Calculation of the area of ​​M.K. Polygon

Question

I am trying to make an area calculation category for MKPolygon. I found the 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 that gave the wrong result (a thousand times the 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 final step for i = N-1 and i+1 = 0 (wrap) is missing in your loop.

Answer 2

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 3

This may help someone ... You need to pass the boundary points of the form below the method and return the correct region of the 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; }