线路交叉点 - GPS 坐标

Question

我需要检测两条线之间是否有交点。线是一对

CLLocationCoordinate2D

。 我发现了这个 https://www.movable-type.co.uk/scripts/latlong.html#intersection 并尝试在 swift 中实现它

static func intersection(point1: CLLocationCoordinate2D, bearing1: Double, point2: CLLocationCoordinate2D, bearing2: Double) -> CLLocationCoordinate2D {
    let lat1 = Math.radians(degrees: point1.latitude)
    let lon1 = Math.radians(degrees: point1.longitude)

    let lat2 = Math.radians(degrees: point2.latitude)
    let lon2 = Math.radians(degrees: point2.longitude)

    let toSqrt = pow(sin((lat2 - lat1) / 2), 2) + cos(lat1) * cos(lat2) * pow(sin((lon2 - lon1) / 2), 2)
    let dist12 = 2 * asin(sqrt(toSqrt))

    let a = acos((sin(lat2) - sin(lat1) * cos(dist12)) / (sin(dist12) * cos(lat1)))
    let b = acos((sin(lat1) - sin(lat2) * cos(dist12)) / (sin(dist12) * cos(lat2)))

    let o12: Double
    let o21: Double

    if sin(lon2 - lon1) > 0 {
        o12 = a
        o21 = 2.0 * .pi - b
    } else {
        o12 = 2.0 * .pi - a
        o21 = b
    }

    let alpha1 = bearing1 - o12
    let alpha2 = o21 - bearing2

    let alpha3 = acos(-cos(alpha1) * cos(alpha2) + sin(alpha1) * sin(alpha2) * cos(dist12))

    let dist13 = atan2(sin(dist12) * sin(alpha1) * sin(alpha2), cos(alpha2) + cos(alpha1) * cos(alpha3))

    let lat3 = asin(sin(lat1) * cos(dist13) + cos(lat1) * sin(dist12) * cos(bearing1))

    let deltaLon13 = atan2(sin(bearing1) * sin(dist12) * cos(lat1), cos(dist12) - sin(lat1) * sin(lat3))

    let lon3 = lon1 + deltaLon13

    return CLLocationCoordinate2D(latitude: Math.degrees(radians: lat3), longitude: Math.degrees(radians: lon3))
}

不幸的是，它没有按预期工作。这是示例输出：

有没有简单的方法来检查这些线是否相交？我什至不需要交点。

Answer 1

我发现执行中存在错误。应该是：

let lat3 = asin(
  sin(lat1) * cos(dist13) + cos(lat1) * sin(dist13) * cos(bearing1)
)

let deltaLon13 = atan2(
  sin(bearing1) * sin(dist13) * cos(lat1), cos(dist13) - sin(lat1) * sin(lat3)
)