61 lines
2.8 KiB
Go
61 lines
2.8 KiB
Go
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package geodata
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import "math"
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// 地球尺度常量 / Earth size constants.
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const (
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// EarthEquatorialRadiusKM 地球赤道半径 / Earth equatorial radius.
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EarthEquatorialRadiusKM = 6378.1366
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// EarthMeanRadiusKM 地球平均半径 / Earth mean radius.
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EarthMeanRadiusKM = 6371.0088
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// EarthWGS84RadiusKM WGS84 椭球长半轴 / WGS84 semi-major axis.
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EarthWGS84RadiusKM = 6378.137
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// EarthKMPerDegree 大圆每度的近似长度 / approximate great-circle length per degree.
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EarthKMPerDegree = 111.195
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// WebMercatorMaxLatitude Web Mercator 可投影的纬度上限 / Web Mercator latitude limit.
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WebMercatorMaxLatitude = 85.05112878
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)
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// NormalizeLongitude 把经度归一化到 [-180, 180) / wraps a longitude into [-180, 180).
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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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// CentralAngle 两点间的球心角（弧度），参数为度 / haversine central angle in radians.
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func CentralAngle(longitude1, latitude1, longitude2, latitude2 float64) float64 {
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firstLatitude := latitude1 * math.Pi / 180
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secondLatitude := latitude2 * math.Pi / 180
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deltaLatitude := secondLatitude - firstLatitude
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deltaLongitude := math.Remainder((longitude2-longitude1)*math.Pi/180, 2*math.Pi)
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haversine := math.Sin(deltaLatitude/2)*math.Sin(deltaLatitude/2) +
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math.Cos(firstLatitude)*math.Cos(secondLatitude)*math.Sin(deltaLongitude/2)*math.Sin(deltaLongitude/2)
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return 2 * math.Asin(math.Sqrt(math.Max(0, math.Min(1, haversine))))
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}
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// EquatorialDistanceKM 以赤道半径计的大圆距离 / great-circle distance on the equatorial-radius sphere.
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func EquatorialDistanceKM(first, second GeoPoint) float64 {
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return EarthEquatorialRadiusKM * CentralAngle(first.Longitude, first.Latitude, second.Longitude, second.Latitude)
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}
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// MeanDistanceKM 以平均半径计的大圆距离 / great-circle distance on the mean-radius sphere.
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func MeanDistanceKM(first, second GeoPoint) float64 {
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return EarthMeanRadiusKM * CentralAngle(first.Longitude, first.Latitude, second.Longitude, second.Latitude)
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}
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// WebMercatorDistanceKM 两点在 Web Mercator 平面上的距离，经差取短弧 / Web Mercator planar distance.
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func WebMercatorDistanceKM(first, second GeoPoint) float64 {
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clampLatitude := func(value float64) float64 {
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return math.Max(-WebMercatorMaxLatitude, math.Min(WebMercatorMaxLatitude, value))
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}
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longitude := math.Remainder(second.Longitude-first.Longitude, 360) * math.Pi / 180
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firstLatitude := clampLatitude(first.Latitude) * math.Pi / 180
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secondLatitude := clampLatitude(second.Latitude) * math.Pi / 180
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firstY := math.Log(math.Tan(math.Pi/4 + firstLatitude/2))
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secondY := math.Log(math.Tan(math.Pi/4 + secondLatitude/2))
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return EarthEquatorialRadiusKM * math.Hypot(longitude, secondY-firstY)
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}
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