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_instant_test.go

@@ -0,0 +1,72 @@
+package basic
+
+import (
+	"errors"
+	"testing"
+	"time"
+)
+
+func TestPlanetOccultationFootprintsAtReturnsExactRequestedInstant(t *testing.T) {
+	start := time.Date(2025, time.January, 5, 0, 0, 0, 0, time.FixedZone("UTC+8", 8*60*60))
+	events, err := FindBestPlanetOccultations(
+		start, start.Add(24*time.Hour), OccultationSaturn, OccultationSearchOptions{MaxEvents: 1},
+	)
+	if err != nil || len(events) != 1 {
+		t.Fatalf("FindBestPlanetOccultations events=%d err=%v, want one", len(events), err)
+	}
+	at := events[0].Greatest.Add(123 * time.Nanosecond)
+	instant, err := PlanetOccultationFootprintsAt(at, OccultationSaturn)
+	if err != nil {
+		t.Fatalf("PlanetOccultationFootprintsAt: %v", err)
+	}
+	if instant.Partial == nil || instant.Total == nil {
+		t.Fatalf("instant footprints partial=%v total=%v, want both", instant.Partial != nil, instant.Total != nil)
+	}
+	for name, footprint := range map[string]*OccultationFootprint{
+		"partial": instant.Partial,
+		"total":   instant.Total,
+	} {
+		if !footprint.Time.Equal(at) {
+			t.Fatalf("%s footprint time=%v, want %v", name, footprint.Time, at)
+		}
+		if len(footprint.Polygons) == 0 || len(footprint.Boundaries) == 0 {
+			t.Fatalf("%s footprint has no visible geometry", name)
+		}
+		for _, boundary := range footprint.Boundaries {
+			for _, point := range boundary {
+				if !point.Time.Equal(at) {
+					t.Fatalf("%s boundary time=%v, want %v", name, point.Time, at)
+				}
+			}
+		}
+	}
+}
+
+func TestStarOccultationFootprintAtReturnsEmptyOutsideEvent(t *testing.T) {
+	star := StarCoordinate{
+		ID: "Antares", RA: 247.35166667, Dec: -26.43194444,
+		Epoch: time.Date(2000, time.January, 1, 12, 0, 0, 0, time.UTC),
+		Frame: CoordinateFrameJ2000,
+	}
+	instant, err := StarOccultationFootprintAt(
+		time.Date(2024, time.March, 1, 17, 0, 0, 0, time.UTC), star,
+	)
+	if err != nil {
+		t.Fatalf("StarOccultationFootprintAt: %v", err)
+	}
+	if instant.Footprint != nil {
+		t.Fatal("outside-event stellar footprint is not nil")
+	}
+}
+
+func TestOccultationFootprintAtValidatesInputs(t *testing.T) {
+	if _, err := PlanetOccultationFootprintsAt(time.Time{}, OccultationSaturn); !errors.Is(err, ErrInvalidOccultationInput) {
+		t.Fatalf("zero time error=%v, want ErrInvalidOccultationInput", err)
+	}
+	if _, err := PlanetOccultationFootprintsAt(time.Now(), OccultationPlanet("earth")); !errors.Is(err, ErrInvalidOccultationInput) {
+		t.Fatalf("invalid planet error=%v, want ErrInvalidOccultationInput", err)
+	}
+	if _, err := StarOccultationFootprintAt(time.Now(), StarCoordinate{}); !errors.Is(err, ErrInvalidOccultationInput) {
+		t.Fatalf("invalid star error=%v, want ErrInvalidOccultationInput", err)
+	}
+}