b612
16c62a97d5
- 新增时标、ΔT 模型、质心时间与 UT1 支持 - 改进日月食、月掩、行星事件及路径边界计算 - 完善恒星三维自行与动态距离传播 - 扩展 SVG、GeoJSON、KML 输出与底层距离换算工具 - 整理中英文手册、示例资源及回归测试
118 lines
5.7 KiB
Go
118 lines
5.7 KiB
Go
// Package lunarhorizon 在等距圆柱地图坐标里细化月食可见区使用的站心地平线。
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//
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// 极点附近一小段球面地平弧可以横跨近 180° 经度，把它的端点直接连成多边形会在极区
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// 切出地平线以外的假可见帽。这里按地图坐标误差自适应细分，并把新增顶点用同一个站心
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// 地平方程校正回零高度。
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//
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// Package lunarhorizon refines the topocentric horizon used by lunar-eclipse visibility
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// regions in equirectangular map coordinates.
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//
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// Near a pole a short spherical horizon arc can span almost 180 degrees of longitude, so
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// joining its endpoints directly cuts a false visible cap outside the horizon. This package
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// subdivides by error measured in map coordinates and corrects every inserted vertex onto the
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// same topocentric zero-altitude curve.
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package lunarhorizon
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import (
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"math"
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"time"
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"b612.me/astro/basic"
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"b612.me/astro/internal/geodata"
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)
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// normalizeLongitude 把经度归一化到 [-180, 180)；internal/geodata 与 geojson 各有一份等价的未导出实现，无法跨包复用。
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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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// defaultToleranceDegrees 是 GeoJSON 导出使用的误差门限。GeoJSON 客户端可以无限放大，
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// 因此这里取远小于任何地图像素的角度。
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// defaultToleranceDegrees is the error tolerance used by the GeoJSON export. GeoJSON clients
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// can zoom without limit, so it stays far below any map pixel.
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const defaultToleranceDegrees = 0.002
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// DefaultToleranceDegrees 暴露默认门限，供固定分辨率的调用方设置下限。
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// DefaultToleranceDegrees exposes the default tolerance so fixed-resolution callers can floor it.
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const DefaultToleranceDegrees = defaultToleranceDegrees
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// Refine 用 GeoJSON 导出的默认门限细分一条站心地平线。
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// Refine subdivides one topocentric horizon with the GeoJSON export's default tolerance.
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//
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// Near a pole, a short spherical horizon arc can span almost 180 degrees of
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// longitude. Refine in map coordinates before clipping; extra vertices are
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// corrected to the same topocentric zero-altitude curve as the source ring.
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func Refine(points []geodata.GeoPoint, at time.Time) []geodata.GeoPoint {
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return RefineWithin(points, at, defaultToleranceDegrees)
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}
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// RefineWithin 用给定误差门限（单位：度）细分一条站心地平线。插入的顶点被校正回零高度，
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// 因此细分只增加描述精度，不改变曲线本身；固定分辨率的目标（例如 SVG 地图）可以用
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// 与像素尺度相称的门限，避免为了显示不出来的精度生成成千上万个顶点。
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// RefineWithin subdivides one topocentric horizon with the given error tolerance in degrees.
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// Inserted vertices are corrected back onto zero altitude, so refinement adds description
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// accuracy without moving the curve. A fixed-resolution target such as an SVG map can pass a
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// tolerance matched to its pixel scale instead of emitting vertices no display can resolve.
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func RefineWithin(points []geodata.GeoPoint, at time.Time, toleranceDegrees float64) []geodata.GeoPoint {
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if !(toleranceDegrees > 0) {
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toleranceDegrees = defaultToleranceDegrees
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}
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if len(points) < 3 {
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return points
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}
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jd := basic.Date2JD(at.UTC())
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tt := basic.UTC2TT(jd)
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ra, dec := basic.HMoonTrueRaDec(tt)
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distanceAU := basic.HMoonAway(tt) / 149597870.7
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sidereal := basic.ApparentSiderealTime(basic.UTC2UT1(jd)) * 15
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center := geodata.GeoPoint{Longitude: normalizeLongitude(ra - sidereal), Latitude: dec}
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// Every correction is at the same instant. Reuse its full ephemeris while
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// retaining the ellipsoid and topocentric transform used by HMoonHeight.
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altitudeAt := func(point geodata.GeoPoint) float64 {
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ra, dec := basic.TopocentricRaDec(ra, dec, point.Latitude, point.Longitude, jd, distanceAU, 0)
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hourAngle := (sidereal + point.Longitude - ra) * math.Pi / 180
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latitude := point.Latitude * math.Pi / 180
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declination := dec * math.Pi / 180
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return math.Asin(math.Sin(latitude)*math.Sin(declination)+
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math.Cos(declination)*math.Cos(latitude)*math.Cos(hourAngle)) * 180 / math.Pi
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}
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result := make([]geodata.GeoPoint, 0, len(points))
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var refine func(geodata.GeoPoint, geodata.GeoPoint, int)
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refine = func(first, second geodata.GeoPoint, depth int) {
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middle := geodata.InterpolateGreatCircle(first, second, 0.5)
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linearLongitude := first.Longitude + math.Remainder(second.Longitude-first.Longitude, 360)/2
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errorDeg := math.Hypot(math.Remainder(middle.Longitude-linearLongitude, 360), middle.Latitude-(first.Latitude+second.Latitude)/2)
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if errorDeg <= toleranceDegrees || depth >= 20 {
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result = append(result, first)
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return
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}
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for iteration := 0; iteration < 5; iteration++ {
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altitude := altitudeAt(middle)
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if math.Abs(altitude) < 1e-10 {
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break
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}
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angleDeg := basic.StarAngularSeparation(middle.Longitude, middle.Latitude, center.Longitude, center.Latitude)
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if !(angleDeg > 0) {
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// 只有传入的环并非地平线、中点与该瞬时月下点重合时才会走到这里；此时无法
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// 沿"朝向月下点"的方向修正，保留未修正的中点比产生 NaN 顶点安全。
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// Reached only when the input ring is not a horizon ring and the midpoint
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// coincides with that instant's sub-lunar point. There is no direction toward
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// the sub-lunar point to correct along, so keep the uncorrected midpoint rather
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// than emit a NaN vertex.
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break
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}
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middle = geodata.InterpolateGreatCircle(middle, center, -altitude/angleDeg)
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}
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refine(first, middle, depth+1)
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refine(middle, second, depth+1)
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}
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for index, point := range points {
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refine(point, points[(index+1)%len(points)], 0)
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}
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return result
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}
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