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

basic/occultation_path_test.go

@@ -0,0 +1,82 @@
+package basic
+
+import (
+	"testing"
+	"time"
+)
+
+// 稠密星历表必须被接受并覆盖完整的路径搜索窗口，否则路径样本会静默退回精确星历。
+func TestDenseOccultationTableCoversPathSearchWindow(t *testing.T) {
+	center := occultationTimeToTT(time.Date(2025, time.January, 5, 12, 0, 0, 0, time.UTC))
+	const toleranceDays = 1e-9
+	for _, planet := range []OccultationPlanet{
+		OccultationMercury, OccultationVenus, OccultationMars, OccultationJupiter,
+		OccultationSaturn, OccultationUranus, OccultationNeptune,
+	} {
+		config, ok := planetOccultationConfigFor(planet)
+		if !ok {
+			t.Fatalf("%s occultation config is unavailable", planet)
+		}
+		cache := newPlanetOccultationEventCache(config)
+		cache.preparePathEphemeris(center, OccultationPathAlgorithmOptimized)
+		if !cache.local.dense {
+			t.Fatalf("%s dense path table was rejected", planet)
+		}
+		nodes := cache.local.nodes
+		if len(nodes) < 2 {
+			t.Fatalf("%s dense path table has %d nodes", planet, len(nodes))
+		}
+		if first := center - occultationPathSearchSpanDays; nodes[0].tt > first+toleranceDays {
+			t.Fatalf("%s dense table starts at %.9f, want at most %.9f", planet, nodes[0].tt, first)
+		}
+		if last := center + occultationPathSearchSpanDays; nodes[len(nodes)-1].tt < last-toleranceDays {
+			t.Fatalf("%s dense table ends at %.9f, want at least %.9f", planet, nodes[len(nodes)-1].tt, last)
+		}
+		// 节点时刻是 JD 浮点相加的结果，相邻差只近似等于步长（约 1e-10 天）。
+		if step := nodes[1].tt - nodes[0].tt; step < occultationDenseEphemerisStepDays-1e-8 ||
+			step > occultationDenseEphemerisStepDays+1e-8 {
+			t.Fatalf("%s dense table step=%g, want %g", planet, step, occultationDenseEphemerisStepDays)
+		}
+	}
+}
+
+func BenchmarkOccultationPlanetPathsMars20250729(b *testing.B) {
+	zone := time.FixedZone("UTC+8", 8*3600)
+	start := time.Date(2025, time.July, 29, 0, 0, 0, 0, zone)
+	options := OccultationPathOptions{
+		Step: 20 * time.Minute, TargetSpacingKM: 900, RiseSetStep: time.Minute,
+		DisableFootprints: true, IncludeFootprintTimeline: true, FootprintTimelineStep: 5 * time.Minute,
+	}
+	b.ReportAllocs()
+	b.ResetTimer()
+	for index := 0; index < b.N; index++ {
+		paths, err := FindPlanetOccultationPaths(start, start.Add(24*time.Hour), OccultationMars, options)
+		if err != nil || len(paths) != 1 {
+			b.Fatalf("paths=%d err=%v", len(paths), err)
+		}
+	}
+}
+
+func BenchmarkOccultationPlanetPathsSaturnDefault(b *testing.B) {
+	start := time.Date(2024, time.August, 21, 0, 0, 0, 0, time.UTC)
+	b.ReportAllocs()
+	b.ResetTimer()
+	for index := 0; index < b.N; index++ {
+		paths, err := FindPlanetOccultationPaths(start, start.Add(24*time.Hour), OccultationSaturn, OccultationPathOptions{})
+		if err != nil || len(paths) != 1 {
+			b.Fatalf("paths=%d err=%v", len(paths), err)
+		}
+	}
+}
+
+func BenchmarkOccultationPathLimitsAndWidth(b *testing.B) {
+	config, _ := planetOccultationConfigFor(OccultationSaturn)
+	cache := newPlanetOccultationEventCache(config)
+	tt := occultationTimeToTT(time.Date(2025, time.January, 5, 4, 0, 0, 0, time.UTC))
+	cache.preparePathEphemeris(tt, OccultationPathAlgorithmOptimized)
+	b.ReportAllocs()
+	b.ResetTimer()
+	for index := 0; index < b.N; index++ {
+		_, _, _, _ = occultationPathLimitsAndWidthForFrame(tt, cache.outerFrameAt)
+	}
+}