# How to Calculate Geolocation Intersection of Two Vectors?

I'm unfamiliar with much GIS terminology but am tasked with solving a specific geolocation problem. For what it is worth, this is for an iOS project, so the data I can collect for analysis is that which is provided by iOS 7.1. I'm a little out of my depth here, but I feel the answer must be trivial.

I have two GPS devices, A and B. Let us say that both have broadcast a start location and a current location. All I have are latitude and longitude readings, nothing fancy, and I cannot rely on any heading data I have available.

If I know A-start and A-current, as well as B-start and B-current, I should be able to extrapolate vectors from those coordinates and determine if those two devices' paths will cross and at what geolocation.

My understanding on this, given that my base use-case is in-city, is that I can consider the world to be flat for this purpose. As well, I do not need a super-accurate answer, just a good, fast, best-guess. Presumably I would need to convert these coordinates to a standard XY cartesian system, calculate, and convert the answer back to real-world geolocation?

For that matter, any resources that collect these types of calculations would be appreciated. As I am unfamiliar with the problem space, I'm having trouble getting good Google results in my searches.

As well, I am open to any libraries that may be recommended for such data analysis.

• If you're willing to assume that the earth is flat, just treat the latitude / longitude pairs as points on a Cartesian plane. – BradHards Mar 19 '14 at 5:40
• That's so simple I realize now I've been overthinking the problem to a drastic degree. – christopherdrum Mar 19 '14 at 7:52
• Although it is simple it is not quite so obvious. The problem, when you start thinking about it, is that a difference in latitudes does not represent the same distance as the same difference in longitudes (except near the Equator). This fact screws up basic geometrical calculations involving distance, area, angle, and orientation. However, it does not affect incidence (a more primitive geometric relationship). Therefore, provided you are not near either pole and provided that all five points--the four given ones and the solution--are reasonably close, @BradHards is perfectly right. – whuber Mar 19 '14 at 14:42
• Thank you @whuber, I appreciate your additional insight on the matter. – christopherdrum Mar 20 '14 at 1:41