MKPolygon area calculation - objective-c

Question

I'm trying to make an area calculation category for MKPolygon.
I found some JS code https://github.com/mapbox/geojson-area/blob/master/index.js#L1 with a link to the algorithm: http://trs-new.jpl.nasa.gov/dspace/handle/2014/40409.
It says:
Here is my code, which gave a wrong result (thousands times more than actual):
#define kEarthRadius 6378137
#implementation MKPolygon (AreaCalculation)
- (double) area {
double area = 0;
NSArray *coords = [self coordinates];
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;
}
#end
What did I miss?

Answer 1

The whole algorithm implemented in Swift 3.0 :
import MapKit
let kEarthRadius = 6378137.0
// CLLocationCoordinate2D uses degrees but we need radians
func radians(degrees: Double) -> Double {
return degrees * M_PI / 180;
}
func regionArea(locations: [CLLocationCoordinate2D]) -> Double {
guard locations.count > 2 else { return 0 }
var area = 0.0
for i in 0..<locations.count {
let p1 = locations[i > 0 ? i - 1 : locations.count - 1]
let p2 = locations[i]
area += radians(degrees: p2.longitude - p1.longitude) * (2 + sin(radians(degrees: p1.latitude)) + sin(radians(degrees: p2.latitude)) )
}
area = -(area * kEarthRadius * kEarthRadius / 2);
return max(area, -area) // In order not to worry about is polygon clockwise or counterclockwise defined.
}

Answer 2

The final step for i = N-1 and i+1 = 0 (wrap around) is missing in your loop.

Answer 3

This may help to someone...
You need to pass the shape edge points into below method and it returns the correct area of a polygon
static double areaOfCurveWithPoints(const NSArray *shapeEdgePoints) {
CGPoint initialPoint = [shapeEdgePoints.firstObject CGPointValue];
CGMutablePathRef cgPath = CGPathCreateMutable();
CGPathMoveToPoint(cgPath, &CGAffineTransformIdentity, initialPoint.x, initialPoint.y);
for (int i = 1;i<shapeEdgePoints.count ;i++) {
CGPoint point = [[shapeEdgePoints objectAtIndex:i] CGPointValue];
CGPathAddLineToPoint(cgPath, &CGAffineTransformIdentity, point.x, point.y);
}
CGPathCloseSubpath(cgPath);
CGRect frame = integralFrameForPath(cgPath);
size_t bytesPerRow = bytesPerRowForWidth(frame.size.width);
CGContextRef gc = createBitmapContextWithFrame(frame, bytesPerRow);
CGContextSetFillColorWithColor(gc, [UIColor whiteColor].CGColor);
CGContextAddPath(gc, cgPath);
CGContextFillPath(gc);
double area = areaFilledInBitmapContext(gc);
CGPathRelease(cgPath);
CGContextRelease(gc);
return area;
}
static CGRect integralFrameForPath(CGPathRef path) {
CGRect frame = CGPathGetBoundingBox(path);
return CGRectIntegral(frame);
}
static size_t bytesPerRowForWidth(CGFloat width) {
static const size_t kFactor = 64;
// Round up to a multiple of kFactor, which must be a power of 2.
return ((size_t)width + (kFactor - 1)) & ~(kFactor - 1);
}
static CGContextRef createBitmapContextWithFrame(CGRect frame, size_t bytesPerRow) {
CGColorSpaceRef grayscale = CGColorSpaceCreateDeviceGray();
CGContextRef gc = CGBitmapContextCreate(NULL, frame.size.width, frame.size.height, 8, bytesPerRow, grayscale, kCGImageAlphaNone);
CGColorSpaceRelease(grayscale);
CGContextTranslateCTM(gc, -frame.origin.x, -frame.origin.x);
return gc;
}
static double areaFilledInBitmapContext(CGContextRef gc) {
size_t width = CGBitmapContextGetWidth(gc);
size_t height = CGBitmapContextGetHeight(gc);
size_t stride = CGBitmapContextGetBytesPerRow(gc);
// Get a pointer to the data
unsigned char *bitmapData = (unsigned char *)CGBitmapContextGetData(gc);
uint64_t coverage = 0;
for (size_t y = 0; y < height; ++y) {
for (size_t x = 0; x < width; ++x) {
coverage += bitmapData[y * stride + x];
}
}
// NSLog(#"coverage =%llu UINT8_MAX =%d",coverage,UINT8_MAX);
return (double)coverage / UINT8_MAX;
}