feat: 新增月掩与日月食地理绘图并提升观测计算精度
- 新增月掩恒星和行星：支持搜索、掩甚点、全球掩带及固定地点轨迹计算 - 支持恒星星表坐标转换、有限盘面行星接触事件和月掩 SVG 输出 - 新增日月食及月掩全球投影图、时间标记和 GeoJSON 地理数据接口 - 扩展日食中心线、南北界及偏食足迹采样，支持极区投影 - 修正站心时角、月出月落、月球视半径、折射和恒星自行计算 - 优化内外行星事件搜索、边界选择、极端输入处理和计算稳定性
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package geodata
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import "math"
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// PolylineSegments 将地理折线裁剪到选定投影并 / PolylineSegments clips a geographic polyline to the selected projection and
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// 在等经纬投影中按日界线拆分路径 / splits equirectangular paths at the antimeridian.
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func PolylineSegments(points []GeoPoint, projection Projection) [][]GeoPoint {
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if projection == ProjectionNorthPolar {
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return clipPolylineHemisphere(points, 1)
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}
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if projection == ProjectionSouthPolar {
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return clipPolylineHemisphere(points, -1)
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}
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return splitPolylineAntimeridian(points)
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}
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// PolygonFragments 将地理多边形裁剪到选定地图范围 / PolygonFragments clips a geographic polygon to the selected map extent.
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func PolygonFragments(points []GeoPoint, projection Projection) [][]GeoPoint {
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if len(points) < 3 {
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return nil
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}
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if projection == ProjectionNorthPolar {
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if clipped := clipPolygonHemisphere(points, 1); len(clipped) >= 3 {
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return [][]GeoPoint{clipped}
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}
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return nil
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}
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if projection == ProjectionSouthPolar {
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if clipped := clipPolygonHemisphere(points, -1); len(clipped) >= 3 {
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return [][]GeoPoint{clipped}
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}
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return nil
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}
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return splitPolygonAntimeridian(points)
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}
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func splitPolylineAntimeridian(points []GeoPoint) [][]GeoPoint {
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if len(points) == 0 {
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return nil
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}
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segments := make([][]GeoPoint, 0, 2)
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current := []GeoPoint{points[0]}
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for index := 1; index < len(points); index++ {
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a, b := points[index-1], points[index]
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if (a.Longitude == -180 && b.Longitude == 180) || (a.Longitude == 180 && b.Longitude == -180) {
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// -180/+180 的精确端点属于同一子午线，不要 / Exact -180/+180 endpoints are the same meridian; do not
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// 不要让它们进入分母为零的交叉插值 / feed them into the crossing interpolation with a zero denominator.
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b.Longitude = a.Longitude
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current = append(current, b)
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continue
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}
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if math.Abs(b.Longitude-a.Longitude) <= 180 {
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current = append(current, b)
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continue
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}
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boundary := 180.0
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adjustedLongitude := b.Longitude
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if a.Longitude < 0 {
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boundary = -180
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adjustedLongitude -= 360
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} else {
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adjustedLongitude += 360
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}
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fraction := (boundary - a.Longitude) / (adjustedLongitude - a.Longitude)
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crossing := GeoPoint{Longitude: boundary, Latitude: a.Latitude + fraction*(b.Latitude-a.Latitude)}
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current = append(current, crossing)
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if len(current) >= 2 {
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segments = append(segments, current)
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}
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crossing.Longitude = -boundary
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current = []GeoPoint{crossing, b}
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}
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if len(current) >= 2 {
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segments = append(segments, current)
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}
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return segments
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}
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func clipPolylineHemisphere(points []GeoPoint, hemisphere float64) [][]GeoPoint {
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if len(points) == 0 {
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return nil
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}
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inside := func(value GeoPoint) bool { return value.Latitude*hemisphere >= 0 }
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var segments [][]GeoPoint
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var current []GeoPoint
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for index, point := range points {
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pointInside := inside(point)
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if index == 0 {
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if pointInside {
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current = append(current, point)
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}
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continue
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}
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previous := points[index-1]
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previousInside := inside(previous)
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if previousInside != pointInside {
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crossing := hemisphereIntersection(previous, point)
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if previousInside {
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current = append(current, crossing)
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if len(current) >= 2 {
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segments = append(segments, current)
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}
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current = nil
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} else {
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current = []GeoPoint{crossing}
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}
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}
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if pointInside {
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current = append(current, point)
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}
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}
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if len(current) >= 2 {
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segments = append(segments, current)
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}
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return segments
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}
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func clipPolygonHemisphere(points []GeoPoint, hemisphere float64) []GeoPoint {
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inside := func(value GeoPoint) bool { return value.Latitude*hemisphere >= 0 }
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return clipPolygon(points, inside, hemisphereIntersection)
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}
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func splitPolygonAntimeridian(points []GeoPoint) [][]GeoPoint {
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unwrapped := make([]GeoPoint, len(points))
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unwrapped[0] = points[0]
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for index := 1; index < len(points); index++ {
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point := points[index]
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previous := unwrapped[index-1].Longitude
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for point.Longitude-previous > 180 {
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point.Longitude -= 360
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}
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for point.Longitude-previous < -180 {
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point.Longitude += 360
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}
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unwrapped[index] = point
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}
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minimum, maximum := unwrapped[0].Longitude, unwrapped[0].Longitude
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for _, point := range unwrapped[1:] {
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minimum = math.Min(minimum, point.Longitude)
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maximum = math.Max(maximum, point.Longitude)
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}
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firstWorld := int(math.Floor((minimum + 180) / 360))
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lastWorld := int(math.Floor((maximum + 180) / 360))
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var fragments [][]GeoPoint
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for world := firstWorld; world <= lastWorld; world++ {
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left := -180.0 + 360*float64(world)
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right := 180.0 + 360*float64(world)
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clipped := clipPolygonLongitude(unwrapped, left, true)
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clipped = clipPolygonLongitude(clipped, right, false)
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if len(clipped) < 3 {
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continue
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}
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for index := range clipped {
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clipped[index].Longitude -= 360 * float64(world)
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}
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if math.Abs(signedPolygonArea(clipped)) < 1e-12 {
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// 边恰好落在日界线上的多边形可能在相邻世界各输出一次 / A polygon whose edge lies exactly on the antimeridian can be
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// 可能在相邻世界各输出一次；丢弃重复的 / emitted once for each adjacent world. Drop the duplicate
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// 零面积片段后再做 GeoJSON 环验证 / zero-area fragment before GeoJSON ring validation.
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continue
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}
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fragments = append(fragments, clipped)
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}
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return fragments
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}
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func signedPolygonArea(points []GeoPoint) float64 {
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if len(points) < 3 {
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return 0
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}
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area := 0.0
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for index, point := range points {
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next := points[(index+1)%len(points)]
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area += point.Longitude*next.Latitude - next.Longitude*point.Latitude
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}
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return area / 2
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}
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func clipPolygonLongitude(points []GeoPoint, boundary float64, keepGreater bool) []GeoPoint {
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inside := func(value GeoPoint) bool {
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if keepGreater {
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return value.Longitude >= boundary
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}
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return value.Longitude <= boundary
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}
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intersection := func(a, b GeoPoint) GeoPoint {
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fraction := (boundary - a.Longitude) / (b.Longitude - a.Longitude)
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return GeoPoint{Longitude: boundary, Latitude: a.Latitude + fraction*(b.Latitude-a.Latitude)}
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}
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return clipPolygon(points, inside, intersection)
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}
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func clipPolygon(
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points []GeoPoint,
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inside func(GeoPoint) bool,
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intersection func(GeoPoint, GeoPoint) GeoPoint,
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) []GeoPoint {
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if len(points) == 0 {
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return nil
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}
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result := make([]GeoPoint, 0, len(points)+2)
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previous := points[len(points)-1]
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previousInside := inside(previous)
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for _, current := range points {
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currentInside := inside(current)
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if currentInside != previousInside {
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result = append(result, intersection(previous, current))
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}
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if currentInside {
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result = append(result, current)
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}
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previous = current
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previousInside = currentInside
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}
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return result
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}
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func hemisphereIntersection(a, b GeoPoint) GeoPoint {
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dLongitude := normalizeLongitude(b.Longitude - a.Longitude)
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fraction := -a.Latitude / (b.Latitude - a.Latitude)
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return GeoPoint{Longitude: normalizeLongitude(a.Longitude + fraction*dLongitude), Latitude: 0}
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}
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func normalizeLongitude(value float64) float64 {
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value = math.Mod(value+180, 360)
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if value < 0 {
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value += 360
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}
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return value - 180
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}
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