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

eclipse/svg/lunar_map_polar_test.go

@@ -0,0 +1,70 @@
+package svg
+
+import (
+	"testing"
+	"time"
+
+	"b612.me/astro/basic"
+	eclipsecore "b612.me/astro/eclipse"
+	"b612.me/astro/internal/svgmap"
+)
+
+// TestLunarEclipseMapSVGPolarWitnessStaysOutsideEquirectangularVisibility 固定全球月食地图在
+// 极区的可见性契约。等距圆柱投影在高纬把经度拉伸：1° 的球面地平弧在极点附近可以横跨近
+// 180° 经度，只连端点就会把地平线以外画进可见区。1904-09-24 的 P1 在南极点附近有一个
+// 月心高度约 −0.05° 的见证点，曾经被画进 visible-at-p1 多边形。
+// TestLunarEclipseMapSVGPolarWitnessStaysOutsideEquirectangularVisibility pins the polar
+// visibility contract of the global lunar-eclipse map. Equirectangular projection stretches
+// longitude near a pole: a 1-degree spherical horizon arc can span almost 180 degrees there, so
+// joining endpoints alone paints sky below the horizon as visible. At P1 of 1904-09-24 a witness
+// near the south pole sits about 0.05 degrees below the Moon's horizon and used to be painted
+// inside the visible-at-p1 polygon.
+func TestLunarEclipseMapSVGPolarWitnessStaysOutsideEquirectangularVisibility(t *testing.T) {
+	date := time.Date(1904, 9, 24, 0, 0, 0, 0, time.UTC)
+	info, ok := eclipsecore.LunarEclipseOnDate(date)
+	if !ok {
+		t.Fatal("missing lunar eclipse")
+	}
+	frame := eclipseMapFrame(lunarEclipseMapDefaultWidth, lunarEclipseMapDefaultHeight,
+		svgmap.ProjectionEquirectangular, 142, 92)
+	path, boundary := lunarEclipseVisibilityPath(info.PenumbralStart, frame)
+	if len(boundary) == 0 {
+		t.Fatal("visibility path has no boundary")
+	}
+	rings := svgClosedPathRings(t, `<path d="`+path+`"/>`)
+	if len(rings) == 0 {
+		t.Fatal("visibility path has no rings")
+	}
+	jd := basic.Date2JDE(info.PenumbralStart)
+	// 只取足够深入地平线以下的见证点：−89.9° 处月心高度约 −0.054°，而更靠近极点的
+	// −89.99° 只有约 −0.004°，落在可见性判定本身的数值容差里，不能作为回归依据。
+	// Only a witness clearly below the horizon is used: at -89.9 degrees the Moon centre sits
+	// about 0.054 degrees down, while -89.99 degrees is only about 0.004 degrees down and lies
+	// inside the numerical tolerance of the visibility test itself.
+	witnesses := []struct {
+		longitude float64
+		latitude  float64
+	}{
+		{-115, -89.9},
+	}
+	for _, witness := range witnesses {
+		altitude := basic.HMoonHeight(jd, witness.longitude, witness.latitude, 0)
+		if altitude >= -0.01 {
+			// 见证点必须先确实是地平线以下，否则这个回归就失去意义。
+			t.Fatalf("witness (%g,%g) altitude=%g, want below the horizon",
+				witness.longitude, witness.latitude, altitude)
+		}
+		x, y, projectable := frame.Project(witness.longitude, witness.latitude)
+		if !projectable {
+			continue
+		}
+		inside := false
+		for _, ring := range rings {
+			inside = inside || pointInLunarVisibilityPolygon(x, y, ring)
+		}
+		if inside {
+			t.Fatalf("below-horizon witness (%g,%g) altitude=%g is painted inside the visible region",
+				witness.longitude, witness.latitude, altitude)
+		}
+	}
+}