feat: 完善水星与金星全球凌日搜索及制图导出

- 基于平均下合周期与节点相位预筛候选，减少无效星历计算；跳过无法求解的单个会合周期，避免有限覆盖星历导致搜索提前终止
- 引入影轴 γ、半影半径及地球尺度几何判定，结合站心可见性识别地心无接触、仅部分地区可见的掠凌
- 添加金星 243 年、水星 46 年周期族编号，并明确编号适用范围及未分配时的零值语义
- 为 SVG、GeoJSON 和 KML 增加站心部分凌日可见区，适配接触等时线、几何元数据、图层样式及取景；为地心无接触凌日事件增加正射图，按可见区球面面积加权居中

eclipse/svg/transit_partial.go

@@ -0,0 +1,94 @@
+package svg
+
+import (
+	"fmt"
+	"math"
+	"strings"
+
+	"b612.me/astro/basic"
+	"b612.me/astro/internal/svgmap"
+)
+
+func transitMapOrthographicCenter(transit basic.PlanetTransitResult) svgmap.GeoPoint {
+	if !transit.HasExternal {
+		if center, ok := transitMapVisibilityCenter(basic.PlanetTransitVisibilityColumns(transit)); ok {
+			return center
+		}
+	}
+	return solarEclipseSubsolarPoint(transitMapContactsOf(transit).greatest)
+}
+
+func transitMapVisibilityCenter(columns []basic.PlanetTransitVisibilityColumn) (svgmap.GeoPoint, bool) {
+	var momentX, momentY, momentZ float64
+	for index, column := range columns {
+		weight := 0.0
+		if index > 0 {
+			weight += (column.Longitude - columns[index-1].Longitude) / 2
+		}
+		if index+1 < len(columns) {
+			weight += (columns[index+1].Longitude - column.Longitude) / 2
+		}
+		longitude := column.Longitude * math.Pi / 180
+		for _, interval := range column.Intervals {
+			lower, upper := interval[0]*math.Pi/180, interval[1]*math.Pi/180
+			horizontalMoment := (upper-lower)/2 + (math.Sin(2*upper)-math.Sin(2*lower))/4
+			verticalMoment := (math.Sin(upper)*math.Sin(upper) - math.Sin(lower)*math.Sin(lower)) / 2
+			momentX += weight * horizontalMoment * math.Cos(longitude)
+			momentY += weight * horizontalMoment * math.Sin(longitude)
+			momentZ += weight * verticalMoment
+		}
+	}
+	if math.Sqrt(momentX*momentX+momentY*momentY+momentZ*momentZ) < 1e-12 {
+		return svgmap.GeoPoint{}, false
+	}
+	return svgmap.GeoPoint{
+		Longitude: math.Atan2(momentY, momentX) * 180 / math.Pi,
+		Latitude:  math.Atan2(momentZ, math.Hypot(momentX, momentY)) * 180 / math.Pi,
+	}, true
+}
+
+func transitMapProjectionLabel(projection svgmap.Projection, hasExternal bool, language string) string {
+	if projection != svgmap.ProjectionOrthographic {
+		return eclipseMapProjectionLabel(projection, language)
+	}
+	if language == "en" {
+		center := "the subsolar point at greatest"
+		if !hasExternal {
+			center = "the topocentric visible footprint"
+		}
+		return "Orthographic globe projection, centred on " + center + "; one hemisphere only"
+	}
+	center := "凌甚太阳直射点"
+	if !hasExternal {
+		center = "站心可见区中心"
+	}
+	return "正射球面投影，视点取" + center + "，只画朝向视点的半个地球"
+}
+
+func writeTransitMapPartialRegions(builder *strings.Builder, frame svgmap.Frame, transit basic.PlanetTransitResult) {
+	fmt.Fprintf(builder, `<g class="transit-visibility-regions" data-source="%s" clip-path="url(#transit-map-clip)">`, eclipseMapSourceTransitPartialVisibility)
+	var path strings.Builder
+	for _, polygon := range basic.PlanetTransitVisibilityPolygons(transit) {
+		points := make([]svgmap.GeoPoint, len(polygon))
+		for index, point := range polygon {
+			points[index] = svgmap.GeoPoint{Longitude: point.Longitude, Latitude: point.Latitude}
+		}
+		path.WriteString(lunarEclipseGeoPolygonPath(points, frame))
+	}
+	if path.Len() > 0 {
+		fmt.Fprintf(builder, `<path class="transit-partial-region" d="%s" fill="%s" fill-opacity="%.2f" fill-rule="nonzero"/>`, path.String(), transitMapColorPartial, transitMapPartialFillOpacity)
+	}
+	builder.WriteString(`</g>`)
+}
+
+func transitMapGeometryNote(transit basic.PlanetTransitResult, language string) string {
+	text := fmt.Sprintf("γ %.4f", transit.Gamma)
+	if transit.Series.Number != 0 {
+		if language == "en" {
+			text += fmt.Sprintf(" | Series %d (%d yr)", transit.Series.Number, transit.Series.PeriodYears)
+		} else {
+			text += fmt.Sprintf(" | 周期族 %d（%d 年）", transit.Series.Number, transit.Series.PeriodYears)
+		}
+	}
+	return text
+}