This question already exists:
I want to build something like that if a user enters in a room he recieve a notification in swift ios is it possible?
Closed 3 months ago.
I want to calculate distance between two coordinates within 5 meters or even within one meters is it possible
I have tried haversine formula but not getting the desired result
func calculateDistanceWithHaversin(crrLat: Double, crrLong: Double, desLat: Double = 23.1780068, desLong: Double = 75.7865060, radius: Double = 6367444.7) -> Double {
print("CrrLat \(crrLat) = CrrLong = \(crrLong)")
let haversin = { (angle: Double) -> Double in
return (1 - cos(angle))/2
}
let ahaversin = { (angle: Double) -> Double in
return 2 * asin(sqrt(angle))
}
// degree to radian
let dToR = { (angle: Double) -> Double in
return (angle / 360) * 2 * .pi
}
let lat1 = dToR(crrLat)
let lon1 = dToR(crrLong)
let lat2 = dToR(desLat)
let lon2 = dToR(desLong)
return radius * ahaversin(haversin(lat2 - lat1) + cos(lat1) * cos(lat2) * haversin(lon2 - lon1))
}
i have tried this also
func calculateDistance(crrLat: Double, crrLong: Double) {
let destinationLocation = CLLocation(latitude: 23.1780068, longitude: 75.7865060)
let currentLocation = CLLocation(latitude: crrLat, longitude: crrLong)
distance = currentLocation.distance(from: destinationLocation)
print(String(format: "The distance to my buddy is %.02f m", distance))
}
You can calculate distance with this Builtin Function provided by CoreLocation . The provided distance will be in meters
import CoreLocation
let locationOne = CLLocation(latitude: 37.899, longitude: 74.8989)
let locationTwo = CLLocation(latitude: 38.0900, longitude: 78.98898)
let distance = locationOne.distance(from: locationTwo)
So I want to set a specific position with a specific region shown at a specific rotation.
I know there is a setRegion that calculates the altitude automatically, but it doesn't let you set a rotation. To set a rotation I need to use setRotation that takes a center, altitude and heading.
I have no idea how to calculate the altitude needed to file the full region on the screen, regardless of screen side.
I'm trying:
func updateUIView(_ view: ZooMap, context: Context) {
let coordinate = CLLocationCoordinate2D(
latitude: 21.270381425220606,
longitude: -157.81908260613335
)
let span = MKCoordinateSpan(latitudeDelta: 0.007075784913642025, longitudeDelta: 0.010196763428524491)
let region = MKCoordinateRegion(center: coordinate, span: span)
let camera = MKMapCamera()
camera.heading = 71
camera.centerCoordinate = coordinate;
camera.altitude = determineAltitudeForRegion(region: region, heading: camera.heading, viewport: UIScreen.main.bounds.size)
view.setCamera(camera, animated: false)
}
func determineAltitudeForRegion(region: MKCoordinateRegion, heading: Double, viewport: CGSize) -> Double {
// Calculate a new bounding rectangle that is corrected for the aspect ratio
// of the viewport/camera -- this will be needed to ensure the resulting
// altitude actually fits the polygon in view for the observer.
let upperLeftCoord = CLLocationCoordinate2DMake(region.center.latitude + region.span.latitudeDelta / 2, region.center.longitude - region.span.longitudeDelta / 2)
let upperRightCoord = CLLocationCoordinate2DMake(region.center.latitude + region.span.latitudeDelta / 2, region.center.longitude + region.span.longitudeDelta / 2)
let lowerLeftCoord = CLLocationCoordinate2DMake(region.center.latitude - region.span.latitudeDelta / 2, region.center.longitude - region.span.longitudeDelta / 2)
let hDist = MKMapPoint(upperLeftCoord).distance(to: MKMapPoint(upperRightCoord));
let vDist = MKMapPoint(upperLeftCoord).distance(to: MKMapPoint(lowerLeftCoord));
var adjacent: Double = 0;
var newHDist: Double = 0;
var newVDist: Double = 0;
let rect = RectForRegion(region: region)
if (rect.size.height > rect.size.width) {
newVDist = (Double(viewport.height) / Double(viewport.width)) * hDist;
adjacent = newVDist;
} else {
newHDist = (Double(viewport.width) / Double(viewport.height)) * vDist;
adjacent = newHDist;
}
return adjacent / tan(heading.degreesToRadians) / 2
}
func RectForRegion(region: MKCoordinateRegion) -> MKMapRect {
let a: MKMapPoint = MKMapPoint(CLLocationCoordinate2DMake(region.center.latitude + region.span.latitudeDelta / 2, region.center.longitude - region.span.longitudeDelta / 2))
let b: MKMapPoint = MKMapPoint(CLLocationCoordinate2DMake(region.center.latitude - region.span.latitudeDelta / 2, region.center.longitude + region.span.longitudeDelta / 2))
return MKMapRect(x: min(a.x, b.x), y: min(a.y, b.y), width: abs(a.x - b.x), height: abs(a.y - b.y))
}
but its not working properly. How do I do this??
I'm doing a very simple operation. I'm sorting through a bunch of locations in a map to create an enclosing circle, like so:
var maxLong: Double = -180
var maxLat: Double = -180
var minLong: Double = 180
var minLat: Double = 180
for coord in inCoordinates {
maxLong = max(coord.longitude, maxLong)
maxLat = max(coord.latitude, maxLat)
minLong = min(coord.longitude, minLong)
minLat = min(coord.latitude, minLat)
}
let nw: CLLocation = CLLocation(latitude: maxLat, longitude: minLong)
let se: CLLocation = CLLocation(latitude: minLat, longitude: maxLong)
let center = CLLocationCoordinate2D(latitude: (maxLat + minLat) / 2.0, longitude: (maxLong + minLong) / 2.0)
let radiusInMeters = abs(nw.distance(from: se)) / 2.0
return MKCircle(center: center, radius: radiusInMeters)
Pretty straightforward (Yeah, I know about the IDL issue, but I want to keep this simple).
What I'd like to know, is if there were some way I could boil the loop into a variant of reduce, where you would end up with something like this:
let enclosingRect: MKMapRect = inCoordinates.magikalReduce {
// Magic Happens Here -Queue Doug Henning GIF
}
So the returned rect contains the distilled points.
Yeah, I know that I can simply extend Array (with maybe a type qualifier) to do this with a calculated property, but that sort of defeats the purpose of this. The above is fairly efficient, and I'd rather not add overhead, just to be fancy (Which means, even if I could do it, it might be too inefficient to use).
This is more of a curiosity exploration than a technical need. The above code does fine for me, and is relatively zippy.
Do you mean
// calculate the enclosing rect with `reduce` and `union`, you have to create an `MKMapRect` from each coordinate
let enclosingRect = inCoordinates.reduce(MKMapRect.null) { $0.union(MKMapRect(origin: MKMapPoint($1), size: MKMapSize())) }
You can create a struct for holding the min/max longitude and latitude values, then use reduce, where you use the initial values for these for creating an initial result, then creating an updated version of the struct with the necessary min/max calculations.
struct MinMaxCoordinates {
let maxLong:Double
let maxLat:Double
let minLong:Double
let minLat:Double
}
let minMaxCoordinates = inCoordinates.reduce(MinMaxCoordinates(maxLong: -180, maxLat: -180, minLong: 180, minLat: 180), {minMax, coord in
return MinMaxCoordinates(maxLong: max(minMax.maxLong, coord.longitude), maxLat: max(minMax.maxLat, coord.latitude), minLong: min(minMax.minLong, coord.longitude), minLat: max(minMax.minLat, coord.latitude))
})
let nw: CLLocation = CLLocation(latitude: minMaxCoordinates.maxLat, longitude: minMaxCoordinates.minLong)
let se: CLLocation = CLLocation(latitude: minMaxCoordinates.minLat, longitude: minMaxCoordinates.maxLong)
let center = CLLocationCoordinate2D(latitude: (minMaxCoordinates.maxLat + minMaxCoordinates.minLat) / 2.0, longitude: (minMaxCoordinates.maxLong + minMaxCoordinates.minLong) / 2.0)
let radiusInMeters = abs(nw.distance(from: se)) / 2.0
return MKCircle(center: center, radius: radiusInMeters)
Does anyone have a calculation that calculates the new
latitude and longitude based on a starting point, bearing and
distance?
I would greatly appreciate any help people might have.
I've used the code from Calculate new coordinate x meters and y degree away from one coordinate:
- (CLLocationCoordinate2D)coordinateFromCoord:(CLLocationCoordinate2D)fromCoord
atDistanceKm:(double)distanceKm
atBearingDegrees:(double)bearingDegrees
{
double distanceRadians = distanceKm / 6371.0;
//6,371 = Earth's radius in km
double bearingRadians = [self radiansFromDegrees:bearingDegrees];
double fromLatRadians = [self radiansFromDegrees:fromCoord.latitude];
double fromLonRadians = [self radiansFromDegrees:fromCoord.longitude];
double toLatRadians = asin(sin(fromLatRadians) * cos(distanceRadians)
+ cos(fromLatRadians) * sin(distanceRadians) * cos(bearingRadians) );
double toLonRadians = fromLonRadians + atan2(sin(bearingRadians)
* sin(distanceRadians) * cos(fromLatRadians), cos(distanceRadians)
- sin(fromLatRadians) * sin(toLatRadians));
// adjust toLonRadians to be in the range -180 to +180...
toLonRadians = fmod((toLonRadians + 3*M_PI), (2*M_PI)) - M_PI;
CLLocationCoordinate2D result;
result.latitude = [self degreesFromRadians:toLatRadians];
result.longitude = [self degreesFromRadians:toLonRadians];
return result;
}
- (double)radiansFromDegrees:(double)degrees
{
return degrees * (M_PI/180.0);
}
- (double)degreesFromRadians:(double)radians
{
return radians * (180.0/M_PI);
}
Or in Swift:
extension CLLocationCoordinate2D {
func adjusted(distance: Double, degrees: Double) -> CLLocationCoordinate2D {
let distanceRadians = distance / 6_371 // 6,371 == Earth's radius in km
let bearingRadians = degrees.radians
let fromLatRadians = latitude.radians
let fromLonRadians = longitude.radians
let toLatRadians = asin(sin(fromLatRadians) * cos(distanceRadians) + cos(fromLatRadians) * sin(distanceRadians) * cos(bearingRadians))
var toLonRadians = fromLonRadians + atan2(sin(bearingRadians)
* sin(distanceRadians) * cos(fromLatRadians), cos(distanceRadians)
- sin(fromLatRadians) * sin(toLatRadians))
// adjust toLonRadians to be in the range -180 to +180...
toLonRadians = fmod((toLonRadians + 3 * .pi), (2 * .pi)) - .pi
return CLLocationCoordinate2D(latitude: toLatRadians.degrees, longitude: toLonRadians.degrees)
}
}
extension CLLocationDegrees {
var radians: Double { self * .pi / 180 }
}
extension Double {
var degrees: CLLocationDegrees { self * 180 / .pi }
}
You will find all the calculations you could possibly want (including explanations etc) at http://www.movable-type.co.uk/scripts/latlong.html
The code you need is (in JavaScript) under the heading "Destination point given distance and bearing from start point". Excerpting:
var lat2 = Math.asin( Math.sin(lat1)*Math.cos(d/R) +
Math.cos(lat1)*Math.sin(d/R)*Math.cos(brng) );
var lon2 = lon1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(lat1),
Math.cos(d/R)-Math.sin(lat1)*Math.sin(lat2));
Where R = radius of the earth, d = distance (in same units), and lat/long are in radians (since that's what the sin function expects). You go from degrees to radians with
radians = pi * degrees / 180;
You should be able to take it from here. Do look at the link I gave for more info.
I need to check if user location belongs to the MKCoordinateRegion.
I was surprised not to find simple function for this, something like: CGRectContainsCGPoint(rect, point).
I found following piece of code:
CLLocationCoordinate2D topLeftCoordinate =
CLLocationCoordinate2DMake(region.center.latitude
+ (region.span.latitudeDelta/2.0),
region.center.longitude
- (region.span.longitudeDelta/2.0));
CLLocationCoordinate2D bottomRightCoordinate =
CLLocationCoordinate2DMake(region.center.latitude
- (region.span.latitudeDelta/2.0),
region.center.longitude
+ (region.span.longitudeDelta/2.0));
if (location.latitude < topLeftCoordinate.latitude || location.latitude > bottomRightCoordinate.latitude || location.longitude < bottomRightCoordinate.longitude || location.longitude > bottomRightCoordinate.longitude) {
// Coordinate fits into the region
}
But, I am not sure if it is accurate as documentation does not specify exactly how the region rectangle is calculated.
There must be simpler way to do it. Have I overlooked some function in the MapKit framework documentation?
I'm posting this answer as the accepted solution is not valid in my opinion. This answer is also not perfect but it handles the case when coordinates wrap around 360 degrees boundaries, which is enough to be suitable in my situation.
+ (BOOL)coordinate:(CLLocationCoordinate2D)coord inRegion:(MKCoordinateRegion)region
{
CLLocationCoordinate2D center = region.center;
MKCoordinateSpan span = region.span;
BOOL result = YES;
result &= cos((center.latitude - coord.latitude)*M_PI/180.0) > cos(span.latitudeDelta/2.0*M_PI/180.0);
result &= cos((center.longitude - coord.longitude)*M_PI/180.0) > cos(span.longitudeDelta/2.0*M_PI/180.0);
return result;
}
You can convert your location to a point with MKMapPointForCoordinate, then use MKMapRectContainsPoint on the mapview's visibleMapRect. This is completely off the top of my head. Let me know if it works.
In case there is anybody else confused with latitudes and longitues, here is tested, working solution:
MKCoordinateRegion region = self.mapView.region;
CLLocationCoordinate2D location = user.gpsposition.coordinate;
CLLocationCoordinate2D center = region.center;
CLLocationCoordinate2D northWestCorner, southEastCorner;
northWestCorner.latitude = center.latitude - (region.span.latitudeDelta / 2.0);
northWestCorner.longitude = center.longitude - (region.span.longitudeDelta / 2.0);
southEastCorner.latitude = center.latitude + (region.span.latitudeDelta / 2.0);
southEastCorner.longitude = center.longitude + (region.span.longitudeDelta / 2.0);
if (
location.latitude >= northWestCorner.latitude &&
location.latitude <= southEastCorner.latitude &&
location.longitude >= northWestCorner.longitude &&
location.longitude <= southEastCorner.longitude
)
{
// User location (location) in the region - OK :-)
NSLog(#"Center (%f, %f) span (%f, %f) user: (%f, %f)| IN!", region.center.latitude, region.center.longitude, region.span.latitudeDelta, region.span.longitudeDelta, location.latitude, location.longitude);
}else {
// User location (location) out of the region - NOT ok :-(
NSLog(#"Center (%f, %f) span (%f, %f) user: (%f, %f)| OUT!", region.center.latitude, region.center.longitude, region.span.latitudeDelta, region.span.longitudeDelta, location.latitude, location.longitude);
}
The other answers all have faults. The accepted answer is a little verbose, and fails near the international dateline. The cosine answer is workable, but fails for very small regions (because delta cosine is sine which tends towards zero near zero, meaning for smaller angular differences we expect zero change) This answer should work correctly for all situations, and is simpler.
Swift:
/* Standardises and angle to [-180 to 180] degrees */
class func standardAngle(var angle: CLLocationDegrees) -> CLLocationDegrees {
angle %= 360
return angle < -180 ? -360 - angle : angle > 180 ? 360 - 180 : angle
}
/* confirms that a region contains a location */
class func regionContains(region: MKCoordinateRegion, location: CLLocation) -> Bool {
let deltaLat = abs(standardAngle(region.center.latitude - location.coordinate.latitude))
let deltalong = abs(standardAngle(region.center.longitude - location.coordinate.longitude))
return region.span.latitudeDelta >= deltaLat && region.span.longitudeDelta >= deltalong
}
Objective C:
/* Standardises and angle to [-180 to 180] degrees */
+ (CLLocationDegrees)standardAngle:(CLLocationDegrees)angle {
angle %= 360
return angle < -180 ? -360 - angle : angle > 180 ? 360 - 180 : angle
}
/* confirms that a region contains a location */
+ (BOOL)region:(MKCoordinateRegion*)region containsLocation:(CLLocation*)location {
CLLocationDegrees deltaLat = fabs(standardAngle(region.center.latitude - location.coordinate.latitude))
CLLocationDegrees deltalong = fabs(standardAngle(region.center.longitude - location.coordinate.longitude))
return region.span.latitudeDelta >= deltaLat && region.span.longitudeDelta >= deltalong
}
This method fails for regions that include either pole though, but then the coordinate system itself fails at the poles. For most applications, this solution should suffice. (Note, not tested on Objective C)
I've used this code to determine if a coordinate is within a circular region (a coordinate with a radius around it).
- (BOOL)location:(CLLocation *)location isNearCoordinate:(CLLocationCoordinate2D)coordinate withRadius:(CLLocationDistance)radius
{
CLCircularRegion *circularRegion = [[CLCircularRegion alloc] initWithCenter:location.coordinate radius:radius identifier:#"radiusCheck"];
return [circularRegion containsCoordinate:coordinate];
}
Works for me like a charm (Swift 5)
func check(
location: CLLocationCoordinate2D,
contains childLocation: CLLocationCoordinate2D,
with radius: Double)
-> Bool
{
let region = CLCircularRegion(center: location, radius: radius, identifier: "SearchId")
return region.contains(childLocation)
}
Owen Godfrey, the objective-C code doesn´t work, this is the good code:
Fails on Objective-C, this is the good code:
/* Standardises and angle to [-180 to 180] degrees */
- (CLLocationDegrees)standardAngle:(CLLocationDegrees)angle {
angle=fmod(angle,360);
return angle < -180 ? -360 - angle : angle > 180 ? 360 - 180 : angle;
}
-(BOOL)thisRegion:(MKCoordinateRegion)region containsLocation:(CLLocation *)location{
CLLocationDegrees deltaLat =fabs([self standardAngle:(region.center.latitude-location.coordinate.latitude)]);
CLLocationDegrees deltaLong =fabs([self standardAngle:(region.center.longitude-location.coordinate.longitude)]);
return region.span.latitudeDelta >= deltaLat && region.span.longitudeDelta >=deltaLong;
}
CLLocationDegrees deltalong = fabs(standardAngle(region.center.longitude - location.coordinate.longitude));
return region.span.latitudeDelta >= deltaLat && region.span.longitudeDelta >= deltalong;
}
Thanks!
I had problem with same calculations. I like conception proposed by Owen Godfrey here, bun even Fernando here missed the fact that latitude is wraped diferently than longitude and has diferent range. To clarify my proposal I post it with tests so you can check it out by your self.
import XCTest
import MapKit
// MARK - The Solution
extension CLLocationDegrees {
enum WrapingDimension: Double {
case latitude = 180
case longitude = 360
}
/// Standardises and angle to [-180 to 180] or [-90 to 90] degrees
func wrapped(diemension: WrapingDimension) -> CLLocationDegrees {
let length = diemension.rawValue
let halfLenght = length/2.0
let angle = self.truncatingRemainder(dividingBy: length)
switch diemension {
case .longitude:
// return angle < -180.0 ? 360.0 + angle : angle > 180.0 ? -360.0 + angle : angle
return angle < -halfLenght ? length + angle : angle > halfLenght ? -length + angle : angle
case .latitude:
// return angle < -90.0 ? -180.0 - angle : angle > 90.0 ? 180.0 - angle : angle
return angle < -halfLenght ? -length - angle : angle > halfLenght ? length - angle : angle
}
}
}
extension MKCoordinateRegion {
/// confirms that a region contains a location
func contains(_ coordinate: CLLocationCoordinate2D) -> Bool {
let deltaLat = abs((self.center.latitude - coordinate.latitude).wrapped(diemension: .latitude))
let deltalong = abs((self.center.longitude - coordinate.longitude).wrapped(diemension: .longitude))
return self.span.latitudeDelta/2.0 >= deltaLat && self.span.longitudeDelta/2.0 >= deltalong
}
}
// MARK - Unit tests
class MKCoordinateRegionContaingTests: XCTestCase {
func testRegionContains() {
var region = MKCoordinateRegionMake(CLLocationCoordinate2DMake(0, 0), MKCoordinateSpan(latitudeDelta: 1, longitudeDelta: 1))
var coords = CLLocationCoordinate2DMake(0, 0)
XCTAssert(region.contains(coords))
coords = CLLocationCoordinate2DMake(0.5, 0.5)
XCTAssert(region.contains(coords))
coords = CLLocationCoordinate2DMake(-0.5, 0.5)
XCTAssert(region.contains(coords))
coords = CLLocationCoordinate2DMake(0.5, 0.5000001)
XCTAssert(!region.contains(coords)) // NOT Contains
coords = CLLocationCoordinate2DMake(0.5, -0.5000001)
XCTAssert(!region.contains(coords)) // NOT Contains
coords = CLLocationCoordinate2DMake(1, 1)
XCTAssert(!region.contains(coords)) // NOT Contains
region = MKCoordinateRegionMake(CLLocationCoordinate2DMake(0, 180), MKCoordinateSpan(latitudeDelta: 1, longitudeDelta: 1))
coords = CLLocationCoordinate2DMake(0, 180.5)
XCTAssert(region.contains(coords))
coords.longitude = 179.5
XCTAssert(region.contains(coords))
coords.longitude = 180.5000001
XCTAssert(!region.contains(coords)) // NOT Contains
coords.longitude = 179.5000001
XCTAssert(region.contains(coords))
coords.longitude = 179.4999999
XCTAssert(!region.contains(coords)) // NOT Contains
region = MKCoordinateRegionMake(CLLocationCoordinate2DMake(90, -180), MKCoordinateSpan(latitudeDelta: 1, longitudeDelta: 1))
coords = CLLocationCoordinate2DMake(90.5, -180.5)
XCTAssert(region.contains(coords))
coords = CLLocationCoordinate2DMake(89.5, -180.5)
XCTAssert(region.contains(coords))
coords = CLLocationCoordinate2DMake(90.50000001, -180.5)
XCTAssert(!region.contains(coords)) // NOT Contains
coords = CLLocationCoordinate2DMake(89.50000001, -180.5)
XCTAssert(region.contains(coords))
coords = CLLocationCoordinate2DMake(89.49999999, -180.5)
XCTAssert(!region.contains(coords)) // NOT Contains
}
func testStandardAngle() {
var angle = 180.5.wrapped(diemension: .longitude)
var required = -179.5
XCTAssert(self.areAngleEqual(angle, required))
angle = 360.5.wrapped(diemension: .longitude)
required = 0.5
XCTAssert(self.areAngleEqual(angle, required))
angle = 359.5.wrapped(diemension: .longitude)
required = -0.5
XCTAssert(self.areAngleEqual(angle, required))
angle = 179.5.wrapped(diemension: .longitude)
required = 179.5
XCTAssert(self.areAngleEqual(angle, required))
angle = 90.5.wrapped(diemension: .latitude)
required = 89.5
XCTAssert(self.areAngleEqual(angle, required))
angle = 90.5000001.wrapped(diemension: .latitude)
required = 89.4999999
XCTAssert(self.areAngleEqual(angle, required))
angle = -90.5.wrapped(diemension: .latitude)
required = -89.5
XCTAssert(self.areAngleEqual(angle, required))
angle = -90.5000001.wrapped(diemension: .latitude)
required = -89.4999999
XCTAssert(self.areAngleEqual(angle, required))
}
/// compare doubles with presition to 8 digits after the decimal point
func areAngleEqual(_ a:Double, _ b:Double) -> Bool {
let presition = 0.00000001
let equal = Int(a / presition) == Int(b / presition)
print(String(format:"%14.9f %# %14.9f", a, equal ? "==" : "!=", b) )
return equal
}
}
Based on Lukasz solution, but in Swift, in case anybody can make use of Swift:
func isInRegion (region : MKCoordinateRegion, coordinate : CLLocationCoordinate2D) -> Bool {
let center = region.center;
let northWestCorner = CLLocationCoordinate2D(latitude: center.latitude - (region.span.latitudeDelta / 2.0), longitude: center.longitude - (region.span.longitudeDelta / 2.0))
let southEastCorner = CLLocationCoordinate2D(latitude: center.latitude + (region.span.latitudeDelta / 2.0), longitude: center.longitude + (region.span.longitudeDelta / 2.0))
return (
coordinate.latitude >= northWestCorner.latitude &&
coordinate.latitude <= southEastCorner.latitude &&
coordinate.longitude >= northWestCorner.longitude &&
coordinate.longitude <= southEastCorner.longitude
)
}
MarekR's answer works for me. This is the extension I've put it in:
extension MKCoordinateRegion {
func contains(coordinate:CLLocationCoordinate2D) -> Bool {
cos((center.latitude - coordinate.latitude) * Double.pi/180) > cos(span.latitudeDelta / 2.0*Double.pi/180) &&
cos((center.longitude - coordinate.longitude) * Double.pi/180) > cos(span.longitudeDelta / 2.0*Double.pi/180)
}
}