430 lines
17 KiB
Go
430 lines
17 KiB
Go
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package basic
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import "math"
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// SolarEclipseShadowKind 阴影类型 / shadow kind.
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type SolarEclipseShadowKind int
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const (
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// SolarEclipseShadowUmbra 本影与反本影 / umbra and antumbra.
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SolarEclipseShadowUmbra SolarEclipseShadowKind = iota
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// SolarEclipseShadowPenumbra 半影，即偏食区 / penumbra, the partial-eclipse region.
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SolarEclipseShadowPenumbra
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)
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// SolarEclipseShadowSolverOptions 单时刻阴影求解器配置 / single-instant shadow solver options.
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type SolarEclipseShadowSolverOptions struct {
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// Model 月亮半径模型，零值为 NASA bulletin Split-K / lunar radius model.
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Model SolarEclipseRadiusModel
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// DeltaTSeconds 显式 ΔT（秒），<=0 用进程级模型，只改变地球自转相位 / explicit ΔT in seconds.
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DeltaTSeconds float64
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// BoundaryPoints 边界角向采样点数，<=0 用 96 / boundary sample count.
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BoundaryPoints int
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// Kind 本影或半影，零值为本影 / umbra or penumbra, zero is the umbra.
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Kind SolarEclipseShadowKind
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// TargetSpacingKM 边界加密目标间距（千米），0 用该类型的整包采样默认值，负值表示不加密 / boundary refinement spacing in km.
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TargetSpacingKM float64
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}
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const (
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solarEclipseShadowDefaultBoundaryPoints = 96
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// 开放足迹的物理边界含擦地点，点数上限沿用整包口径。
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solarEclipseShadowMaximumBoundaryPoints = 1440
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// 半个朔望月：窗口内缓存锚点必为最近朔月。
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solarEclipseShadowAnchorHalfWindowDays = 14.7652944265
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// 批量条数上限，超出返回 nil。
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solarEclipseShadowMaximumBatchCount = 262144
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)
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// SolarEclipseShadowTopology 瞬时足迹拓扑签名，用于插值门控 / footprint topology signature.
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type SolarEclipseShadowTopology struct {
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// Kind 阴影类型，签名以 umbra 或 penumbra 开头 / shadow kind, the signature prefix.
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Kind SolarEclipseShadowKind
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// Vertices 物理边界顶点总数 / boundary vertex count.
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Vertices int
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// Segments 边界分段数，换日线会拆分 / segment count.
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Segments int
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// Closed 边界是否由阴影自身闭合 / self-closed boundary.
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Closed bool
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// EnclosesPole 环绕过极点，经度已展开，不能按下标插值 / pole-winding ring.
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EnclosesPole bool
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}
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// Signature 稳定签名字符串，可直接作为能否插值的比较键 / stable interpolation key.
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func (topology SolarEclipseShadowTopology) Signature() string {
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if topology.Vertices == 0 {
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return "empty"
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}
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builder := make([]byte, 0, 32)
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if topology.Kind == SolarEclipseShadowPenumbra {
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builder = append(builder, "penumbra"...)
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} else {
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builder = append(builder, "umbra"...)
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}
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if topology.Closed {
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builder = append(builder, "-closed"...)
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} else {
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builder = append(builder, "-horizon"...)
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}
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builder = append(builder, "-seg"...)
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builder = appendInt(builder, topology.Segments)
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builder = append(builder, "-pt"...)
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builder = appendInt(builder, topology.Vertices)
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if topology.EnclosesPole {
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builder = append(builder, "-pole"...)
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}
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return string(builder)
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}
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func appendInt(target []byte, value int) []byte {
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if value == 0 {
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return append(target, '0')
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}
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if value < 0 {
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target = append(target, '-')
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value = -value
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}
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var digits [20]byte
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position := len(digits)
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for value > 0 {
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position--
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digits[position] = byte('0' + value%10)
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value /= 10
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}
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return append(target, digits[position:]...)
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}
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// SolarEclipseShadowInstant 某瞬时（TT）的全球本影或半影足迹 / instantaneous shadow footprint.
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type SolarEclipseShadowInstant struct {
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// JDE 输入的力学时儒略日 / requested TT instant.
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JDE float64
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// Model 本次使用的月亮半径模型 / lunar radius model used.
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Model SolarEclipseRadiusModel
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// DeltaTSeconds 实际使用的 ΔT / ΔT actually used.
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DeltaTSeconds float64
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// Kind 本次计算的阴影类型 / shadow kind of this computation.
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Kind SolarEclipseShadowKind
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// Closed 边界由阴影自身闭合，false 表示被地平线切断 / self-closed or horizon-cut.
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Closed bool
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// Boundaries 物理边界分段，反经线会拆分 / physical boundary segments.
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Boundaries [][]SolarEclipsePathPoint
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// HorizonEnds 两端在地平圈上的擦地点，顺序与 Boundaries 一致 / horizon grazing points.
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HorizonEnds []SolarEclipsePathPoint
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// Topology 插值判定用的拓扑签名 / interpolation signature.
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Topology SolarEclipseShadowTopology
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}
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// Empty 该时刻阴影未落在地球表面 / no footprint on the Earth.
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func (instant SolarEclipseShadowInstant) Empty() bool {
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return len(instant.Boundaries) == 0
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}
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// SolarEclipseShadowSolver 可复用的单时刻求解器；非并发安全，宿主每条 lane 各持一个 / reusable solver, one per lane.
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type SolarEclipseShadowSolver struct {
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options SolarEclipseShadowSolverOptions
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anchorSet bool
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anchorJDE float64
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anchorSolver solarEclipseSolver
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}
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// NewSolarEclipseShadowSolver 构造单时刻求解器 / builds a single-instant solver.
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func NewSolarEclipseShadowSolver(options SolarEclipseShadowSolverOptions) *SolarEclipseShadowSolver {
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if options.Model != SolarEclipseModelIAUSingleK {
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options.Model = SolarEclipseModelNASABulletinSplitK
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}
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if options.BoundaryPoints <= 0 {
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options.BoundaryPoints = solarEclipseShadowDefaultBoundaryPoints
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}
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// 下界与整包采样同口径，个位数采样点会产出无意义的足迹。
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if options.BoundaryPoints < solarEclipsePartialFootprintMinBoundaryPoints {
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options.BoundaryPoints = solarEclipsePartialFootprintMinBoundaryPoints
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}
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if options.BoundaryPoints > solarEclipseShadowMaximumBoundaryPoints {
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options.BoundaryPoints = solarEclipseShadowMaximumBoundaryPoints
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}
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if options.Kind != SolarEclipseShadowPenumbra {
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options.Kind = SolarEclipseShadowUmbra
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}
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if options.TargetSpacingKM == 0 && options.Kind == SolarEclipseShadowPenumbra {
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// 半影的整包采样默认带空间加密，单时刻要用同一默认值才能与采样逐点一致。
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options.TargetSpacingKM = solarEclipsePartialFootprintTargetSpacingKM
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}
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if options.TargetSpacingKM < 0 {
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options.TargetSpacingKM = 0
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}
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return &SolarEclipseShadowSolver{options: options}
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}
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// ShadowAtJDE 给定 TT 时刻的阴影足迹；不在地球上时返回 (零值, false) / footprint at one TT instant.
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func (solver *SolarEclipseShadowSolver) ShadowAtJDE(jdeTT float64) (SolarEclipseShadowInstant, bool) {
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if !finite(jdeTT) {
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return SolarEclipseShadowInstant{}, false
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}
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deltaT := solver.effectiveDeltaT(jdeTT)
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inner := solver.solverFor(jdeTT)
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moon, axis, sun := solver.besselGeometryAt(jdeTT, inner, deltaT)
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footprint := inner.shadowFootprintAtWithGeometry(
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jdeTT, moon, axis, sun, solver.options.BoundaryPoints,
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solver.options.shadowKind(), solver.options.TargetSpacingKM,
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)
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if len(footprint.Boundaries) == 0 {
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return SolarEclipseShadowInstant{
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JDE: jdeTT, Model: solver.options.Model,
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Kind: solver.options.Kind, DeltaTSeconds: deltaT,
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}, false
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}
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return SolarEclipseShadowInstant{
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JDE: jdeTT,
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Model: solver.options.Model,
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Kind: solver.options.Kind,
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DeltaTSeconds: deltaT,
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Closed: footprint.Closed,
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Boundaries: footprint.Boundaries,
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HorizonEnds: footprint.HorizonEnds,
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Topology: solarEclipseShadowFootprintTopology(footprint, solver.options.Kind),
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}, true
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}
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func (options SolarEclipseShadowSolverOptions) shadowKind() solarEclipseShadowKind {
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if options.Kind == SolarEclipseShadowPenumbra {
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return solarEclipsePenumbralShadow
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}
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return solarEclipseCentralShadow
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}
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func (solver *SolarEclipseShadowSolver) effectiveDeltaT(jdeTT float64) float64 {
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override := solver.options.DeltaTSeconds
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if override <= 0 {
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// 选项 0/负值表示"未覆盖"，用模型；显式 ΔT=0 需走 DeltaTSecondsAt 的直接调用。
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override = math.NaN()
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}
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return DeltaTSecondsAt(jdeTT, override)
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}
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func (solver *SolarEclipseShadowSolver) solverFor(jdeTT float64) solarEclipseSolver {
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if solver.anchorSet && math.Abs(jdeTT-solver.anchorJDE) <= solarEclipseShadowAnchorHalfWindowDays {
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return solver.anchorSolver
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}
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anchor := CalcMoonSHByJDE(jdeTT, 0)
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solver.anchorSet = true
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solver.anchorJDE = anchor
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solver.anchorSolver = newSolarEclipseSolver(anchor, solver.options.Model)
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return solver.anchorSolver
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}
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func (solver *SolarEclipseShadowSolver) besselGeometryAt(
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jdeTT float64,
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inner solarEclipseSolver,
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deltaTSeconds float64,
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) ([3]float64, solarEclipseAxis, [3]float64) {
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if solver.options.DeltaTSeconds <= 0 {
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return inner.besselGeometryAt(jdeTT)
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}
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sunEquatorial, moonEquatorial := solarEclipseSunMoonEquatorial(jdeTT)
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axis := solarEclipseBesselAxisFromEquatorialWithDeltaT(
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jdeTT, sunEquatorial, moonEquatorial, deltaTSeconds,
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)
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return solarEclipseBesselMoonFromEquatorial(moonEquatorial, axis), axis, sunEquatorial
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}
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// SolarEclipseShadowAtJDE 是无状态版本：自建一次内部状态后求单时刻足迹，任意并发安全。
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// SolarEclipseShadowAtJDE is the stateless variant: it builds its own state per call and
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// is therefore safe for concurrent use.
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func SolarEclipseShadowAtJDE(
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jdeTT float64,
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options SolarEclipseShadowSolverOptions,
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) (SolarEclipseShadowInstant, bool) {
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return NewSolarEclipseShadowSolver(options).ShadowAtJDE(jdeTT)
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}
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func solarEclipseShadowFootprintTopology(
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footprint SolarEclipsePartialFootprint,
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kind SolarEclipseShadowKind,
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) SolarEclipseShadowTopology {
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topology := SolarEclipseShadowTopology{
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Kind: kind,
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Segments: len(footprint.Boundaries),
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Closed: footprint.Closed,
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}
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winding := 0.0
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for _, segment := range footprint.Boundaries {
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topology.Vertices += len(segment)
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for index := 1; index < len(segment); index++ {
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winding += math.Remainder(segment[index].Longitude-segment[index-1].Longitude, 360)
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}
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// 只有真正闭合的分段才把"末点回到首点"计入绕极判定；开放分段的收口边是虚拟的。
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if len(segment) > 2 && solarEclipsePathDistanceKM(segment[0], segment[len(segment)-1]) < 1e-6 {
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winding += math.Remainder(segment[0].Longitude-segment[len(segment)-1].Longitude, 360)
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}
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}
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if topology.Segments == 1 && math.Abs(winding) >= 180 {
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topology.EnclosesPole = true
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}
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return topology
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}
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// SolarEclipseStationState 某瞬时的站心日月几何 / topocentric geometry at one instant.
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type SolarEclipseStationState struct {
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// JDE 输入的 TT 时刻，DeltaTSeconds 实际使用的 ΔT / requested instant and ΔT used.
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JDE float64
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DeltaTSeconds float64
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// SeparationDeg 与 SeparationArcsec 是日月中心的站心角距，极小化用的连续量 / topocentric separation.
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SeparationDeg float64
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SeparationArcsec float64
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// 三个半径字段是日月站心视半径 / topocentric apparent radii.
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SunRadiusDeg float64
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MoonOuterRadiusDeg float64
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MoonInnerRadiusDeg float64
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// SunAltitudeDeg 与 SunAzimuthDeg 是站心太阳高度角与方位角，方位角自北向东 / solar altitude and azimuth.
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SunAltitudeDeg float64
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SunAzimuthDeg float64
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// Magnitude 瞬时食分，Obscuration 太阳视面积遮蔽率 / instantaneous magnitude and obscuration.
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Magnitude float64
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Obscuration float64
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// InCentralPhase 该瞬时站点位于本影或反本影内 / station inside the central shadow now.
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InCentralPhase bool
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// CentralPhaseType 中心食类型，非中心食为 SolarEclipseNone / central phase kind.
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CentralPhaseType SolarEclipseType
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// HasTotalPhase 与 HasAnnularPhase 表示该瞬时是否处于全食或环食 / total or annular now.
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HasTotalPhase bool
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HasAnnularPhase bool
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// Visible 太阳中心高于几何地平，海拔用俯仰角修正阈值 / Sun center above the horizon.
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Visible bool
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}
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// StationStateAtJDE 给定 TT 时刻与站点的站心情形，任何时刻可调用且不报错 / topocentric state at one instant.
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func (solver *SolarEclipseShadowSolver) StationStateAtJDE(
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jdeTT, lonDeg, latDeg, heightMeters float64,
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) SolarEclipseStationState {
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if !finite(jdeTT) || !finite(lonDeg) || !finite(latDeg) {
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return SolarEclipseStationState{JDE: jdeTT}
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}
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deltaT := solver.effectiveDeltaT(jdeTT)
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heightKM := heightMeters / 1000
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state := localSolarEclipseStateAtWithDeltaT(
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jdeTT, deltaT, lonDeg*rad, latDeg*rad, heightKM, solarEclipseModelParams(solver.options.Model),
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)
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contact := state.movingDiskContactState()
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central := contact.internalContactGap() <= 0
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result := SolarEclipseStationState{
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JDE: jdeTT,
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DeltaTSeconds: deltaT,
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SeparationDeg: state.separationRad / rad,
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SeparationArcsec: state.separationRad / rad * 3600,
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SunRadiusDeg: state.sunRadiusRad / rad,
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MoonOuterRadiusDeg: state.moonOuterRadiusRad / rad,
|
||
|
|
MoonInnerRadiusDeg: state.moonInnerRadiusRad / rad,
|
||
|
|
SunAltitudeDeg: state.sunAltitudeRad / rad,
|
||
|
|
SunAzimuthDeg: state.sunAzimuthRad / rad,
|
||
|
|
Obscuration: localSolarEclipseObscuration(state.sunRadiusRad, state.moonOuterRadiusRad, state.separationRad),
|
||
|
|
InCentralPhase: central,
|
||
|
|
}
|
||
|
|
visibleThreshold := 0.0
|
||
|
|
if heightMeters > 0 {
|
||
|
|
visibleThreshold = -HeightDegreeByLat(heightMeters, latDeg) * rad
|
||
|
|
}
|
||
|
|
result.Visible = state.sunAltitudeRad > visibleThreshold
|
||
|
|
if central {
|
||
|
|
result.Magnitude = state.moonInnerRadiusRad / state.sunRadiusRad
|
||
|
|
if state.moonInnerRadiusRad >= state.sunRadiusRad {
|
||
|
|
result.CentralPhaseType = SolarEclipseTotal
|
||
|
|
result.HasTotalPhase = true
|
||
|
|
} else {
|
||
|
|
result.CentralPhaseType = SolarEclipseAnnular
|
||
|
|
result.HasAnnularPhase = true
|
||
|
|
}
|
||
|
|
return result
|
||
|
|
}
|
||
|
|
result.Magnitude = (state.moonOuterRadiusRad + state.sunRadiusRad - state.separationRad) / (2 * state.sunRadiusRad)
|
||
|
|
if result.Magnitude < 0 {
|
||
|
|
result.Magnitude = 0
|
||
|
|
}
|
||
|
|
return result
|
||
|
|
}
|
||
|
|
|
||
|
|
// SolarEclipseStationStateAtJDE 无状态版本，可并发调用 / stateless, concurrency-safe variant.
|
||
|
|
func SolarEclipseStationStateAtJDE(
|
||
|
|
jdeTT, lonDeg, latDeg, heightMeters float64,
|
||
|
|
options SolarEclipseShadowSolverOptions,
|
||
|
|
) SolarEclipseStationState {
|
||
|
|
return NewSolarEclipseShadowSolver(options).StationStateAtJDE(jdeTT, lonDeg, latDeg, heightMeters)
|
||
|
|
}
|
||
|
|
|
||
|
|
func localSolarEclipseStateAtWithDeltaT(
|
||
|
|
jdTT, deltaTSeconds, lonRad, latRad, heightKM float64,
|
||
|
|
params solarEclipseModelParameters,
|
||
|
|
) localSolarEclipseState {
|
||
|
|
context := newLocalSolarEclipseStateContextWithDeltaT(jdTT, deltaTSeconds, params)
|
||
|
|
return context.stateAt(lonRad, latRad, heightKM)
|
||
|
|
}
|
||
|
|
|
||
|
|
func newLocalSolarEclipseStateContextWithDeltaT(
|
||
|
|
jdTT, deltaTSeconds float64,
|
||
|
|
params solarEclipseModelParameters,
|
||
|
|
) localSolarEclipseStateContext {
|
||
|
|
sunEquatorial, moonEquatorial := solarEclipseSunMoonEquatorial(jdTT)
|
||
|
|
utJDE := jdTT - deltaTSeconds/86400
|
||
|
|
return localSolarEclipseStateContext{
|
||
|
|
sunXYZ: solarEclipseLLRToXYZ(sunEquatorial[0], sunEquatorial[1], sunEquatorial[2]),
|
||
|
|
moonXYZ: solarEclipseLLRToXYZ(moonEquatorial[0], moonEquatorial[1], moonEquatorial[2]),
|
||
|
|
gst: ApparentSiderealTime(utJDE) * 15 * rad,
|
||
|
|
params: params,
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
// ShadowBetweenJDE 区间内等步长逐时刻的阴影足迹，无阴影时刻为空条目 / per-step footprints.
|
||
|
|
func (solver *SolarEclipseShadowSolver) ShadowBetweenJDE(
|
||
|
|
startJDE, endJDE, stepDays float64,
|
||
|
|
) []SolarEclipseShadowInstant {
|
||
|
|
if !finite(startJDE) || !finite(endJDE) || !finite(stepDays) || stepDays <= 0 || endJDE < startJDE {
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
count := solarEclipseShadowBatchCount(startJDE, endJDE, stepDays)
|
||
|
|
if count <= 0 || count > solarEclipseShadowMaximumBatchCount {
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
result := make([]SolarEclipseShadowInstant, 0, count)
|
||
|
|
for index := 0; index < count; index++ {
|
||
|
|
instant, _ := solver.ShadowAtJDE(startJDE + float64(index)*stepDays)
|
||
|
|
result = append(result, instant)
|
||
|
|
}
|
||
|
|
return result
|
||
|
|
}
|
||
|
|
|
||
|
|
// StationStatesBetweenJDE 区间内等步长逐时刻的站心情形 / per-step station states.
|
||
|
|
func (solver *SolarEclipseShadowSolver) StationStatesBetweenJDE(
|
||
|
|
startJDE, endJDE, stepDays, lonDeg, latDeg, heightMeters float64,
|
||
|
|
) []SolarEclipseStationState {
|
||
|
|
if !finite(startJDE) || !finite(endJDE) || !finite(stepDays) || stepDays <= 0 || endJDE < startJDE {
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
count := solarEclipseShadowBatchCount(startJDE, endJDE, stepDays)
|
||
|
|
if count <= 0 || count > solarEclipseShadowMaximumBatchCount {
|
||
|
|
return nil
|
||
|
|
}
|
||
|
|
result := make([]SolarEclipseStationState, 0, count)
|
||
|
|
for index := 0; index < count; index++ {
|
||
|
|
result = append(result, solver.StationStateAtJDE(
|
||
|
|
startJDE+float64(index)*stepDays, lonDeg, latDeg, heightMeters,
|
||
|
|
))
|
||
|
|
}
|
||
|
|
return result
|
||
|
|
}
|
||
|
|
|
||
|
|
// solarEclipseShadowBatchTimeTolerance 是批量采样末点的时刻容差（天，约 0.9 ms）：
|
||
|
|
// 起止点由浮点运算给出时末点会落在 end 之外若干个 ULP，容差内仍算入，避免丢掉本应包含的采样。
|
||
|
|
const solarEclipseShadowBatchTimeTolerance = 1e-8
|
||
|
|
|
||
|
|
// solarEclipseShadowBatchCount 返回闭区间上按 stepDays 采样的格点数。
|
||
|
|
func solarEclipseShadowBatchCount(startJDE, endJDE, stepDays float64) int {
|
||
|
|
return int(math.Floor((endJDE-startJDE+solarEclipseShadowBatchTimeTolerance)/stepDays)) + 1
|
||
|
|
}
|
||
|
|
|
||
|
|
// SolarEclipseShadowBetweenJDE 无状态批量版本 / stateless batch variant.
|
||
|
|
func SolarEclipseShadowBetweenJDE(
|
||
|
|
startJDE, endJDE, stepDays float64, options SolarEclipseShadowSolverOptions,
|
||
|
|
) []SolarEclipseShadowInstant {
|
||
|
|
return NewSolarEclipseShadowSolver(options).ShadowBetweenJDE(startJDE, endJDE, stepDays)
|
||
|
|
}
|