mirror of https://github.com/tidwall/tile38.git
91 lines
2.6 KiB
Go
91 lines
2.6 KiB
Go
// Copyright 2018 Joshua J Baker. All rights reserved.
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// Use of this source code is governed by an MIT-style
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// license that can be found in the LICENSE file.
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package geo
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import (
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"math"
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)
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const (
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earthRadius = 6371e3
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radians = math.Pi / 180
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degrees = 180 / math.Pi
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piR = math.Pi * earthRadius
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twoPiR = 2 * piR
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)
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// Haversine ...
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func Haversine(latA, lonA, latB, lonB float64) float64 {
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φ1 := latA * radians
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λ1 := lonA * radians
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φ2 := latB * radians
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λ2 := lonB * radians
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Δφ := φ2 - φ1
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Δλ := λ2 - λ1
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sΔφ2 := math.Sin(Δφ / 2)
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sΔλ2 := math.Sin(Δλ / 2)
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return sΔφ2*sΔφ2 + math.Cos(φ1)*math.Cos(φ2)*sΔλ2*sΔλ2
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}
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// NormalizeDistance ...
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func NormalizeDistance(meters float64) float64 {
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m1 := math.Mod(meters, twoPiR)
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if m1 <= piR {
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return m1
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}
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return twoPiR - m1
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}
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// DistanceToHaversine ...
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func DistanceToHaversine(meters float64) float64 {
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// convert the given distance to its haversine
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sin := math.Sin(0.5 * meters / earthRadius)
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return sin * sin
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}
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// DistanceFromHaversine...
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func DistanceFromHaversine(haversine float64) float64 {
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return earthRadius * 2 * math.Asin(math.Sqrt(haversine))
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}
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// DistanceTo return the distance in meters between two point.
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func DistanceTo(latA, lonA, latB, lonB float64) (meters float64) {
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a := Haversine(latA, lonA, latB, lonB)
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return DistanceFromHaversine(a)
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}
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// DestinationPoint return the destination from a point based on a
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// distance and bearing.
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func DestinationPoint(lat, lon, meters, bearingDegrees float64) (
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destLat, destLon float64,
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) {
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// see http://williams.best.vwh.net/avform.htm#LL
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δ := meters / earthRadius // angular distance in radians
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θ := bearingDegrees * radians
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φ1 := lat * radians
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λ1 := lon * radians
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φ2 := math.Asin(math.Sin(φ1)*math.Cos(δ) +
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math.Cos(φ1)*math.Sin(δ)*math.Cos(θ))
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λ2 := λ1 + math.Atan2(math.Sin(θ)*math.Sin(δ)*math.Cos(φ1),
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math.Cos(δ)-math.Sin(φ1)*math.Sin(φ2))
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λ2 = math.Mod(λ2+3*math.Pi, 2*math.Pi) - math.Pi // normalise to -180..+180°
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return φ2 * degrees, λ2 * degrees
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}
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// BearingTo returns the (initial) bearing from point 'A' to point 'B'.
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func BearingTo(latA, lonA, latB, lonB float64) float64 {
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// tanθ = sinΔλ⋅cosφ2 / cosφ1⋅sinφ2 − sinφ1⋅cosφ2⋅cosΔλ
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// see mathforum.org/library/drmath/view/55417.html for derivation
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φ1 := latA * radians
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φ2 := latB * radians
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Δλ := (lonB - lonA) * radians
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y := math.Sin(Δλ) * math.Cos(φ2)
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x := math.Cos(φ1)*math.Sin(φ2) - math.Sin(φ1)*math.Cos(φ2)*math.Cos(Δλ)
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θ := math.Atan2(y, x)
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return math.Mod(θ*degrees+360, 360)
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}
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