How to get area for MKPolygon in iOS - ios

Question

How to you get the area of a MKPolygon or MKOverlay in iOS?
I have been able to breakup the Polygon into triangles and do some math to get the area. But, doesn't work well with irregular polygons.
I was thinking about doing something like the "A more complex case" here: http://www.mathopenref.com/coordpolygonarea2.html
I was hoping there is a simpler solution with MapKit.
Thanks,
Tim

Answer 1

Here's the implementation I'm using.
#define kEarthRadius 6378137
#implementation MKPolygon (AreaCalculation)
- (double) area {
double area = 0;
NSMutableArray *coords = [[self coordinates] mutableCopy];
[coords addObject:[coords firstObject]];
if (coords.count > 2) {
CLLocationCoordinate2D p1, p2;
for (int i = 0; i < coords.count - 1; i++) {
p1 = [coords[i] MKCoordinateValue];
p2 = [coords[i + 1] MKCoordinateValue];
area += degreesToRadians(p2.longitude - p1.longitude) * (2 + sinf(degreesToRadians(p1.latitude)) + sinf(degreesToRadians(p2.latitude)));
}
area = - (area * kEarthRadius * kEarthRadius / 2);
}
return area;
}
- (NSArray *)coordinates {
NSMutableArray *points = [NSMutableArray arrayWithCapacity:self.pointCount];
for (int i = 0; i < self.pointCount; i++) {
MKMapPoint *point = &self.points[i];
[points addObject:[NSValue valueWithMKCoordinate:MKCoordinateForMapPoint(* point)]];
}
return points.copy;
}
double degreesToRadians(double radius) {
return radius * M_PI / 180;
}
In Swift 3:
let kEarthRadius = 6378137.0
extension MKPolygon {
func degreesToRadians(_ radius: Double) -> Double {
return radius * .pi / 180.0
}
func area() -> Double {
var area: Double = 0
var coords = self.coordinates()
coords.append(coords.first!)
if (coords.count > 2) {
var p1: CLLocationCoordinate2D, p2: CLLocationCoordinate2D
for i in 0..<coords.count-1 {
p1 = coords[i]
p2 = coords[i+1]
area += degreesToRadians(p2.longitude - p1.longitude) * (2 + sin(degreesToRadians(p1.latitude)) + sin(degreesToRadians(p2.latitude)))
}
area = abs(area * kEarthRadius * kEarthRadius / 2)
}
return area
}
func coordinates() -> [CLLocationCoordinate2D] {
var points: [CLLocationCoordinate2D] = []
for i in 0..<self.pointCount {
let point = self.points()[i]
points.append(MKCoordinateForMapPoint(point))
}
return Array(points)
}
}

Answer 2

I figured this out by doing a little loop through the points in the polygon. For every 3 points, I check if the center of that triangle is in the polygon. If it is continue, if not, connect the polygon so that there are no dips in the polygon. Once done, get the triangles in the polygon and do the math to get the area. Then subtract the triangles that were removed.
Hope this helps someone.