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I have a series of nature reserves that need to be plotted, as polygon overlays, on a map using the coordinates contained within KML data. I’ve found a tutorial on the Apple website for displaying KML overlays on map instances.

The problem is that the reserves vary in size greatly - from a small pond right up to several hundred kilometers in size. As a result I can’t use the coordinates of the center point to find the nearest reserves. Instead I need to calculate the nearest point of the reserves polygon to find the nearest one. With the data in KML - how would I go about trying to achieve this?

I've only managed to find one other person ask this and no one had replied :(

Chris Morgan
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Stuart
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  • Can you provide a link to the other question? Do you need the actual nearest point in the nearest polygon or just the nearest polygon from a given point? –  Jan 05 '11 at 20:28
  • Stuart, are you calculation on the back-end or in the app? – Jé Queue Jan 05 '11 at 21:10
  • How about adding meanRadius parameter. Calculate the distance to the centre of the reserve, then subtract the meanRadius of the reserve. – Phil Jun 05 '11 at 22:58
  • What solution did you implement? I am looking forward to do something in same lines: http://stackoverflow.com/questions/16190882/point-in-kml-polygon-c-c-code – Raj Pawan Gumdal Apr 25 '13 at 11:14

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Well, there are a couple different solutions depending on your needs. The higher the accuracy required, the more work required. I like Phil's meanRadius parameter idea. That would give you a rough idea of which polygon is closest and would be pretty easy to calculate. This idea works best if the polygons are "circlish". If the polygon are very irregular in shape, this idea loses it's accuracy.

From a math standpoint, here is what you want to do. Loop through all points of all polygons. Calculate the distance from those points to your current coordinate. Then just keep track of which one is closest. There is one final wrinkle. Imagine a two points making a line segment that is very long. You are located one meter away from the midpoint of the line. Well, the distance to these two points is very large, while, in fact you are very close to the polygon. You will need to calculate the distance from your coordinate to every possible line segment which you can do in a variety of manners which are outlined here:

http://www.worsleyschool.net/science/files/linepoint/distance.html

Finally, you need to ask yourself, am I in any polygons? If you're 10 meters away from a point on a polygon, but are, in fact, inside the polygon, obviously, you need to consider that. The best way to do that is to use a ray casting algorithm:

http://en.wikipedia.org/wiki/Point_in_polygon#Ray_casting_algorithm

Landon
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