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326 lines
12 KiB
Go
326 lines
12 KiB
Go
package basic
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import (
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"math"
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"sort"
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)
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const (
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localSolarEclipseDiagramDefaultStepDays = 5.0 / 1440.0
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localSolarEclipseDiagramMinStepDays = 1.0 / 86400.0
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localSolarEclipseDiagramMaxSamples = 2000
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localSolarEclipseDiagramDuplicateDays = 1e-10
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)
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// LocalSolarEclipseDiagramOptions 控制站心日食视圆图采样。
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// LocalSolarEclipseDiagramOptions controls local solar eclipse disk diagram sampling.
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type LocalSolarEclipseDiagramOptions struct {
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// StepDays 是路径采样步长，单位为日；<=0 时使用 5 分钟。
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// StepDays is the path sampling step in days; values <= 0 use five minutes.
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StepDays float64
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}
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// LocalSolarEclipseDiagramFrame 表示一个时刻的站心日月视圆几何。
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// LocalSolarEclipseDiagramFrame is local Sun-Moon disk geometry at one instant.
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type LocalSolarEclipseDiagramFrame struct {
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// JDE 是力学时儒略日, TT Julian ephemeris day.
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JDE float64
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// MoonX / MoonY 是以太阳视半径为单位的月心相对日心坐标，X 向东为正，Y 向北为正。
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// MoonX/MoonY are Moon-center coordinates relative to the Sun center in Sun-radius units; X east, Y north.
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MoonX float64
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MoonY float64
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// SunRadius 是太阳视半径，单位为图上太阳半径；固定为 1。
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// SunRadius is the Sun radius in diagram Sun-radius units; always 1.
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SunRadius float64
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// MoonRadius 是月球视半径，单位为图上太阳半径。
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// MoonRadius is the Moon apparent radius in Sun-radius units.
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MoonRadius float64
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// Separation 是日月中心角距，单位为度。
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// Separation is the Sun-Moon center separation in degrees.
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Separation float64
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// PositionAngle 是月心相对日心的位置角，从北点起向东量，单位为度。
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// PositionAngle is the Moon-center position angle from north toward east, in degrees.
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PositionAngle float64
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// SunAltitude / SunAzimuth 是太阳站心高度角 / 方位角，单位为度。
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// SunAltitude/SunAzimuth are local Sun altitude/azimuth in degrees.
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SunAltitude float64
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SunAzimuth float64
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// Label 是关键阶段标签，如 C1/Greatest/C4。
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// Label is a key phase label such as C1/Greatest/C4.
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Label string
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// Labels 是该点对应的全部关键阶段标签；若事件重合，这里会有多个值。
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// Labels contains all phase labels attached to this point.
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Labels []string
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}
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// LocalSolarEclipseDiagramResult 表示站心日食视圆图几何结果。
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// LocalSolarEclipseDiagramResult is the geometry result for a local solar eclipse disk diagram.
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type LocalSolarEclipseDiagramResult struct {
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// Eclipse 是对应的站心日食结果。
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// Eclipse is the local eclipse result used for the diagram.
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Eclipse LocalSolarEclipseResult
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// Frames 是采样帧，太阳固定在 (0,0)，月球按 MoonX/MoonY 绘制。
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// Frames are sampled frames; the Sun is fixed at (0,0), and the Moon uses MoonX/MoonY.
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Frames []LocalSolarEclipseDiagramFrame
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// StepDays 是实际采用的路径采样步长，单位为日。
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// StepDays is the effective path sampling step in days.
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StepDays float64
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}
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type localSolarEclipseDiagramTime struct {
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jde float64
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labels []string
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}
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// LocalSolarEclipseDiagram 计算站心日食视圆图几何数据，默认使用 NASA bulletin Split-K 模型。
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// LocalSolarEclipseDiagram computes local solar eclipse disk diagram geometry, using NASA bulletin Split-K by default.
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func LocalSolarEclipseDiagram(seedJDE, lon, lat, height float64, options LocalSolarEclipseDiagramOptions) LocalSolarEclipseDiagramResult {
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return LocalSolarEclipseDiagramNASABulletinSplitK(seedJDE, lon, lat, height, options)
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}
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// LocalSolarEclipseDiagramIAUSingleK 计算站心日食视圆图几何数据，使用 IAU Single-K 模型。
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// LocalSolarEclipseDiagramIAUSingleK computes local solar eclipse disk diagram geometry with the IAU Single-K model.
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func LocalSolarEclipseDiagramIAUSingleK(seedJDE, lon, lat, height float64, options LocalSolarEclipseDiagramOptions) LocalSolarEclipseDiagramResult {
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return localSolarEclipseDiagram(seedJDE, lon, lat, height, SolarEclipseModelIAUSingleK, options)
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}
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// LocalSolarEclipseDiagramNASABulletinSplitK 计算站心日食视圆图几何数据，使用 NASA bulletin Split-K 模型。
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// LocalSolarEclipseDiagramNASABulletinSplitK computes local solar eclipse disk diagram geometry with the NASA bulletin Split-K model.
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func LocalSolarEclipseDiagramNASABulletinSplitK(seedJDE, lon, lat, height float64, options LocalSolarEclipseDiagramOptions) LocalSolarEclipseDiagramResult {
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return localSolarEclipseDiagram(seedJDE, lon, lat, height, SolarEclipseModelNASABulletinSplitK, options)
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}
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func localSolarEclipseDiagram(
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seedJDE, lonDeg, latDeg, heightMeters float64,
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model SolarEclipseRadiusModel,
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options LocalSolarEclipseDiagramOptions,
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) LocalSolarEclipseDiagramResult {
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options = normalizeLocalSolarEclipseDiagramOptions(options)
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eclipse := localSolarEclipse(seedJDE, lonDeg, latDeg, heightMeters, model)
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result := LocalSolarEclipseDiagramResult{
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Eclipse: eclipse,
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StepDays: options.StepDays,
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}
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if !eclipse.HasPartial {
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return result
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}
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lonRad := lonDeg * rad
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latRad := latDeg * rad
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heightKM := heightMeters / 1000.0
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params := solarEclipseModelParams(model)
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times, stepDays := localSolarEclipseDiagramTimes(eclipse, options.StepDays)
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result.StepDays = stepDays
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result.Frames = make([]LocalSolarEclipseDiagramFrame, 0, len(times))
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for _, item := range times {
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frame := localSolarEclipseDiagramFrameAt(item.jde, lonRad, latRad, heightKM, params)
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frame.Label = localSolarEclipseDiagramPrimaryLabel(item.labels)
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frame.Labels = append([]string(nil), item.labels...)
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result.Frames = append(result.Frames, frame)
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}
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return result
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}
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func normalizeLocalSolarEclipseDiagramOptions(options LocalSolarEclipseDiagramOptions) LocalSolarEclipseDiagramOptions {
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if options.StepDays <= 0 || math.IsNaN(options.StepDays) || math.IsInf(options.StepDays, 0) {
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options.StepDays = localSolarEclipseDiagramDefaultStepDays
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}
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if options.StepDays < localSolarEclipseDiagramMinStepDays {
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options.StepDays = localSolarEclipseDiagramMinStepDays
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}
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return options
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}
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func localSolarEclipseDiagramTimes(
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eclipse LocalSolarEclipseResult,
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stepDays float64,
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) ([]localSolarEclipseDiagramTime, float64) {
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startJDE := eclipse.PartialStart
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endJDE := eclipse.PartialEnd
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if startJDE == 0 || endJDE == 0 || endJDE <= startJDE {
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return nil, stepDays
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}
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if sampleCount := int(math.Ceil((endJDE-startJDE)/stepDays)) + 1; sampleCount > localSolarEclipseDiagramMaxSamples {
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stepDays = (endJDE - startJDE) / float64(localSolarEclipseDiagramMaxSamples-1)
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}
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times := []localSolarEclipseDiagramTime{
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{jde: startJDE, labels: []string{"C1"}},
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{jde: eclipse.GreatestEclipse, labels: []string{"Greatest"}},
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{jde: endJDE, labels: []string{"C4"}},
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}
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if eclipse.HasCentral {
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times = append(times,
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localSolarEclipseDiagramTime{jde: eclipse.CentralStart, labels: []string{"C2"}},
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localSolarEclipseDiagramTime{jde: eclipse.CentralEnd, labels: []string{"C3"}},
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)
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}
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for jde := startJDE + stepDays; jde < endJDE; jde += stepDays {
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times = append(times, localSolarEclipseDiagramTime{jde: jde})
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}
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sort.SliceStable(times, func(i, j int) bool {
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if times[i].jde == times[j].jde {
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return localSolarEclipseDiagramLabelPriority(times[i].labels) < localSolarEclipseDiagramLabelPriority(times[j].labels)
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}
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return times[i].jde < times[j].jde
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})
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return uniqueLocalSolarEclipseDiagramTimes(times), stepDays
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}
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func uniqueLocalSolarEclipseDiagramTimes(times []localSolarEclipseDiagramTime) []localSolarEclipseDiagramTime {
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if len(times) < 2 {
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return times
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}
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unique := times[:0]
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for _, item := range times {
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if item.jde == 0 {
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continue
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}
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if len(unique) == 0 || math.Abs(item.jde-unique[len(unique)-1].jde) > localSolarEclipseDiagramDuplicateDays {
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item.labels = append([]string(nil), item.labels...)
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unique = append(unique, item)
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continue
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}
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unique[len(unique)-1].labels = mergeLocalSolarEclipseDiagramLabels(unique[len(unique)-1].labels, item.labels)
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}
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return unique
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}
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func mergeLocalSolarEclipseDiagramLabels(existing, incoming []string) []string {
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if len(incoming) == 0 {
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return existing
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}
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if len(existing) == 0 {
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return append([]string(nil), incoming...)
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}
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for _, label := range incoming {
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found := false
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for _, current := range existing {
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if current == label {
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found = true
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break
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}
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}
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if !found {
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existing = append(existing, label)
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}
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}
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return existing
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}
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func localSolarEclipseDiagramPrimaryLabel(labels []string) string {
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for _, label := range labels {
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if label == "Greatest" {
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return label
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}
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}
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if len(labels) == 0 {
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return ""
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}
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return labels[0]
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}
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func localSolarEclipseDiagramLabelPriority(labels []string) int {
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if len(labels) == 0 {
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return 99
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}
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switch labels[0] {
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case "C1":
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return 0
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case "C2":
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return 1
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case "Greatest":
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return 2
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case "C3":
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return 3
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case "C4":
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return 4
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default:
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return 99
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}
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}
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func localSolarEclipseDiagramFrameAt(
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jdTT, lonRad, latRad, heightKM float64,
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params solarEclipseModelParameters,
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) LocalSolarEclipseDiagramFrame {
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sunEquatorial, moonEquatorial := solarEclipseSunMoonEquatorial(jdTT)
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sunXYZ := solarEclipseLLRToXYZ(sunEquatorial[0], sunEquatorial[1], sunEquatorial[2])
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moonXYZ := solarEclipseLLRToXYZ(moonEquatorial[0], moonEquatorial[1], moonEquatorial[2])
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utJDE := TD2UT(jdTT, false)
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gst := ApparentSiderealTime(utJDE) * 15 * rad
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observerXYZ := localSolarEclipseObserverXYZ(gst, lonRad, latRad, heightKM)
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sunTopocentric := solarEclipseXYZToLLR(
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sunXYZ[0]-observerXYZ[0],
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sunXYZ[1]-observerXYZ[1],
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sunXYZ[2]-observerXYZ[2],
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)
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moonTopocentric := solarEclipseXYZToLLR(
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moonXYZ[0]-observerXYZ[0],
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moonXYZ[1]-observerXYZ[1],
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moonXYZ[2]-observerXYZ[2],
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)
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sunUnit := solarEclipseLLRToXYZ(sunTopocentric[0], sunTopocentric[1], 1)
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moonUnit := solarEclipseLLRToXYZ(moonTopocentric[0], moonTopocentric[1], 1)
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dot := localSolarEclipseClampUnit(
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sunUnit[0]*moonUnit[0] + sunUnit[1]*moonUnit[1] + sunUnit[2]*moonUnit[2],
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)
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sunRadiusRad := math.Asin(localSolarEclipseClampUnit(
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solarEclipseEarthEquatorialRadiusKM * solarEclipseSolarRadiusRatio / sunTopocentric[2],
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))
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moonRadiusRad := math.Asin(localSolarEclipseClampUnit(
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solarEclipseEarthEquatorialRadiusKM * solarEclipsePenumbralK * localSolarMoonRadiusScale / moonTopocentric[2],
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))
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if params.umbralK > solarEclipsePenumbralK {
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moonRadiusRad = math.Asin(localSolarEclipseClampUnit(
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solarEclipseEarthEquatorialRadiusKM * params.umbralK * localSolarMoonRadiusScale / moonTopocentric[2],
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))
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}
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east := [3]float64{-math.Sin(sunTopocentric[0]), math.Cos(sunTopocentric[0]), 0}
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north := [3]float64{
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-math.Cos(sunTopocentric[0]) * math.Sin(sunTopocentric[1]),
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-math.Sin(sunTopocentric[0]) * math.Sin(sunTopocentric[1]),
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math.Cos(sunTopocentric[1]),
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}
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denominator := dot
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if math.Abs(denominator) < 1e-12 {
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denominator = 1
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}
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xRad := (moonUnit[0]*east[0] + moonUnit[1]*east[1] + moonUnit[2]*east[2]) / denominator
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yRad := (moonUnit[0]*north[0] + moonUnit[1]*north[1] + moonUnit[2]*north[2]) / denominator
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positionAngle := math.Atan2(xRad, yRad) / rad
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if positionAngle < 0 {
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positionAngle += 360
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}
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sunHorizontal := solarEclipseEquatorialToHorizontal(
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sunTopocentric[0],
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sunTopocentric[1],
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sunTopocentric[2],
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lonRad,
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latRad,
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gst,
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)
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return LocalSolarEclipseDiagramFrame{
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JDE: jdTT,
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MoonX: xRad / sunRadiusRad,
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MoonY: yRad / sunRadiusRad,
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SunRadius: 1,
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MoonRadius: moonRadiusRad / sunRadiusRad,
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Separation: math.Acos(dot) / rad,
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PositionAngle: positionAngle,
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SunAltitude: sunHorizontal[1] / rad,
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SunAzimuth: solarEclipseNormalizeRadians(sunHorizontal[0]+math.Pi) / rad,
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}
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}
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