270 lines
8.7 KiB
Go
270 lines
8.7 KiB
Go
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package basic
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import (
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"math"
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"b612.me/astro/internal/geodata"
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)
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// SkyBody 通用天象搜索支持的天体 / body for generic sky event searches.
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type SkyBody int
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const (
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// SkySun 太阳 / the Sun.
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SkySun SkyBody = iota
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// SkyMoon 月球 / the Moon.
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SkyMoon
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// SkyMercury 水星 / Mercury.
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SkyMercury
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// SkyVenus 金星 / Venus.
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SkyVenus
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// SkyMars 火星 / Mars.
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SkyMars
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// SkyJupiter 木星 / Jupiter.
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SkyJupiter
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// SkySaturn 土星 / Saturn.
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SkySaturn
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// SkyUranus 天王星 / Uranus.
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SkyUranus
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// SkyNeptune 海王星 / Neptune.
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SkyNeptune
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)
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// SkyEvent 通用天象事件：TT 儒略日与事件时的角量（度）/ generic sky event at TT JDE with its angle in degrees.
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type SkyEvent struct {
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JDE float64
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Value float64
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}
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func (body SkyBody) valid() bool { return body >= SkySun && body <= SkyNeptune }
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// skyScanStep 保证相邻采样间视黄经变化远小于 180°，逆行回转也不会漏根。
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func skyScanStep(bodies ...SkyBody) float64 {
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step := 2.0
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for _, b := range bodies {
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switch b {
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case SkyMoon:
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step = math.Min(step, 0.25)
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case SkyMercury, SkyVenus, SkySun:
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step = math.Min(step, 1.0)
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}
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}
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return step
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}
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// SkyBodyApparentLoBoWithInstance 地心视黄经、视黄纬（度）/ geocentric apparent ecliptic longitude and latitude.
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func SkyBodyApparentLoBoWithInstance(body SkyBody, jde float64, inst *Instance) (float64, float64) {
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switch body {
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case SkySun:
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return sunApparentLoBoN(jde, -1, inst)
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case SkyMoon:
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return moonApparentLoBoN(jde, -1, inst)
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case SkyMercury, SkyVenus, SkyMars, SkyJupiter, SkySaturn, SkyUranus, SkyNeptune:
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return planetApparentLoBoWithInstance(int(body-SkyMercury)+1, jde, inst)
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}
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return math.NaN(), math.NaN()
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}
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// skyGridMaxIntervals 网格段数上限；须能放进 32 位 int，超出时扫描本身也不可能完成。
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const skyGridMaxIntervals = 1 << 30
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// skyGrid 把 [start, end] 均分为至少 minIntervals 段、每段不超过 step；按下标取点，浮点下必然前进且末点恰为 end。
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func skyGrid(start, end, step float64, minIntervals int) (count int, at func(int) float64, ok bool) {
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span := end - start
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if !finite(start) || !finite(end) || !(span > 0) || !(step > 0) {
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return 0, nil, false
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}
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ratio := math.Ceil(span / step)
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if !(ratio < skyGridMaxIntervals) {
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return 0, nil, false
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}
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count = minIntervals
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if ratio > float64(count) {
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count = int(ratio)
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}
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return count, func(index int) float64 {
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if index == count {
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return end
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}
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return start + span*float64(index)/float64(count)
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}, true
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}
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// skyRoots 在闭区间 [start, end] 内按 step 扫描 f 的零点并二分到约 0.1 秒；f 须连续（已处理 360° 回绕）。
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func skyRoots(start, end, step float64, f func(float64) float64) []float64 {
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count, at, ok := skyGrid(start, end, step, 1)
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if !ok {
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return nil
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}
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var roots []float64
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prevT, prev := start, f(start)
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if prev == 0 {
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roots = append(roots, start)
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}
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for index := 1; index <= count; index++ {
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t := at(index)
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cur := f(t)
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switch {
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case cur == 0:
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roots = append(roots, t)
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// 回绕跳变时 |差| 接近 360，不是真根；prev 为 0 的根已在上一点记过。
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case prev != 0 && !math.IsNaN(prev) && !math.IsNaN(cur) && (prev < 0) != (cur < 0) && math.Abs(cur-prev) < 180:
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lo, hi, flo := prevT, t, prev
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// 迭代上限防止大 JDE 下浮点间隔大于容差时不收敛。
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for i := 0; i < 100 && hi-lo > 1e-6; i++ {
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mid := (lo + hi) / 2
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fm := f(mid)
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if fm == 0 {
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lo, hi = mid, mid
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break
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}
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if (fm < 0) == (flo < 0) {
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lo, flo = mid, fm
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} else {
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hi = mid
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}
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}
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roots = append(roots, (lo+hi)/2)
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}
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prevT, prev = t, cur
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}
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return roots
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}
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// SkyLongitudeCrossingsWithInstance body 视黄经经过 longitude 的全部时刻 / times when the apparent longitude equals longitude.
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func SkyLongitudeCrossingsWithInstance(body SkyBody, longitude, startJDE, endJDE float64, inst *Instance) []SkyEvent {
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if !body.valid() || !(endJDE > startJDE) {
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return nil
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}
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f := func(t float64) float64 {
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lo, _ := SkyBodyApparentLoBoWithInstance(body, t, inst)
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return geodata.NormalizeLongitude(lo - longitude)
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}
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var out []SkyEvent
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for _, t := range skyRoots(startJDE, endJDE, skyScanStep(body), f) {
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out = append(out, SkyEvent{JDE: t, Value: longitude})
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}
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return out
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}
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// SkyStationsWithInstance 视黄经留（速度过零）的时刻，Value 为留时视黄经 / longitude stations; Value is the longitude.
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func SkyStationsWithInstance(body SkyBody, startJDE, endJDE float64, inst *Instance) []SkyEvent {
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if !body.valid() || body == SkySun || body == SkyMoon || !(endJDE > startJDE) {
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return nil
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}
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const h = 0.05
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rate := func(t float64) float64 {
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a, _ := SkyBodyApparentLoBoWithInstance(body, t-h, inst)
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b, _ := SkyBodyApparentLoBoWithInstance(body, t+h, inst)
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return geodata.NormalizeLongitude(b - a)
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}
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var out []SkyEvent
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for _, t := range skyRoots(startJDE, endJDE, skyScanStep(body), rate) {
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lo, _ := SkyBodyApparentLoBoWithInstance(body, t, inst)
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out = append(out, SkyEvent{JDE: t, Value: lo})
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}
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return out
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}
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// SkyAspectCrossingsWithInstance a 与 b 视黄经差（a − b）等于 angle 的时刻；angle 0 为黄经合 / times when lon(a) − lon(b) equals angle.
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func SkyAspectCrossingsWithInstance(a, b SkyBody, angle, startJDE, endJDE float64, inst *Instance) []SkyEvent {
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if !a.valid() || !b.valid() || a == b || !(endJDE > startJDE) {
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return nil
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}
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f := func(t float64) float64 {
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la, _ := SkyBodyApparentLoBoWithInstance(a, t, inst)
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lb, _ := SkyBodyApparentLoBoWithInstance(b, t, inst)
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return geodata.NormalizeLongitude(la - lb - angle)
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}
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var out []SkyEvent
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for _, t := range skyRoots(startJDE, endJDE, skyScanStep(a, b), f) {
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out = append(out, SkyEvent{JDE: t, Value: angle})
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}
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return out
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}
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func skyAngularDistance(lon1, lat1, lon2, lat2 float64) float64 {
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v1, v2 := sphericalUnit(lon1, lat1), sphericalUnit(lon2, lat2)
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cross := [3]float64{v1[1]*v2[2] - v1[2]*v2[1], v1[2]*v2[0] - v1[0]*v2[2], v1[0]*v2[1] - v1[1]*v2[0]}
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return math.Atan2(math.Sqrt(cross[0]*cross[0]+cross[1]*cross[1]+cross[2]*cross[2]), v1[0]*v2[0]+v1[1]*v2[1]+v1[2]*v2[2]) / rad
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}
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// skyGoldenMin 黄金分割求 [lo, hi] 内单峰 f 的极小点。
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func skyGoldenMin(lo, hi float64, f func(float64) float64) (float64, float64) {
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const g = 0.6180339887498949
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x1, x2 := hi-g*(hi-lo), lo+g*(hi-lo)
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fx1, fx2 := f(x1), f(x2)
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for i := 0; i < 200 && hi-lo > 1e-6; i++ {
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if fx1 < fx2 {
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hi, x2, fx2 = x2, x1, fx1
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x1 = hi - g*(hi-lo)
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fx1 = f(x1)
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} else {
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lo, x1, fx1 = x1, x2, fx2
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x2 = lo + g*(hi-lo)
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fx2 = f(x2)
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}
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}
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t := (lo + hi) / 2
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return t, f(t)
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}
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// skyMinima 扫描 f 在 [start, end] 内的局部极小并用黄金分割细化；只保留 ≤ maxValue 的极小。
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func skyMinima(start, end, step, maxValue float64, f func(float64) float64) []SkyEvent {
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count, at, ok := skyGrid(start, end, step, 2)
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if !ok {
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return nil
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}
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var out []SkyEvent
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add := func(lo, hi, boundary float64) {
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// 端点段细化值须低于边界采样值，否则极小在窗口外，不是窗口内的局部极小。
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if t, v := skyGoldenMin(lo, hi, f); v <= maxValue && v < boundary {
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out = append(out, SkyEvent{JDE: t, Value: v})
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}
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}
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t0, t1 := at(0), at(1)
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f0, f1 := f(t0), f(t1)
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if f0 < f1 {
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add(t0, t1, f0)
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}
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for index := 2; index <= count; index++ {
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t2 := at(index)
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f2 := f(t2)
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if f1 <= f0 && f1 < f2 {
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add(t0, t2, math.Inf(1))
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}
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t0, t1, f0, f1 = t1, t2, f1, f2
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}
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if f1 < f0 {
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add(t0, t1, f1)
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}
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return out
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}
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// SkySeparationMinimaWithInstance a、b 地心视角距的局部极小（度），只返回 ≤ maxSeparation 的 / closest approaches within maxSeparation degrees.
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func SkySeparationMinimaWithInstance(a, b SkyBody, maxSeparation, startJDE, endJDE float64, inst *Instance) []SkyEvent {
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if !a.valid() || !b.valid() || a == b || !(endJDE > startJDE) {
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return nil
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}
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f := func(t float64) float64 {
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la, ba := SkyBodyApparentLoBoWithInstance(a, t, inst)
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lb, bb := SkyBodyApparentLoBoWithInstance(b, t, inst)
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return skyAngularDistance(la, ba, lb, bb)
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}
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return skyMinima(startJDE, endJDE, skyScanStep(a, b)/2, maxSeparation, f)
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}
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// SkyStarSeparationMinimaWithInstance 天体与恒星地心视角距的局部极小（度）/ closest approaches of a body to a star within maxSeparation degrees.
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func SkyStarSeparationMinimaWithInstance(body SkyBody, star StarCoordinate, maxSeparation, startJDE, endJDE float64, inst *Instance) []SkyEvent {
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if !body.valid() || !(endJDE > startJDE) {
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return nil
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}
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f := func(t float64) float64 {
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ra, dec := starApparentRaDecGeocentric(t, star, inst)
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sl, sb := RaDecToLoBo(t, ra, dec)
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lo, bo := SkyBodyApparentLoBoWithInstance(body, t, inst)
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return skyAngularDistance(lo, bo, sl, sb)
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}
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return skyMinima(startJDE, endJDE, skyScanStep(body)/2, maxSeparation, f)
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}
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