Find the precise centroid (as an MKMapPoint) of an MKPolygon - ios

Question

This means excluding the area(s) of any interiorPolygons.
Once one has the centroid of the outer points polygon, how does one (i.e., in the form of an Objective-C example) adjust the centroid by the subtractive interiorPolygons? Or is there a more elegant way to compute the centroid in one go?
If you help get the code working, it will be open sourced (WIP here).
Might be helpful:
http://www.ecourses.ou.edu/cgi-bin/eBook.cgi?topic=st&chap_sec=07.2&page=case_sol
https://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon

Answer 1

Thinking about it today, it makes qualitative sense that adding each interior centroid weighted by area to the exterior centroid would arrive at something sensible. (A square with an interior polygon (hole) on the left side would displace the centroid right, directly proportional to the area of the hole.)
Not to scale:
- (MKMapPoint)calculateCentroid
{
switch (self.pointCount) {
case 0: return MKMapPointMake(0.0,
0.0);
case 1: return MKMapPointMake(self.points[0].x,
self.points[0].y);
case 2: return MKMapPointMake((self.points[0].x + self.points[1].x) / 2.0,
(self.points[0].y + self.points[1].y) / 2.0);
}
// onward implies pointCount >= 3
MKMapPoint centroid;
MKMapPoint *previousPoint = &(self.points[self.pointCount-1]); // for i=0, wrap around to the last point
for (NSUInteger i = 0; i < self.pointCount; ++i) {
MKMapPoint *point = &(self.points[i]);
double delta = (previousPoint->x * point->y) - (point->x * previousPoint->y); // x[i-1]*y[i] + x[i]*y[i-1]
centroid.x += (previousPoint->x + point->x) * delta; // (x[i-1] + x[i]) / delta
centroid.y += (previousPoint->y + point->y) * delta; // (y[i-1] + y[i]) / delta
previousPoint = point;
}
centroid.x /= 6.0 * self.area;
centroid.y /= 6.0 * self.area;
// interiorPolygons are holes (subtractive geometry model)
for (MKPolygon *interiorPoly in self.interiorPolygons) {
if (interiorPoly.area == 0.0) {
continue; // avoid div-by-zero
}
centroid.x += interiorPoly.centroid.x / interiorPoly.area;
centroid.y += interiorPoly.centroid.y / interiorPoly.area;
}
return centroid;
}

Answer 2

in Swift 5
private func centroidForCoordinates(_ coords: [CLLocationCoordinate2D]) -> CLLocationCoordinate2D? {
guard let firstCoordinate = coordinates.first else {
return nil
}
guard coords.count > 1 else {
return firstCoordinate
}
var minX = firstCoordinate.longitude
var maxX = firstCoordinate.longitude
var minY = firstCoordinate.latitude
var maxY = firstCoordinate.latitude
for i in 1..<coords.count {
let current = coords[i]
if minX > current.longitude {
minX = current.longitude
} else if maxX < current.longitude {
maxX = current.longitude
} else if minY > current.latitude {
minY = current.latitude
} else if maxY < current.latitude {
maxY = current.latitude
}
}
let centerX = minX + ((maxX - minX) / 2)
let centerY = minY + ((maxY - minY) / 2)
return CLLocationCoordinate2D(latitude: centerY, longitude: centerX)
}