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

basic/planet_transit_geometry.go

@@ -0,0 +1,67 @@
+package basic
+
+import "math"
+
+const (
+	planetTransitEarthRadiusKM            = 6378.137
+	planetTransitEarthEccentricitySquared = 0.00669437999014
+)
+
+func planetTransitShadowGeometry(tt float64, cfg planetTransitConfig, inst *Instance) (float64, float64, Observer, bool) {
+	sunRA, sunDec := HSunApparentRaDecNWithInstance(tt, -1, inst)
+	planetRA, planetDec := cfg.apparentRaDecN(tt, -1)
+	sunDistance := EarthAwayNWithInstance(tt, -1, inst) * angularDiameterAstronomicalUnitKM
+	planetDistance := cfg.earthDistanceN(tt, -1) * angularDiameterAstronomicalUnitKM
+	sun := eclipticCartesian(sunRA, sunDec, sunDistance)
+	body := eclipticCartesian(planetRA, planetDec, planetDistance)
+	axis, length := pn(Vector3{body[0] - sun[0], body[1] - sun[1], body[2] - sun[2]})
+	projection := -(body[0]*axis[0] + body[1]*axis[1] + body[2]*axis[2])
+	impact := Vector3{body[0] + projection*axis[0], body[1] + projection*axis[1], body[2] + projection*axis[2]}
+	_, distance := pn(impact)
+	planetRadius := venusEquatorialRadiusKM
+	if cfg.planetIndex == 1 {
+		planetRadius = mercuryEquatorialRadiusKM
+	}
+	sine := (sunEquatorialRadiusKM + planetRadius) / length
+	cosine := math.Sqrt(1 - sine*sine)
+	penumbra := (planetRadius + projection*sine) / cosine / planetTransitEarthRadiusKM
+	gamma := math.Copysign(distance/planetTransitEarthRadiusKM, impact[2])
+	sidereal := ApparentSiderealTime(TT2UT1(tt)) * 15
+	seed := Observer{
+		Longitude: normalizeLongitude180(math.Atan2(impact[1], impact[0])*180/math.Pi - sidereal),
+		Latitude:  math.Atan2(impact[2], math.Hypot(impact[0], impact[1])*(1-planetTransitEarthEccentricitySquared)) * 180 / math.Pi,
+	}
+	possible := isFiniteFloat(gamma) && isFiniteFloat(penumbra) && projection > 0 && planetDistance < sunDistance && math.Abs(gamma) <= penumbra+1/cosine
+	return gamma, penumbra, seed, possible
+}
+
+func planetTransitSurfaceOverlap(transit PlanetTransitResult, seed Observer, inst *Instance) bool {
+	snapshot, ok := buildPlanetTransitSnapshot(transit, inst)
+	if !ok {
+		return false
+	}
+	best := math.Inf(1)
+	for step := 4.0; step > 0.0001; step /= 2 {
+		center := seed
+		for _, latitudeStep := range []float64{-step, 0, step} {
+			for _, longitudeStep := range []float64{-step, 0, step} {
+				observer := Observer{Longitude: normalizeLongitude180(center.Longitude + longitudeStep), Latitude: math.Max(-90, math.Min(90, center.Latitude+latitudeStep))}
+				tt, valid := snapshot.localGreatestTT(UTC2TT(transit.Greatest), observer)
+				state, stateOK := snapshot.stateAt(tt, observer)
+				if !valid || !stateOK {
+					continue
+				}
+				if state.external < 0 {
+					local := snapshot.local(transit, observer)
+					if local.Valid && local.Visible {
+						return true
+					}
+				}
+				if state.external < best {
+					best, seed = state.external, observer
+				}
+			}
+		}
+	}
+	return false
+}