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

moon/svg/occultation_band_cache.go

@@ -0,0 +1,120 @@
+package svg
+
+import (
+	"math"
+	"sync"
+
+	"b612.me/astro/internal/geodata"
+	"b612.me/astro/moon"
+)
+
+// occultationBandPolygons 是一次紧凑掩带合并的只读结果。
+type occultationBandPolygons struct {
+	polygons      [][]geodata.GeoPoint
+	authoritative bool
+}
+
+type occultationBandCacheKey struct {
+	kind   occultationFootprintSweepKind
+	digest [2]uint64
+}
+
+// occultationBandCacheCapacity 限制常驻的合并结果数量；掩带多边形可能上万点。
+const occultationBandCacheCapacity = 6
+
+var occultationBandCache = struct {
+	sync.RWMutex
+	entries map[occultationBandCacheKey]occultationBandPolygons
+	order   []occultationBandCacheKey
+}{entries: make(map[occultationBandCacheKey]occultationBandPolygons, occultationBandCacheCapacity)}
+
+func lookupOccultationBandPolygons(key occultationBandCacheKey) (occultationBandPolygons, bool) {
+	occultationBandCache.RLock()
+	value, ok := occultationBandCache.entries[key]
+	occultationBandCache.RUnlock()
+	return value, ok
+}
+
+func storeOccultationBandPolygons(key occultationBandCacheKey, value occultationBandPolygons) {
+	occultationBandCache.Lock()
+	defer occultationBandCache.Unlock()
+	if _, exists := occultationBandCache.entries[key]; exists {
+		return
+	}
+	if len(occultationBandCache.order) >= occultationBandCacheCapacity {
+		delete(occultationBandCache.entries, occultationBandCache.order[0])
+		occultationBandCache.order = occultationBandCache.order[1:]
+	}
+	occultationBandCache.entries[key] = value
+	occultationBandCache.order = append(occultationBandCache.order, key)
+}
+
+// occultationBandDigest 汇总合并的全部输入；按 64 位字混合而不是逐字节，摘要成本必须远低于合并本身。
+func occultationBandDigest(s occultationFootprintSweep) [2]uint64 {
+	const (
+		seed1 = 0x9e3779b97f4a7c15
+		seed2 = 0xc2b2ae3d27d4eb4f
+		prime = 0x100000001b3
+	)
+	first, second := uint64(seed1), uint64(seed2)
+	write := func(value uint64) {
+		first = (first ^ value) * prime
+		first ^= first >> 31
+		second = (second + value) * prime
+		second ^= second >> 33
+	}
+	writeFloat := func(value float64) { write(math.Float64bits(value)) }
+	writeTime := func(value int64) { write(uint64(value)) }
+	writePoint := func(point moon.OccultationPathPoint) {
+		writeTime(point.Time.UnixNano())
+		writeFloat(point.Longitude)
+		writeFloat(point.Latitude)
+		writeFloat(point.MoonAltitude)
+		writeFloat(point.WidthKM)
+		writeFloat(point.LimitSeparationKM)
+	}
+	writePolygons := func(polygons [][]moon.OccultationPathPoint) {
+		write(uint64(len(polygons)))
+		for _, polygon := range polygons {
+			write(uint64(len(polygon)))
+			for _, point := range polygon {
+				writePoint(point)
+			}
+		}
+	}
+	writeString := func(value string) {
+		write(uint64(len(value)))
+		for index := 0; index < len(value); index++ {
+			write(uint64(value[index]))
+		}
+	}
+	writeFootprints := func(footprints []moon.PlanetOccultationFootprint) {
+		write(uint64(len(footprints)))
+		for _, footprint := range footprints {
+			writeTime(footprint.Time.UnixNano())
+			writePolygons(footprint.Polygons)
+			writePolygons(footprint.InteriorPolygons)
+			writePolygons(footprint.Boundaries)
+			if footprint.Closed {
+				write(1)
+			} else {
+				write(0)
+			}
+		}
+	}
+	writeCurves := func(curves []moon.OccultationRiseSetCurve) {
+		write(uint64(len(curves)))
+		for _, curve := range curves {
+			writeString(string(curve.Phase))
+			writeString(string(curve.Direction))
+			writePolygons(curve.Segments)
+		}
+	}
+	write(uint64(s.kind))
+	writeFootprints(s.footprints)
+	writePolygons(s.contours)
+	writePolygons(s.visibilityContours)
+	writePolygons([][]moon.OccultationPathPoint{s.northern, s.southern})
+	writeCurves(s.curves)
+	return [2]uint64{first, second}
+}