How to find closest position on a line from another point - swift

Question

MKMapView - I have a road, consisting of many location points.
A line is drawn from each point to the next, making it a visible road line.
I have a user location, and I would like to draw a line to the closest point of that road.
That means - I need to iterate over each two points, and determine the closest point to user location.
It's all working well, but the problem is - the calculated closest point on a line is sometimes not directly at 90 degrees against the said line. (In some situations the angle is almost 45 degrees).
It seems it depends on the angle of the line.
Please see the example video:
https://imgur.com/a/27QFmHx
(Or screenshot from the video:)
In this visible example, there are 3 black static lines drawn, two of them are perpendicular (right ones).
Red lines - are calculated on the fly, to be the drawn between user location (center of the map) to the closest point on each of the lines.
It is visible, that the top line is straight (no angle), and the found closest point, and it's drawn line is perpendicular.
But there is issue with the right black lines. The found point (and red line) clearly is not 90 degrees.
This is the code I am using, to determine the closest point on the line:
func distanceBetweenTwoPointsFrom(origin: CLLocationCoordinate2D, pointOne: CLLocationCoordinate2D, pointTwo: CLLocationCoordinate2D) -> CLLocationCoordinate2D {
let A: Double = origin.latitude - pointOne.latitude
let B: Double = origin.longitude - pointOne.longitude
let C: Double = pointTwo.latitude - pointOne.latitude
let D: Double = pointTwo.longitude - pointOne.longitude
let dot: Double = A * C + B * D
let len_sq: Double = C * C + D * D
var param: Double = -1
if len_sq != 0 {
param = dot / len_sq
}
var xx: Double = 0
var yy: Double = 0
if param < 0 || (pointOne.latitude == pointTwo.latitude && pointOne.longitude == pointTwo.longitude) {
xx = pointOne.latitude
yy = pointOne.longitude
} else if param > 1 {
xx = pointTwo.latitude
yy = pointTwo.longitude
} else {
xx = pointOne.latitude + param * C
yy = pointOne.longitude + param * D
}
return CLLocationCoordinate2D.init(latitude: xx, longitude: yy)
}
Question: How can I fix it, so that the found point on the black line would be directly 90 degrees from the user? (Visibly the most straight line to get from user location to the said line)

Answer 1

You should calculate the distance between two points as follows:
import MapKit
func distance(
from: CLLocationCoordinate2D,
to: CLLocationCoordinate2D
) -> CLLocationDistance {
MKMapPoint(from).distance(to: MKMapPoint(to))
}
Note though, you will only find the shortest distance from the given points, which may not be the actual shortest distance from the user's location to any point on the path.
Unless you have many points which approximate your path very closely, you may add this step:
In order to increase accuracy, you may create a line from the two points which are closest to the user's point using this formula,
https://en.wikipedia.org/wiki/Linear_equation
This basically creates an approximation to the actual path, using a line - but with infinite points.
Then search the point which is the shortest distance from the user's location and this line using this formula:
https://en.wikipedia.org/wiki/Distance_from_a_point_to_a_line
This also does not guarantie that you get the actual point with the shortest distance, but it is certainly a better approximation.