342.076161025543,28755.431035040714
|
||||
399,10,3834580.5701606283,9405204.221269751,-139358576.64296761,-59103067.286608391,2534599.5405020132,133017.98091655353,50789.583741701332
|
||||
4,0,3834580.5701606283,29516095.384629518,203706099.97997683,92900516.91818732,-2049868.1870130436,415844.78661446413,226667.14325408835
|
||||
5,0,3834580.5701606283,-371200085.35698694,627660660.21616507,275552739.2545166,-1017293.8578416235,-451944.25969808834,-168779.90464435017
|
||||
6,0,3834580.5701606283,-507658683.27496737,-1277452240.2328758,-514585155.63071573,750671.6282941422,-266367.20192498312,-147012.10059947686
|
||||
10,0,3910956.9868338462,-823352.60858663369,490566.91939699929,231245.27904739059,-653.29376559545597,-987.25368986948058,-398.67024979475588
|
||||
399,0,3910956.9868338462,96325284.770029023,-106783928.10711445,-45431995.074282996,1942068.0538848715,1503359.0934856324,631825.10601398477
|
||||
301,399,3910956.9868338462,-371632.0856950134,-41567.144876942039,-18264.739269733429,13175.107528721002,-85340.008891380843,-27427.286465473204
|
||||
399,10,3910956.9868338462,97148637.378615662,-107274495.02651145,-45663240.353330389,1942721.347650467,1504346.347175502,632223.77626377961
|
||||
4,0,3910956.9868338462,-193357361.18872902,138419750.19079736,66749778.316729128,-1281215.4629124489,-1316389.4258152,-581799.86757568538
|
||||
5,0,3910956.9868338462,671788294.6619041,-299853309.26521522,-142972153.54205498,475988.33237460459,986190.30174423137,408380.35906515794
|
||||
6,0,3910956.9868338462,343420180.64587504,-1325383717.8671291,-574855251.42316818,779387.15365075762,177938.25150005514,38821.473902110672
|
||||
10,0,4365292.1955561377,-470374.2744229791,719087.26395662525,320974.87432991189,-1008.5554868662208,-487.0203112786117,-183.64967498500494
|
||||
399,0,4365292.1955561377,-5750755.8401075527,-138739515.2606073,-58329470.302606203,2538700.1776225176,-96168.255539441321,-50063.812880695114
|
||||
301,399,4365292.1955561377,-243764.10760402028,-298089.83240705729,-128006.42416021228,66667.136080273616,-49133.028098025243,-12662.460558734794
|
||||
399,10,4365292.1955561377,-5280381.5656845737,-139458602.52456394,-58650445.176936112,2539708.7331093843,-95681.23522816271,-49880.163205710109
|
||||
4,0,4365292.1955561377,-76559620.544616058,-199719487.22411439,-90369076.555136099,1982576.3446111742,-426385.9889402978,-222358.75762053896
|
||||
5,0,4365292.1955561377,182541035.42921939,-702097613.83341956,-301890822.59975803,1068779.2520816161,302366.42139532743,103613.76622325028
|
||||
6,0,4365292.1955561377,1456873485.2846169,33833994.359257981,-53476710.24123054,-29364.095312228514,749910.36466922332,319878.90951038041
|
||||
10,0,4463509.6345559489,639504.67060380266,-590639.79318482406,-255308.714329521,337.85074212211907,832.51658640487756,340.94897714311895
|
||||
399,0,4463509.6345559489,-90608047.768275201,-110874952.9112087,-46217868.76097665,2014780.522994169,-1452693.1890121682,-618495.60598176473
|
||||
301,399,4463509.6345559489,-362781.14446261525,10094.23956592381,40846.71286958456,-3364.0845679902441,-84539.849233664165,-38129.234658447291
|
||||
399,10,4463509.6345559489,-91247552.438878998,-110284313.11802389,-45962560.046647131,2014442.6722520471,-1453525.705598573,-618836.55495890789
|
||||
4,0,4463509.6345559489,-114968253.74590702,-189421257.1374996,-85126135.027471319,1828903.1487474276,-732030.5240922462,-358727.11019392632
|
||||
5,0,4463509.6345559489,-809346194.34945035,64826353.12935394,46094099.236987948,-137489.75002276772,-984921.15119858074,-414195.04978393327
|
||||
6,0,4463509.6345559489,986281932.7473886,953654197.24144268,359736542.11237872,-620872.80976204283,507632.53366210917,244891.31186404263
|
||||
10,0,4751511.2397211073,-1278750.4926174963,496098.03276931861,250535.50718434656,-536.74401684777592,-1178.3893216467079,-484.12407730399491
|
||||
399,0,4751511.2397211073,101158078.0482174,100659938.92773394,41652031.146709815,-1900858.6012568541,1608766.0190202908,682868.52102462621
|
||||
301,399,4751511.2397211073,-217888.51695020497,-250589.93884703517,-133041.22438909113,74101.887946953982,-56325.203597452477,-19409.344885480819
|
||||
399,10,4751511.2397211073,102436828.5408349,100163840.89496462,41401495.639525466,-1900321.8572400063,1609944.4083419375,683352.64510193013
|
||||
4,0,4751511.2397211073,173930387.85539088,-102606239.04772317,-48747151.470482536,1130625.6138269848,1788251.7112173592,804166.9911084004
|
||||
5,0,4751511.2397211073,684770744.50092375,-273367029.58197844,-131425566.09753555,425193.59897124337,1006172.0457672633,415798.55149978586
|
||||
6,0,4751511.2397211073,1213120755.735692,-745148971.79660988,-374763263.34684646,451727.17128783627,622565.34559361369,245042.74254368604
|
||||
10,0,4836805.5100452611,646160.01533393026,898467.49851627753,373476.73622960848,-972.99975365246075,561.2671002800937,263.65117268101028
|
||||
399,0,4836805.5100452611,-82575890.962881774,-114750134.24058118,-47527007.7198359,2113739.7911811168,-1327325.8525787718,-566239.19191721221
|
||||
301,399,4836805.5100452611,-402155.54529306293,1885.0866488218307,42435.933481320739,-2821.6779986591064,-77381.229878840517,-31802.026990421127
|
||||
399,10,4836805.5100452611,-83222050.978215709,-115648601.73909746,-47900484.456065506,2114712.790934769,-1327887.1196790517,-566502.84308989323
|
||||
4,0,4836805.5100452611,169464054.64476943,112264292.64707901,49443175.507166527,-1242163.035353398,1729950.8117033236,802265.87650657562
|
||||
5,0,4836805.5100452611,-565420673.10670328,-551200605.52353716,-219982708.5710074,784528.31695648807,-660029.57833945099,-297163.11511526589
|
||||
6,0,4836805.5100452611,766622704.27409041,-1139498209.7470298,-523092481.01549476,692558.16035834036,395590.08065576403,137090.35458151219
|
||||
10,0,5068732.0711162677,19759.105967778785,-1078942.3415830047,-464503.99274743145,1176.342698814386,-323.72504105309946,-166.79642805755026
|
||||
399,0,5068732.0711162677,-105286780.42409669,-99728462.699190646,-40928112.502778672,1806285.4610295116,-1684448.0395283443,-713564.38401092531
|
||||
301,399,5068732.0711162677,59486.241197779775,361505.9684292078,174887.50090330839,-82687.210992255728,7942.0264184957887,10462.228980136808
|
||||
399,10,5068732.0711162677,-105306539.53006446,-98649520.357607648,-40463608.510031238,1805109.1183306973,-1684124.3144872913,-713397.58758286771
|
||||
4,0,5068732.0711162677,-127010563.11985897,-187575532.2808592,-84301907.109550267,1755079.4423116748,-812883.81732467737,-385531.8344932078
|
||||
5,0,5068732.0711162677,340585519.16016114,606363667.78401947,248084703.0578481,-1036177.7135462891,521316.01795226993,244164.95776344181
|
||||
6,0,5068732.0711162677,-1070545138.4277253,788559457.47666681,387919578.88665009,-543310.5874553062,-619354.33147116797,-240875.91829927298
|
||||
10,0,5113926.4576401599,854767.93400613242,614094.04534067481,237352.59922297261,-710.04915282154991,942.94605792769676,418.97025374472969
|
||||
399,0,5113926.4576401599,-89796110.63870123,107981215.8489171,45552490.783726625,-2058009.9968769827,-1480411.3970171621,-603602.8961995882
|
||||
301,399,5113926.4576401599,-279628.51858134568,254850.43192119896,87815.91144477576,-58379.281437255107,-63076.772211217954,-18480.713162779135
|
||||
399,10,5113926.4576401599,-90650878.57270737,107367121.80357642,45315138.184503652,-2057299.9477241612,-1481354.3430750896,-604021.86645333294
|
||||
4,0,5113926.4576401599,-247460203.20961854,24666852.381610889,13271222.264282024,-257319.7562977038,-1707187.9148789735,-775130.22432834352
|
||||
5,0,5113926.4576401599,-677494336.7458601,-433903246.67988849,-167390901.73140791,603727.88849768543,-803099.71704461752,-352988.18109985162
|
||||
6,0,5113926.4576401599,-1146308434.5083432,-779755748.28337586,-282225950.6534313,473385.7972441407,-629623.09217070509,-292360.65799079748
|
||||
|
Reference in New Issue
Block a user