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_planet_projection_test.go

@@ -0,0 +1,47 @@
+package basic
+
+import (
+	"math"
+	"testing"
+	"time"
+)
+
+func TestMars20250729FiniteContactContoursRespectWebMercatorSpacing(t *testing.T) {
+	zone := time.FixedZone("UTC+8", 8*60*60)
+	start := time.Date(2025, time.July, 29, 0, 0, 0, 0, zone)
+	paths, err := FindPlanetOccultationPaths(start, start.Add(24*time.Hour), OccultationMars, OccultationPathOptions{
+		Step: 20 * time.Minute, TargetSpacingKM: 900, RiseSetStep: time.Minute,
+		DisableFootprints: true, IncludeFootprintTimeline: true, FootprintTimelineStep: 5 * time.Minute,
+	})
+	if err != nil || len(paths) != 1 {
+		t.Fatalf("FindPlanetOccultationPaths() paths=%d err=%v, want one", len(paths), err)
+	}
+	for _, item := range []struct {
+		name     string
+		contours [][]OccultationPathPoint
+	}{
+		{name: "partial", contours: paths[0].PartialBandContours},
+		{name: "total", contours: paths[0].TotalBandContours},
+	} {
+		for contourIndex, contour := range item.contours {
+			for pointIndex := 1; pointIndex < len(contour); pointIndex++ {
+				spacing := webMercatorGeoPointSpacingKM(contour[pointIndex-1], contour[pointIndex])
+				if spacing > 45 {
+					t.Fatalf("%s contour %d edge %d has %.1f km Web Mercator spacing, want <=45 km", item.name, contourIndex, pointIndex, spacing)
+				}
+			}
+		}
+	}
+}
+
+func webMercatorGeoPointSpacingKM(first, second OccultationPathPoint) float64 {
+	const maxLatitude = 85.05112878
+	const radiusKM = 6378.1366
+	clamp := func(value float64) float64 { return math.Max(-maxLatitude, math.Min(maxLatitude, value)) }
+	longitude := math.Remainder(second.Longitude-first.Longitude, 360) * math.Pi / 180
+	firstLatitude := clamp(first.Latitude) * math.Pi / 180
+	secondLatitude := clamp(second.Latitude) * math.Pi / 180
+	firstY := math.Log(math.Tan(math.Pi/4 + firstLatitude/2))
+	secondY := math.Log(math.Tan(math.Pi/4 + secondLatitude/2))
+	return radiusKM * math.Hypot(longitude, secondY-firstY)
+}