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

internal/occultationgeo/curve_sampling.go

@@ -0,0 +1,105 @@
+package occultationgeo
+
+import (
+	"math"
+	"time"
+
+	"b612.me/astro/basic"
+	"b612.me/astro/internal/geodata"
+)
+
+const defaultRiseSetProjectedSpacingKM = 35.0
+
+// DensifyRiseSetCurves 按投影距离插入大地线样本，且不改变端点和分支拓扑。
+// DensifyRiseSetCurves inserts geodesic samples using the projected distance
+// consumed by map renderers. Rise/set solvers intentionally use a coarser time
+// step for performance; using those raw vertices as SVG/GeoJSON linework makes
+// high-latitude curves visibly angular even when the physical path is smooth.
+// Endpoints, phase, direction, and segment topology are preserved exactly.
+func DensifyRiseSetCurves(
+	curves []basic.OccultationRiseSetCurve,
+	maximumProjectedSpacingKM float64,
+) []basic.OccultationRiseSetCurve {
+	if len(curves) == 0 || maximumProjectedSpacingKM <= 0 {
+		return curves
+	}
+	result := make([]basic.OccultationRiseSetCurve, len(curves))
+	for curveIndex, curve := range curves {
+		result[curveIndex] = basic.OccultationRiseSetCurve{
+			Phase: curve.Phase, Direction: curve.Direction,
+			Segments: make([][]basic.OccultationPathPoint, len(curve.Segments)),
+		}
+		for segmentIndex, segment := range curve.Segments {
+			result[curveIndex].Segments[segmentIndex] = densifyRiseSetSegment(segment, maximumProjectedSpacingKM)
+		}
+	}
+	return result
+}
+
+// DensifyOccultationPathPoints 将相同的投影感知间距应用于单条月掩路径。
+// DensifyOccultationPathPoints applies the same projection-aware spacing to a
+// standalone geographic line such as a horizon connector. It keeps both
+// endpoints and does not attach phase metadata to the result.
+func DensifyOccultationPathPoints(
+	points []basic.OccultationPathPoint,
+	maximumProjectedSpacingKM float64,
+) []basic.OccultationPathPoint {
+	return densifyRiseSetSegment(points, maximumProjectedSpacingKM)
+}
+
+func densifyRiseSetSegment(
+	segment []basic.OccultationPathPoint,
+	maximumProjectedSpacingKM float64,
+) []basic.OccultationPathPoint {
+	if len(segment) < 2 {
+		return append([]basic.OccultationPathPoint(nil), segment...)
+	}
+	result := make([]basic.OccultationPathPoint, 0, len(segment)*2)
+	// The interpolation is geodesic on the sphere, while the spacing check is
+	// made in Web Mercator.  A chord that is exactly at the projected limit can
+	// grow slightly after interpolation because Mercator is nonlinear in
+	// latitude.  Keep a small margin so the emitted linework stays below the
+	// requested limit after projection.
+	effectiveSpacingKM := maximumProjectedSpacingKM * 0.75
+	for index, point := range segment {
+		result = append(result, point)
+		if index+1 >= len(segment) {
+			continue
+		}
+		next := segment[index+1]
+		steps := int(math.Ceil(projectedGeoPointDistanceKM(point, next) / effectiveSpacingKM))
+		if steps < 2 {
+			continue
+		}
+		for step := 1; step < steps; step++ {
+			fraction := float64(step) / float64(steps)
+			middle := interpolateOccultationGeoPoint(
+				geodata.GeoPoint{Longitude: point.Longitude, Latitude: point.Latitude},
+				geodata.GeoPoint{Longitude: next.Longitude, Latitude: next.Latitude},
+				fraction,
+			)
+			result = append(result, basic.OccultationPathPoint{
+				Time:         point.Time.Add(time.Duration(float64(next.Time.Sub(point.Time)) * fraction)),
+				Longitude:    middle.Longitude,
+				Latitude:     middle.Latitude,
+				MoonAltitude: point.MoonAltitude + (next.MoonAltitude-point.MoonAltitude)*fraction,
+				WidthKM:      point.WidthKM + (next.WidthKM-point.WidthKM)*fraction,
+			})
+		}
+	}
+	return result
+}
+
+func projectedGeoPointDistanceKM(first, second basic.OccultationPathPoint) float64 {
+	const maxLatitude = 85.05112878
+	const radiusKM = 6378.1366
+	clampLatitude := func(value float64) float64 {
+		return math.Max(-maxLatitude, math.Min(maxLatitude, value))
+	}
+	longitude := math.Remainder(second.Longitude-first.Longitude, 360) * math.Pi / 180
+	firstLatitude := clampLatitude(first.Latitude) * math.Pi / 180
+	secondLatitude := clampLatitude(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)
+}