315 lines
12 KiB
Go
315 lines
12 KiB
Go
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package basic
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import "math"
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const (
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solarEclipseGreatestTimeContourSeedLatitudeStepDegrees = 5.0
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solarEclipseGreatestTimeContourSeedLongitudeStepDegrees = 5.0
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solarEclipseGreatestTimeContourSeedLatitudeLimitDegrees = 85.0
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solarEclipseGreatestTimeContourArcStepDegrees = 1.5
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solarEclipseGreatestTimeContourMinArcStepDegrees = 0.01
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solarEclipseGreatestTimeContourMaxArcSteps = 4000
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solarEclipseGreatestTimeContourCorrectionIterations = 12
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solarEclipseGreatestTimeContourGradientStepDegrees = 1e-4
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solarEclipseGreatestTimeContourLatitudeLimitDegrees = 88.0
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)
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// solarEclipseGreatestTimeArc 固定一个食甚时刻后的等时线求根器。
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// 时刻固定后 g = ∂(separation²)/∂t 只随经纬度变化，其零集就是该时刻的食甚等值线：
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// 一个约束、两个未知量，所以结果是曲线而不是区域，延拓成本正比于曲线长度。
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type solarEclipseGreatestTimeArc struct {
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evaluation solarEclipseRiseSetEvaluation
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}
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// sample 返回残差与中心状态；离开可见偏食域、非极小点或数值无效时 ok 为 false。
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func (arc solarEclipseGreatestTimeArc) sample(longitude, latitude float64) (float64, localSolarEclipseState, bool) {
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var state localSolarEclipseState
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if latitude <= -90 || latitude >= 90 {
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return 0, state, false
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}
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lonRad, latRad := longitude*rad, latitude*rad
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before := arc.evaluation.before.stateAt(lonRad, latRad, 0)
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state = arc.evaluation.center.stateAt(lonRad, latRad, 0)
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after := arc.evaluation.after.stateAt(lonRad, latRad, 0)
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if !finite(state.separationSquared) || state.sunAltitudeRad <= 0 {
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return 0, state, false
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}
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// 角距极小值处处存在，等时线必须再要求日月盘面真的相交，否则会在无食可见的海面上画出曲线。
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if solarEclipsePartialContactGap(state) > 1e-7 {
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return 0, state, false
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}
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stepSquared := solarEclipseRiseSetDerivativeStepDays * solarEclipseRiseSetDerivativeStepDays
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// separation² 在此取极小值才算食甚；二阶导非正说明该时刻不是本地的极大食。
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if (after.separationSquared-2*state.separationSquared+before.separationSquared)/stepSquared <= 0 {
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return 0, state, false
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}
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value := (after.separationSquared - before.separationSquared) / (2 * solarEclipseRiseSetDerivativeStepDays)
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if !finite(value) {
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return 0, state, false
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}
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return value, state, true
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}
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func (arc solarEclipseGreatestTimeArc) residual(longitude, latitude float64) float64 {
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value, _, ok := arc.sample(longitude, latitude)
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if !ok {
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return math.NaN()
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}
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return value
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}
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func (arc solarEclipseGreatestTimeArc) point(longitude, latitude float64, state localSolarEclipseState) SolarEclipsePathPoint {
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return SolarEclipsePathPoint{
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JDE: arc.evaluation.jd,
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Longitude: normalizeLongitude(longitude),
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Latitude: latitude,
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SunAltitude: state.sunAltitudeRad / rad,
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}
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}
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// metricGradient 返回 g 对地面东向、北向角度的偏导；东向角度 = 经度差 × cos(纬度)。
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func (arc solarEclipseGreatestTimeArc) metricGradient(longitude, latitude float64) (float64, float64, bool) {
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step := solarEclipseGreatestTimeContourGradientStepDegrees
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value, _, ok := arc.sample(longitude, latitude)
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if !ok {
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return 0, 0, false
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}
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cosine := math.Cos(latitude * rad)
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if cosine < 1e-6 {
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return 0, 0, false
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}
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eastValue, _, eastOK := arc.sample(longitude+step, latitude)
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westValue, _, westOK := arc.sample(longitude-step, latitude)
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northValue, _, northOK := arc.sample(longitude, latitude+step)
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southValue, _, southOK := arc.sample(longitude, latitude-step)
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longitudeDerivative, ok := greatestTimeContourDifference(value, eastValue, westValue, step, eastOK, westOK)
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if !ok {
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return 0, 0, false
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}
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latitudeDerivative, ok := greatestTimeContourDifference(value, northValue, southValue, step, northOK, southOK)
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if !ok {
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return 0, 0, false
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}
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return longitudeDerivative / cosine, latitudeDerivative, true
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}
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// correct 把预测点沿残差梯度投影回零集；失败说明该方向已离开等时线定义域。
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func (arc solarEclipseGreatestTimeArc) correct(longitude, latitude float64) (float64, float64, localSolarEclipseState, bool) {
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var state localSolarEclipseState
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for iteration := 0; iteration < solarEclipseGreatestTimeContourCorrectionIterations; iteration++ {
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value, current, ok := arc.sample(longitude, latitude)
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if !ok {
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return 0, 0, state, false
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}
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state = current
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if math.Abs(value) <= greatestTimeContourResidualTolerance {
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return longitude, latitude, state, true
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}
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east, north, ok := arc.metricGradient(longitude, latitude)
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if !ok {
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return 0, 0, state, false
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}
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denominator := east*east + north*north
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cosine := math.Cos(latitude * rad)
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if denominator < 1e-18 || cosine < 1e-6 {
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return 0, 0, state, false
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}
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// 完整牛顿步可能一步跨出可见域；逐步二分回退，只要还有一步落在域内就继续投影。
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scale, advanced := 1.0, false
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for attempt := 0; attempt < greatestTimeContourCorrectionBacktracking; attempt++ {
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nextLongitude := longitude - scale*value*east/denominator/cosine
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nextLatitude := latitude - scale*value*north/denominator
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scale /= 2
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if nextLatitude <= -90 || nextLatitude >= 90 {
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continue
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}
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if _, _, ok := arc.sample(nextLongitude, nextLatitude); !ok {
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continue
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}
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longitude, latitude = nextLongitude, nextLatitude
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advanced = true
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break
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}
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if !advanced {
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return 0, 0, state, false
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}
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}
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value, current, ok := arc.sample(longitude, latitude)
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if !ok || math.Abs(value) > 1e-6 {
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return 0, 0, state, false
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}
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return longitude, latitude, current, true
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}
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// traceGreatestTimeArc 从种子沿一个方向按弧长延拓，预测点落到定义域外时步长减半。
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func (solver solarEclipseSolver) traceGreatestTimeArc(
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evaluation solarEclipseRiseSetEvaluation,
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longitude, latitude, direction float64,
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) []SolarEclipsePathPoint {
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arc := solarEclipseGreatestTimeArc{evaluation: evaluation}
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_, state, ok := arc.sample(longitude, latitude)
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if !ok {
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return nil
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}
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points := []SolarEclipsePathPoint{arc.point(longitude, latitude, state)}
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step := solarEclipseGreatestTimeContourArcStepDegrees
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previousEast, previousNorth := 0.0, 0.0
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for count := 0; count < solarEclipseGreatestTimeContourMaxArcSteps; count++ {
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east, north, ok := arc.metricGradient(longitude, latitude)
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if !ok {
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break
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}
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norm := math.Hypot(east, north)
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cosine := math.Cos(latitude * rad)
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if norm < 1e-12 || cosine < 1e-6 {
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break
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}
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tangentEast, tangentNorth := -north/norm, east/norm
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if previousEast != 0 || previousNorth != 0 {
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if tangentEast*previousEast+tangentNorth*previousNorth < 0 {
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tangentEast, tangentNorth = -tangentEast, -tangentNorth
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}
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}
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nextLongitude, nextLatitude, nextState, ok := arc.correct(
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longitude+direction*step*tangentEast/cosine,
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latitude+direction*step*tangentNorth,
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)
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if !ok {
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step /= 2
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if step < solarEclipseGreatestTimeContourMinArcStepDegrees {
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break
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}
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continue
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}
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if math.Abs(nextLatitude) > solarEclipseGreatestTimeContourLatitudeLimitDegrees {
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break
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}
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next := arc.point(nextLongitude, nextLatitude, nextState)
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distance := solarEclipsePathDistanceKM(points[len(points)-1], next)
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// 校正回到原点说明该方向已经走到支路端点，继续只会原地打转。
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if distance < 1e-9 || distance > 4*step*greatestTimeContourKMPerDegree {
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break
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}
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points = append(points, next)
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longitude, latitude = nextLongitude, nextLatitude
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previousEast, previousNorth = tangentEast, tangentNorth
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step = math.Min(solarEclipseGreatestTimeContourArcStepDegrees, step*1.5)
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}
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return points
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}
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// greatestTimeContourSeeds 用粗扫找延拓种子；扫描只用于定位零集，不参与曲线成型。
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func (solver solarEclipseSolver) greatestTimeContourSeeds(evaluation solarEclipseRiseSetEvaluation) []SolarEclipsePathPoint {
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arc := solarEclipseGreatestTimeArc{evaluation: evaluation}
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seeds := make([]SolarEclipsePathPoint, 0, 16)
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latitudeStep := solarEclipseGreatestTimeContourSeedLatitudeStepDegrees
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longitudeStep := solarEclipseGreatestTimeContourSeedLongitudeStepDegrees
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limit := solarEclipseGreatestTimeContourSeedLatitudeLimitDegrees
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for latitude := -limit; latitude <= limit; latitude += latitudeStep {
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previousLongitude := -180.0
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previousValue := arc.residual(previousLongitude, latitude)
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for longitude := previousLongitude + longitudeStep; longitude <= 180; longitude += longitudeStep {
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value := arc.residual(longitude, latitude)
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if finite(previousValue) && finite(value) && previousValue*value <= 0 {
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root, ok := greatestTimeContourBisect(arc.residual, previousLongitude, longitude, latitude, previousValue)
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if !ok {
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continue
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}
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if _, state, sampled := arc.sample(root, latitude); sampled {
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seeds = append(seeds, arc.point(root, latitude, state))
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}
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}
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previousLongitude, previousValue = longitude, value
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}
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}
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return seeds
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}
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func solarEclipseGreatestTimeContourCovered(segments [][]SolarEclipsePathPoint, point SolarEclipsePathPoint) bool {
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for _, segment := range segments {
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for index := 1; index < len(segment); index++ {
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if greatestTimeContourPointSegmentKM(
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point.Longitude, point.Latitude,
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segment[index-1].Longitude, segment[index-1].Latitude,
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segment[index].Longitude, segment[index].Latitude,
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) <= greatestTimeContourCoverToleranceKM {
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return true
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}
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}
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}
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return false
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}
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// solarEclipseGreatestTimeContourSegmentCovered 判断整条支路是否已落在已绘曲线上（同一曲线被先后延拓两次时后一条可能更长）。
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func solarEclipseGreatestTimeContourSegmentCovered(segments [][]SolarEclipsePathPoint, segment []SolarEclipsePathPoint) bool {
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for _, point := range segment {
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if !solarEclipseGreatestTimeContourCovered(segments, point) {
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return false
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}
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}
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return true
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}
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// solarEclipseGreatestTimeContourPruneCovered 丢弃已被新支路整条覆盖的旧支路。
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func solarEclipseGreatestTimeContourPruneCovered(segments [][]SolarEclipsePathPoint, added []SolarEclipsePathPoint) [][]SolarEclipsePathPoint {
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kept := segments[:0]
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for _, segment := range segments {
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if solarEclipseGreatestTimeContourSegmentCovered([][]SolarEclipsePathPoint{added}, segment) {
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continue
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}
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kept = append(kept, segment)
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}
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return kept
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}
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// greatestTimeContourSegments 汇总一个时刻取值上的全部等时线支路。
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func (solver solarEclipseSolver) greatestTimeContourSegments(level float64) [][]SolarEclipsePathPoint {
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evaluation := solver.magnitudeEvaluationAt(level)
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seeds := solver.greatestTimeContourSeeds(evaluation)
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segments := make([][]SolarEclipsePathPoint, 0, 2)
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for _, seed := range seeds {
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if solarEclipseGreatestTimeContourCovered(segments, seed) {
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continue
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}
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forward := solver.traceGreatestTimeArc(evaluation, seed.Longitude, seed.Latitude, 1)
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backward := solver.traceGreatestTimeArc(evaluation, seed.Longitude, seed.Latitude, -1)
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segment := make([]SolarEclipsePathPoint, 0, len(forward)+len(backward))
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for index := len(backward) - 1; index >= 1; index-- {
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segment = append(segment, backward[index])
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}
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segment = append(segment, forward...)
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if len(segment) < 2 {
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continue
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}
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// 先按整条支路去重：种子检查只能拦住"较短者先画"的情况，反序时需要在这里收口。
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if solarEclipseGreatestTimeContourSegmentCovered(segments, segment) {
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continue
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}
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segments = solarEclipseGreatestTimeContourPruneCovered(segments, segment)
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segments = append(segments, segment)
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}
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return segments
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}
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// greatestTimeContours 计算请求时刻取值的地方食甚时刻等值线。
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func (solver solarEclipseSolver) greatestTimeContours(
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startJDE, endJDE float64,
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options SolarEclipsePartialFootprintOptions,
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) []SolarEclipseGreatestTimeContour {
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if len(options.GreatestTimeValues) == 0 || startJDE == 0 || endJDE == 0 || endJDE <= startJDE {
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return nil
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}
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contours := make([]SolarEclipseGreatestTimeContour, 0, len(options.GreatestTimeValues))
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for _, level := range options.GreatestTimeValues {
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if !finite(level) || level < startJDE || level > endJDE {
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continue
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}
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segments := solver.greatestTimeContourSegments(level)
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if len(segments) == 0 {
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continue
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}
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contours = append(contours, SolarEclipseGreatestTimeContour{JDE: level, Segments: segments})
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}
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return contours
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}
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