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
This commit is contained in:
+275
-14
@@ -4,21 +4,42 @@ 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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func PolylineSegments(points []GeoPoint, view ClipView) [][]GeoPoint {
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prepared, ok := prepareTopologyPoints(points)
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if !ok {
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return nil
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}
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points = prepared
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if view.Orthographic() {
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return clipPolylineOrthographic(points, view.Center)
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}
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projection := view.Projection
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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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if shift := equirectangularSeamShift(view); shift != 0 {
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return splitPolylineAtSeam(points, shift)
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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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func PolygonFragments(points []GeoPoint, view ClipView) [][]GeoPoint {
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if len(points) < 3 {
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return nil
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}
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prepared, ok := prepareTopologyPoints(points)
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if !ok {
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return nil
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}
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points = prepared
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if view.Orthographic() {
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return polygonFragmentsOrthographic(points, view.Center)
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}
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projection := view.Projection
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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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@@ -31,9 +52,39 @@ func PolygonFragments(points []GeoPoint, projection Projection) [][]GeoPoint {
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}
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return nil
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}
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if shift := equirectangularSeamShift(view); shift != 0 {
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return splitPolygonAtSeam(points, shift)
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}
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return splitPolygonAntimeridian(points)
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}
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// prepareTopologyPoints 校验裁剪输入：NaN 与 ±Inf 直接拒绝，经度超出 ±180 时按 360 取模归一化
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// （同一子午线的等价表示），只有真的越界才复制，正常输入保持零分配。
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func prepareTopologyPoints(points []GeoPoint) ([]GeoPoint, bool) {
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for _, point := range points {
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if math.IsNaN(point.Longitude) || math.IsNaN(point.Latitude) ||
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math.IsInf(point.Longitude, 0) || math.IsInf(point.Latitude, 0) {
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return nil, false
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}
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}
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shifted := false
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for _, point := range points {
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if point.Longitude < -180 || point.Longitude > 180 {
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shifted = true
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break
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}
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}
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if !shifted {
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return points, true
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}
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normalized := make([]GeoPoint, len(points))
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copy(normalized, points)
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for index := range normalized {
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normalized[index].Longitude = normalizeLongitude(normalized[index].Longitude)
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}
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return normalized, true
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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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@@ -61,8 +112,7 @@ func splitPolylineAntimeridian(points []GeoPoint) [][]GeoPoint {
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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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crossing := sphericalLongitudeIntersection(a, b, boundary, adjustedLongitude)
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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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@@ -126,19 +176,22 @@ func splitPolygonAntimeridian(points []GeoPoint) [][]GeoPoint {
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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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// 一次取整到最近的 360 倍数，等价于反复加减 360 但不随偏移量增长。
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if offset := point.Longitude - previous; offset > 180 || offset < -180 {
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point.Longitude -= 360 * math.Round(offset/360)
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}
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unwrapped[index] = point
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}
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unwrapped = closePoleEnclosingPolygon(unwrapped)
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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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if span := maximum - minimum; !(span >= 0 && span <= 3*360) {
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// 经度归一化后每个点最多偏离 ±180 再加一次 360 的展开，跨度不可能超过三个世界。
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return nil
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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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@@ -164,6 +217,113 @@ func splitPolygonAntimeridian(points []GeoPoint) [][]GeoPoint {
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return fragments
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}
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// closePoleEnclosingPolygon adds the equirectangular map-edge closure for a
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// simple spherical ring that winds once around a pole. Without this edge, the
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// implicit last-to-first segment cuts across the map instead of representing
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// the cap at +90 or -90 degrees.
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func closePoleEnclosingPolygon(points []GeoPoint) []GeoPoint {
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if len(points) < 3 {
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return points
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}
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first := points[0].Longitude
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closure := first
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last := points[len(points)-1].Longitude
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for closure-last > 180 {
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closure -= 360
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}
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for closure-last < -180 {
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closure += 360
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}
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winding := math.Round((closure - first) / 360)
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if math.Abs(winding) != 1 {
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return points
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}
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// Choose the smaller map-edge closure from edge geometry. Unlike a vertex
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// average, its result is unchanged when a straight boundary edge is resampled.
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north := appendPoleClosure(points, closure, first, 90)
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south := appendPoleClosure(points, closure, first, -90)
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northInside := sphericalPolygonContainsOrTouches(points, GeoPoint{Longitude: first, Latitude: 90})
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southInside := sphericalPolygonContainsOrTouches(points, GeoPoint{Longitude: first, Latitude: -90})
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northArea := math.Abs(signedPolygonArea(north))
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southArea := math.Abs(signedPolygonArea(south))
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if northInside == southInside && math.Abs(northArea-southArea) <= 1e-12 {
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return points
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}
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pole := -90.0
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if (northInside != southInside && northInside) || (northInside == southInside && northArea < southArea) {
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pole = 90
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}
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// The closure must not cross the physical boundary again. For a concave
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// polar ring, only the poleward-most seam crossing has a clear path to
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// the pole; the first crossing can turn an excluded pocket into a fill.
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points = rotatePoleRingToMapEdge(points, pole)
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first = points[0].Longitude
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return appendPoleClosure(points, first+360*winding, first, pole)
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}
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func rotatePoleRingToMapEdge(points []GeoPoint, poleLatitude float64) []GeoPoint {
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if len(points) < 3 {
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return points
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}
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bestIndex := -1
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bestScore := math.Inf(-1)
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var crossing GeoPoint
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for index := 0; index < len(points); index++ {
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next := (index + 1) % len(points)
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a, b := points[index], points[next]
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bLongitude := b.Longitude
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for bLongitude-a.Longitude > 180 {
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bLongitude -= 360
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}
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for bLongitude-a.Longitude < -180 {
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bLongitude += 360
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}
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if math.Abs(a.Longitude-bLongitude) <= 1e-12 {
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continue
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}
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target := 180 + 360*math.Ceil((math.Min(a.Longitude, bLongitude)-180-1e-12)/360)
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for ; target <= math.Max(a.Longitude, bLongitude)+1e-12; target += 360 {
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candidate := sphericalLongitudeIntersection(a, b, target, bLongitude)
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if score := candidate.Latitude * poleLatitude; score > bestScore {
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bestIndex, bestScore, crossing = index, score, candidate
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}
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}
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}
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if bestIndex < 0 {
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return points
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}
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rotated := make([]GeoPoint, 1, len(points)+1)
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rotated[0] = crossing
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for offset := 1; offset <= len(points); offset++ {
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point := points[(bestIndex+offset)%len(points)]
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previous := rotated[len(rotated)-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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rotated = append(rotated, point)
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}
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return sweepDeduplicateAdjacent(rotated)
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}
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func appendPoleClosure(points []GeoPoint, closure, first, poleLatitude float64) []GeoPoint {
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result := append([]GeoPoint(nil), points...)
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// The unwrapped ring ends in the world adjacent to its first vertex. Repeat
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// that vertex in the adjacent world before climbing to the map edge;
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// otherwise the last boundary point is connected diagonally to the pole and
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// a triangular gap is cut out after antimeridian clipping.
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result = append(result, GeoPoint{
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Longitude: closure,
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Latitude: points[0].Latitude,
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})
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return append(result,
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GeoPoint{Longitude: closure, Latitude: poleLatitude},
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GeoPoint{Longitude: first, Latitude: poleLatitude},
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)
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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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@@ -184,8 +344,7 @@ func clipPolygonLongitude(points []GeoPoint, boundary float64, keepGreater bool)
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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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return sphericalLongitudeIntersection(a, b, boundary, b.Longitude)
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}
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return clipPolygon(points, inside, intersection)
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}
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@@ -216,9 +375,63 @@ func clipPolygon(
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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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first := a
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second := b
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firstVector := geoPointVector(first)
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secondVector := geoPointVector(second)
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firstSign := firstVector.z
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secondSign := secondVector.z
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if math.Abs(firstSign) <= 1e-15 {
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return GeoPoint{Longitude: normalizeLongitude(first.Longitude), Latitude: 0}
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}
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if math.Abs(secondSign) <= 1e-15 {
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return GeoPoint{Longitude: normalizeLongitude(second.Longitude), Latitude: 0}
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}
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left, right := 0.0, 1.0
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for iteration := 0; iteration < 64; iteration++ {
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middle := (left + right) / 2
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point := sphericalInterpolate(first, second, middle)
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if point.Latitude == 0 || right-left <= 1e-13 {
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return GeoPoint{Longitude: normalizeLongitude(point.Longitude), Latitude: 0}
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}
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if point.Latitude*first.Latitude > 0 {
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left = middle
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} else {
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right = middle
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}
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}
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point := sphericalInterpolate(first, second, (left+right)/2)
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return GeoPoint{Longitude: normalizeLongitude(point.Longitude), Latitude: 0}
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}
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func sphericalLongitudeIntersection(a, b GeoPoint, boundary, adjustedLongitude float64) GeoPoint {
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firstLongitude := a.Longitude
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secondLongitude := adjustedLongitude
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if math.Abs(secondLongitude-firstLongitude) <= 1e-14 {
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return GeoPoint{Longitude: boundary, Latitude: a.Latitude}
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}
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left, right := 0.0, 1.0
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for iteration := 0; iteration < 64; iteration++ {
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middle := (left + right) / 2
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point := sphericalInterpolate(a, b, middle)
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middleLongitude := point.Longitude
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for middleLongitude-firstLongitude > 180 {
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middleLongitude -= 360
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}
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for middleLongitude-firstLongitude < -180 {
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middleLongitude += 360
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}
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if math.Abs(middleLongitude-boundary) <= 1e-12 || right-left <= 1e-13 {
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return GeoPoint{Longitude: boundary, Latitude: point.Latitude}
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}
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if (firstLongitude-boundary)*(middleLongitude-boundary) <= 0 {
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right = middle
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} else {
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left = middle
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}
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}
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point := sphericalInterpolate(a, b, (left+right)/2)
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return GeoPoint{Longitude: boundary, Latitude: point.Latitude}
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}
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func normalizeLongitude(value float64) float64 {
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@@ -228,3 +441,51 @@ func normalizeLongitude(value float64) float64 {
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}
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return value - 180
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}
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// equirectangularSeamShift 返回把等经纬接缝从 ±180 搬到视图中心对面所需的经度旋转量。
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// 视图中心为 0 时返回 0，调用方即可沿用未旋转的原有路径，保证既有输出逐字节不变。
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func equirectangularSeamShift(view ClipView) float64 {
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if view.Projection != ProjectionEquirectangular || view.Center.Longitude == 0 {
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return 0
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}
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return view.Center.Longitude
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}
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// splitPolylineAtSeam 先把经度旋转到接缝落在 ±180 的坐标系，交给原有分割逻辑，再旋转回来。
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func splitPolylineAtSeam(points []GeoPoint, shift float64) [][]GeoPoint {
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segments := splitPolylineAntimeridian(rotateLongitudes(points, -shift))
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for _, segment := range segments {
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rotateLongitudesInPlace(segment, shift)
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}
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return segments
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}
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// splitPolygonAtSeam 与 splitPolylineAtSeam 同理，供多边形使用。
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func splitPolygonAtSeam(points []GeoPoint, shift float64) [][]GeoPoint {
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fragments := splitPolygonAntimeridian(rotateLongitudes(points, -shift))
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for _, fragment := range fragments {
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rotateLongitudesInPlace(fragment, shift)
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}
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return fragments
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}
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func rotateLongitudes(points []GeoPoint, shift float64) []GeoPoint {
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rotated := make([]GeoPoint, len(points))
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copy(rotated, points)
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rotateLongitudesInPlace(rotated, shift)
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return rotated
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}
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func rotateLongitudesInPlace(points []GeoPoint, shift float64) {
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for index := range points {
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points[index].Longitude = normalizeLongitude180(points[index].Longitude + shift)
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}
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}
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func normalizeLongitude180(longitude float64) float64 {
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value := math.Mod(longitude+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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Block a user