用起始位置和距离计算新坐标

Posted 2023-03-05

【中文标题】用起始位置和距离计算新坐标

【英文标题】：Calculate new coordinates with starting position and distance

【发布时间】：2016-02-18 15:41:23

【问题描述】：

我正在尝试获取一个点的坐标，即距起始位置一定距离，但最终结果是错误的。

首先，我计算起始位置和所需目的地之间的角度：

private func calculateAngleBetweenLocations(currentLocation: CLLocationCoordinate2D, targetLocation: CLLocationCoordinate2D) -> Double 
    let fLat = self.degreesToRadians(currentLocation.latitude);
    let fLng = self.degreesToRadians(currentLocation.longitude);
    let tLat = self.degreesToRadians(targetLocation.latitude);
    let tLng = self.degreesToRadians(targetLocation.longitude);
    let deltaLng = tLng - fLng

    let y = sin(deltaLng) * cos(tLat)
    let x = cos(fLat) * sin(tLat) - sin(fLat) * cos(tLat) * cos(deltaLng)

    let bearing = atan2(y, x)

    return self.radiansToDegrees(bearing)

然后，我计算新点，给定距离：

private func coordinatesForMovement(endLocation: CLLocationCoordinate2D, distance: Double) -> CLLocationCoordinate2D 
    let angle = self.calculateAngleBetweenLocations(self.currentLocation, targetLocation: endLocation)
    let x = self.currentLocation.latitude + distance * cos(angle)
    let y = self.currentLocation.longitude + distance * sin(angle)

    return CLLocationCoordinate2D(latitude: x, longitude: y)

this 是结果（脚是起始位置，蓝色标记是目的地，红色标记是新计算点的位置）。我尝试过以米和公里为单位的距离以及所有其他浮点位置，但从未得到正确的结果。有任何想法吗？

【问题讨论】：

coordinatesForMovement 似乎是混合维度。 currentCoordinate.latitude 是角度（以度为单位？），distance 是长度，cos() 是无量纲的。所以程序在长度上加上一个角度，这总是错误的。角度增加角度，长度增加长度。

好的，那我该如何解决呢？

【参考方案1】：

好的，经过一番挖掘，我找到了this 的答案，这解决了我的问题。这是我在 swift 中的完整解决方案：

internal func moveToLocation(location: CLLocationCoordinate2D, distance: Double) 
    let angle = self.calculateAngleBetweenLocations(self.currentLocation, targetLocation: location)
    let newLocation = self.coordinates(self.currentLocation, atDistance: distance, atAngle: angle)

    self.moveUser(newLocation: newLocation) 


private func coordinates(startingCoordinates: CLLocationCoordinate2D, atDistance: Double, atAngle: Double) -> CLLocationCoordinate2D 
    let distanceRadians = atDistance / 6371
    let bearingRadians = self.degreesToRadians(atAngle)
    let fromLatRadians = self.degreesToRadians(startingCoordinates.latitude)
    let fromLonRadians = self.degreesToRadians(startingCoordinates.longitude)

    let toLatRadians = asin(sin(fromLatRadians) * cos(distanceRadians) + cos(fromLatRadians) * sin(distanceRadians) * cos(bearingRadians))
    var toLonRadians = fromLonRadians + atan2(sin(bearingRadians) * sin(distanceRadians) * cos(fromLatRadians), cos(distanceRadians) - sin(fromLatRadians) * sin(toLatRadians));

    toLonRadians = fmod((toLonRadians + 3 * M_PI), (2 * M_PI)) - M_PI

    let lat = self.radiansToDegrees(toLatRadians)
    let lon = self.radiansToDegrees(toLonRadians)

    return CLLocationCoordinate2D(latitude: lat, longitude: lon)


private func calculateAngleBetweenLocations(currentLocation: CLLocationCoordinate2D, targetLocation: CLLocationCoordinate2D) -> Double 
    let fLat = self.degreesToRadians(currentLocation.latitude);
    let fLng = self.degreesToRadians(currentLocation.longitude);
    let tLat = self.degreesToRadians(targetLocation.latitude);
    let tLng = self.degreesToRadians(targetLocation.longitude);
    let deltaLng = tLng - fLng

    let y = sin(deltaLng) * cos(tLat)
    let x = cos(fLat) * sin(tLat) - sin(fLat) * cos(tLat) * cos(deltaLng)

    let bearing = atan2(y, x)

    return self.radiansToDegrees(bearing)


private func degreesToRadians(x: Double) -> Double 
    return M_PI * x / 180.0


private func radiansToDegrees(x: Double) -> Double 
    return x * 180.0 / M_PI