Building an MKPolygon using outer boundary of a set of coordinates - How do I split coordinates that fall on either side of a line?

Question

I'm trying to build a MKPolygon using the outer boundary of a set of coordinates.

From what I can tell, there is no delivered functionality to achieve this in Xcode (the MKPolygon methods would use all points to build the polygon, including interior points).

After some research I've found that a convex-hull solves this problem. After looking into various algorithms, the one I can best wrap my head around to implement is QuickHull.

This takes the outer lat coords and draws a line between the two. From there, you split your points based on that line into two subsets and process distance between the outer lats to start building triangles and eliminating points within until you are left with the outer boundary.

I can find the outer points just by looking at min/max lat and can draw a line between the two (MKPolyline) - but how would I determine whether a point falls on one side or the other of this MKPolyline?

A follow up question is whether there is a hit test to determine whether points fall within an MKPolygon.

Thanks!

Answer 1

I ended up using a variation of the gift wrap algorithm. Certainly not a trivial task.

Having trouble with formatting of the full code so I'll have to just put my steps (probably better because I have some clean up to do!)

I started with an array of MKPointAnnotations

1) I got the lowest point that is furthest left. To do this, I looped through all of the points and compared lat/lng to get lowest point. This point will definitely be in the convex hull, so add it to a NSMutableArray that will store our convex hull points (cvp)

2) Get all points to the left of the lowest point and loop through them, calculating the angle of the cvp to the remaining points on the left. Whichever has the greatest angle, will be the point you need to add to the array.
atan(cos(lat1)sin(lat2)-sin(lat1)*cos(lat2)*cos(lon2-lon1), sin(lon2-lon1)*cos(lat2))

• For each point found, create a triangle (by using lat from new point and long from previous point) and create a polygon. I used this code to do a hit test on my polygon: BOOL mapCoordinateIsInPolygon = CGPathContainsPoint(polygonView.path, NULL, polygonViewPoint, NO); If anything was found in the hit test, remove it from the comparison array (all those on the left of the original array minus the hull points)

• Once you have at least 3 points in your cvp array, build another polygon with all of the cvp's in the array and remove anything within using the hit test.

3) Once you've worked through all of the left points, create a new comparison array of the remaining points that haven't been eliminated or added to the hull

4) Use the same calculations and polygon tests to remove points and add the cvp's found At the end, you're left with a list of points in that make up your convex hull.