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

geojson/lunar_visibility_ring_test.go

@@ -0,0 +1,80 @@
+package geojson_test
+
+import (
+	"encoding/json"
+	"math"
+	"testing"
+	"time"
+
+	"b612.me/astro/eclipse"
+	"b612.me/astro/geojson"
+)
+
+// TestLunarGeoJSONDropsAntimeridianSlivers 固定月食可见区的环卫生契约：日界线剪裁会在相邻
+// 世界各输出一次"全部顶点落在同一条子午线、平面面积只剩浮点噪声"的零宽薄片（实测
+// 1.8e-12 deg²，刚好越过共享剪裁器 1e-12 的零面积阈值），导出时必须在月食这一层丢弃，
+// 同时不能连带丢掉有面积的面。
+// TestLunarGeoJSONDropsAntimeridianSlivers pins the ring-hygiene contract of the lunar
+// visibility export: the antimeridian split emits one zero-width sliver per adjacent world whose
+// vertices all sit on one meridian with a planar area of floating-point noise (measured
+// 1.8e-12 deg^2, just past the shared splitter's 1e-12 zero-area floor). The lunar export must
+// drop it without dropping polygons that do have area.
+func TestLunarGeoJSONDropsAntimeridianSlivers(t *testing.T) {
+	for _, day := range []string{"2022-11-08", "2026-03-03", "4026-03-16", "1904-09-24", "2025-03-14"} {
+		t.Run(day, func(t *testing.T) {
+			date, err := time.Parse("2006-01-02", day)
+			if err != nil {
+				t.Fatal(err)
+			}
+			info, ok := eclipse.LunarEclipseOnDate(date)
+			if !ok {
+				t.Fatal("missing lunar eclipse")
+			}
+			data, err := geojson.MarshalLunarEclipse(info, 360)
+			if err != nil {
+				t.Fatal(err)
+			}
+			collection := decodeCollection(t, data)
+			for _, role := range []string{"visible-at-p1", "visible-at-p4"} {
+				feature := featureWithRole(t, collection, role)
+				var polygons [][][][]float64
+				if err := json.Unmarshal(feature.Geometry.Coordinates, &polygons); err != nil {
+					t.Fatal(err)
+				}
+				if len(polygons) == 0 {
+					t.Fatalf("%s has no polygons", role)
+				}
+				for index, polygon := range polygons {
+					area := 0.0
+					for _, ring := range polygon {
+						if len(ring) < 4 {
+							t.Fatalf("%s polygon %d ring has %d positions", role, index, len(ring))
+						}
+						distinct := 0
+						for position, point := range ring {
+							if position == 0 || math.Abs(point[0]-ring[position-1][0]) > 1e-9 ||
+								math.Abs(point[1]-ring[position-1][1]) > 1e-9 {
+								distinct++
+							}
+						}
+						if distinct > 1 &&
+							math.Abs(ring[0][0]-ring[len(ring)-1][0]) <= 1e-9 &&
+							math.Abs(ring[0][1]-ring[len(ring)-1][1]) <= 1e-9 {
+							// 闭合点不是独立顶点 / The closing position is not a distinct vertex.
+							distinct--
+						}
+						if distinct < 3 {
+							t.Fatalf("%s polygon %d is a zero-width sliver: %v", role, index, ring)
+						}
+						for position := 0; position+1 < len(ring); position++ {
+							area += ring[position][0]*ring[position+1][1] - ring[position+1][0]*ring[position][1]
+						}
+					}
+					if math.Abs(area/2) < 1e-12 {
+						t.Fatalf("%s polygon %d has no area: %v", role, index, polygon)
+					}
+				}
+			}
+		})
+	}
+}