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_station_envelope.go

@@ -0,0 +1,78 @@
+package basic
+
+import (
+	"math"
+	"time"
+)
+
+// occultationStationDensifyContours applies the map's projection metric after
+// station correction. The correction can move adjacent geocentric samples by
+// tens of kilometres, so a contour that was dense before correction can still
+// contain a long Web Mercator chord. A spatial arclength plane selects the
+// midpoint branch even where time reverses and a fixed-time solve is singular.
+// The refined curve is split again at time folds for the public time contract.
+func occultationStationDensifyContours(
+	contours [][]OccultationPathPoint,
+	cache *occultationRiseSetEvaluationCache,
+	location *time.Location,
+) [][]OccultationPathPoint {
+	if len(contours) == 0 || cache == nil {
+		return contours
+	}
+	const (
+		targetSpacingKM = 30.0
+		maxDepth        = 10
+	)
+	result := make([][]OccultationPathPoint, 0, len(contours))
+	for _, contour := range contours {
+		if len(contour) < 2 {
+			continue
+		}
+		var refine func(OccultationPathPoint, OccultationPathPoint, int, *[]OccultationPathPoint)
+		refine = func(start, end OccultationPathPoint, depth int, output *[]OccultationPathPoint) {
+			if depth >= maxDepth || occultationStationProjectedSpacingKM(start, end) <= targetSpacingKM {
+				*output = append(*output, end)
+				return
+			}
+			startTT, endTT := centerTimeTT(start.Time), centerTimeTT(end.Time)
+			chord := [3]float64{math.Remainder(end.Longitude-start.Longitude, 360), end.Latitude - start.Latitude,
+				(endTT - startTT) * occultationStationEnvelopeTimeScale}
+			length := math.Sqrt(dotSolarEclipse3(chord, chord))
+			if length <= 1e-12 {
+				*output = append(*output, end)
+				return
+			}
+			predictor := [3]float64{start.Longitude + chord[0]/2, start.Latitude + chord[1]/2, chord[2] / 2}
+			for index := range chord {
+				chord[index] /= length
+			}
+			midpoint, _, ok := occultationStationCorrectEnvelopeArc(predictor, chord, startTT, cache,
+				occultationStationEnvelopeModel{kind: occultationStationContactEnvelope}, (start.WidthKM+end.WidthKM)/2, location)
+			if ok && occultationPathDistanceKM(start, midpoint.point) < occultationPathDistanceKM(start, end) &&
+				occultationPathDistanceKM(midpoint.point, end) < occultationPathDistanceKM(start, end) {
+				refine(start, midpoint.point, depth+1, output)
+				refine(midpoint.point, end, depth+1, output)
+				return
+			}
+			// Leave a failed local solve untouched. Retrying with an unrelated
+			// branch would be less accurate than retaining the source sample.
+			*output = append(*output, end)
+		}
+		refined := []OccultationPathPoint{contour[0]}
+		for index := 1; index < len(contour); index++ {
+			refine(refined[len(refined)-1], contour[index], 0, &refined)
+		}
+		result = append(result, occultationStationSplitEnvelopeAtTimeFolds(refined)...)
+	}
+	return result
+}
+
+func occultationStationProjectedSpacingKM(first, second OccultationPathPoint) float64 {
+	const maxLatitude = 85.05112878
+	firstLatitude := math.Max(-maxLatitude, math.Min(maxLatitude, first.Latitude)) * rad
+	secondLatitude := math.Max(-maxLatitude, math.Min(maxLatitude, second.Latitude)) * rad
+	longitudeDelta := math.Remainder(second.Longitude-first.Longitude, 360) * rad
+	firstY := math.Log(math.Tan(math.Pi/4 + firstLatitude/2))
+	secondY := math.Log(math.Tan(math.Pi/4 + secondLatitude/2))
+	return 6378.1366 * math.Hypot(longitudeDelta, secondY-firstY)
+}