feat: 完善日月食与月掩几何链路并扩展历法接口
- 新增日月食中心带、偏食带、阴影足迹、等时线、食分线及升落边界计算，支持极区与混合食拓扑 - 新增日食单时刻阴影求解器、站心状态查询、批量采样和 ΔT 覆盖接口 - 重构恒星与行星月掩路径，补充有限盘面接触、站心修正、掩带宽度、极区投影及升落边界 - 扩展 SVG 与 GeoJSON 输出，支持详细面板、全球/极区/地球投影、边界闭合、时间标记和拓扑签名 - 扩展日月食候选搜索、局地搜索、沙罗序列预计算与范围外推，补充系列锚点和成员一致性校验 - 补齐古历纪年、儒略历独有闰日、多公历候选、历法改革跨日及精确日期运算接口 - 优化 ΔT、章动、恒星时、月球地平线、事件根搜索和本地星历缓存，降低重复计算开销并提升边界稳定
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package basic
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import "math"
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// localEphemerisVectorNode is a pair of Cartesian ephemeris samples at one
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// TT. Cartesian interpolation avoids right-ascension wraparound at 0/360.
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type localEphemerisVectorNode struct {
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tt float64
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first, next [3]float64
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}
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const (
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solarLocalEphemerisNodeCount = 13
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solarLocalEphemerisStepDays = 1.0 / 24.0
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occultationLocalEphemerisNodeCount = 49
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occultationLocalEphemerisStepDays = 2.0 / 24.0
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)
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func interpolateLocalEphemerisVectors(
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nodes []localEphemerisVectorNode,
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tt float64,
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) ([3]float64, [3]float64, bool) {
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const interpolationPoints = 6
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if len(nodes) < interpolationPoints || !finite(tt) {
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return [3]float64{}, [3]float64{}, false
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}
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step := nodes[1].tt - nodes[0].tt
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if !finite(step) || step <= 0 {
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return [3]float64{}, [3]float64{}, false
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}
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u := (tt - nodes[0].tt) / step
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if u < 0 || u > float64(len(nodes)-1) {
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return [3]float64{}, [3]float64{}, false
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}
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start := int(math.Floor(u)) - 2
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if start < 0 {
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start = 0
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}
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if start > len(nodes)-interpolationPoints {
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start = len(nodes) - interpolationPoints
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}
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var weights [interpolationPoints]float64
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for point := 0; point < interpolationPoints; point++ {
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x := float64(start + point)
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weight := 1.0
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for other := 0; other < interpolationPoints; other++ {
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if other == point {
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continue
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}
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xOther := float64(start + other)
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weight *= (u - xOther) / (x - xOther)
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}
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weights[point] = weight
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}
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var first, next [3]float64
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for coordinate := 0; coordinate < 3; coordinate++ {
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for point := 0; point < interpolationPoints; point++ {
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first[coordinate] += weights[point] * nodes[start+point].first[coordinate]
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next[coordinate] += weights[point] * nodes[start+point].next[coordinate]
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}
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}
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return first, next, finiteVector3(first) && finiteVector3(next)
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}
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func finiteVector3(value [3]float64) bool {
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return finite(value[0]) && finite(value[1]) && finite(value[2])
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}
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func occultationPathVectorRaDec(vector occultationPathVector) (float64, float64, float64, bool) {
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distance := occultationPathNorm(vector)
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if !finite(distance) || distance <= 0 {
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return 0, 0, 0, false
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}
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ra := math.Atan2(vector.y, vector.x) / rad
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dec := math.Asin(math.Max(-1, math.Min(1, vector.z/distance))) / rad
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return ra, dec, distance, finite(ra) && finite(dec)
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}
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type solarEclipseLocalEphemeris struct {
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nodes []localEphemerisVectorNode
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}
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func newSolarEclipseLocalEphemeris(center float64) *solarEclipseLocalEphemeris {
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half := solarLocalEphemerisNodeCount / 2
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nodes := make([]localEphemerisVectorNode, solarLocalEphemerisNodeCount)
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for index := range nodes {
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tt := center + float64(index-half)*solarLocalEphemerisStepDays
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sun, moon := solarEclipseSunMoonEquatorial(tt)
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nodes[index] = localEphemerisVectorNode{
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tt: tt,
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first: solarEclipseLLRToXYZ(sun[0], sun[1], sun[2]),
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next: solarEclipseLLRToXYZ(moon[0], moon[1], moon[2]),
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}
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}
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return &solarEclipseLocalEphemeris{nodes: nodes}
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}
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func (ephemeris *solarEclipseLocalEphemeris) equatorialAt(tt float64) ([3]float64, [3]float64, bool) {
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var empty [3]float64
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if ephemeris == nil {
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return empty, empty, false
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}
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sunXYZ, moonXYZ, ok := interpolateLocalEphemerisVectors(ephemeris.nodes, tt)
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if !ok {
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return empty, empty, false
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}
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return solarEclipseXYZToLLR(sunXYZ[0], sunXYZ[1], sunXYZ[2]),
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solarEclipseXYZToLLR(moonXYZ[0], moonXYZ[1], moonXYZ[2]), true
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}
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type starOccultationLocalEphemeris struct {
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star StarCoordinate
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nodes []localEphemerisVectorNode
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dense bool
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}
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func newStarOccultationLocalEphemeris(center float64, star StarCoordinate) *starOccultationLocalEphemeris {
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half := occultationLocalEphemerisNodeCount / 2
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nodes := make([]localEphemerisVectorNode, occultationLocalEphemerisNodeCount)
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for index := range nodes {
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tt := center + float64(index-half)*occultationLocalEphemerisStepDays
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state := starOccultationEphemerisStateAt(tt, star)
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moon := occultationPathRaDecVector(state.moonRA, state.moonDec, state.moonDistanceKM)
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targetDistance := state.starDistanceKM
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if targetDistance <= 0 {
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// 恒星距离未知时只需方向：按单位球方向装配，几何只用归一化后的矢量。
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targetDistance = 1
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}
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target := occultationPathRaDecVector(state.starRA, state.starDec, targetDistance)
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nodes[index] = localEphemerisVectorNode{
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tt: tt,
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first: [3]float64{moon.x, moon.y, moon.z},
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next: [3]float64{target.x, target.y, target.z},
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}
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}
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return &starOccultationLocalEphemeris{star: star, nodes: nodes}
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}
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func (ephemeris *starOccultationLocalEphemeris) stateAt(tt float64) (starOccultationEphemerisState, bool) {
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moonXYZ, targetXYZ, ok := ephemeris.vectorsAt(tt)
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if !ok {
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return starOccultationEphemerisState{}, false
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}
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moonRA, moonDec, moonDistance, moonOK := occultationPathVectorRaDec(occultationPathVector{
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x: moonXYZ[0], y: moonXYZ[1], z: moonXYZ[2],
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})
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targetRA, targetDec, _, targetOK := occultationPathVectorRaDec(occultationPathVector{
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x: targetXYZ[0], y: targetXYZ[1], z: targetXYZ[2],
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})
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if !moonOK || !targetOK {
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return starOccultationEphemerisState{}, false
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}
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return starOccultationEphemerisState{
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moonRA: moonRA, moonDec: moonDec, moonDistanceKM: moonDistance,
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starRA: targetRA, starDec: targetDec, starDistanceKM: ephemeris.starDistanceKM(),
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valid: true,
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}, true
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}
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func (ephemeris *starOccultationLocalEphemeris) vectorsAt(tt float64) ([3]float64, [3]float64, bool) {
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if ephemeris == nil {
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return [3]float64{}, [3]float64{}, false
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}
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if ephemeris.dense {
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return interpolateDenseOccultationVectors(ephemeris.nodes, tt)
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}
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return interpolateLocalEphemerisVectors(ephemeris.nodes, tt)
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}
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func (ephemeris *starOccultationLocalEphemeris) starDistanceKM() float64 {
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if ephemeris.star.ParallaxMas <= 0 {
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return 0
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}
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return 206264806.247 / ephemeris.star.ParallaxMas * occultationPathAstronomicalUnitKM
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}
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type planetOccultationLocalEphemeris struct {
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nodes []localEphemerisVectorNode
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dense bool
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}
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func newPlanetOccultationLocalEphemeris(center float64, config planetOccultationConfig) *planetOccultationLocalEphemeris {
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half := occultationLocalEphemerisNodeCount / 2
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nodes := make([]localEphemerisVectorNode, occultationLocalEphemerisNodeCount)
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for index := range nodes {
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tt := center + float64(index-half)*occultationLocalEphemerisStepDays
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state := planetOccultationEphemerisStateAt(tt, config)
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moon := occultationPathRaDecVector(state.moonRA, state.moonDec, state.moonDistanceKM)
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target := occultationPathRaDecVector(state.planetRA, state.planetDec, state.planetDistanceKM)
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nodes[index] = localEphemerisVectorNode{
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tt: tt,
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first: [3]float64{moon.x, moon.y, moon.z},
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next: [3]float64{target.x, target.y, target.z},
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}
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}
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return &planetOccultationLocalEphemeris{nodes: nodes}
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}
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func (ephemeris *planetOccultationLocalEphemeris) stateAt(tt float64) (planetOccultationEphemerisState, bool) {
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moonXYZ, targetXYZ, ok := ephemeris.vectorsAt(tt)
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if !ok {
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return planetOccultationEphemerisState{}, false
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}
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moonRA, moonDec, moonDistance, moonOK := occultationPathVectorRaDec(occultationPathVector{
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x: moonXYZ[0], y: moonXYZ[1], z: moonXYZ[2],
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})
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targetRA, targetDec, planetDistance, targetOK := occultationPathVectorRaDec(occultationPathVector{
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x: targetXYZ[0], y: targetXYZ[1], z: targetXYZ[2],
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})
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if !moonOK || !targetOK {
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return planetOccultationEphemerisState{}, false
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}
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return planetOccultationEphemerisState{
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moonRA: moonRA, moonDec: moonDec, moonDistanceKM: moonDistance,
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planetRA: targetRA, planetDec: targetDec, planetDistanceKM: planetDistance,
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valid: true,
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}, true
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}
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func (ephemeris *planetOccultationLocalEphemeris) vectorsAt(tt float64) ([3]float64, [3]float64, bool) {
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if ephemeris == nil {
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return [3]float64{}, [3]float64{}, false
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}
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if ephemeris.dense {
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return interpolateDenseOccultationVectors(ephemeris.nodes, tt)
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}
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return interpolateLocalEphemerisVectors(ephemeris.nodes, tt)
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}
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