MKPolygon area calculation

Solution 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.
}

Solution 2:

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

Solution 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;
}