检查纬度和经度是否在一个圆圈内谷歌地图

Question

Below is the desired result, which I'm looking for

What I would like to know is:

I have created the circle using center point lat lang and radius around it. Now I want to know, how to check (calculate) if a latitude and longitude is either inside or outside the area I would appreciate if you can give me code example in Javascript. I'm using Google Maps API V3.

I found this function but not working as expected for me:

function arePointsNear(checkPoint, centerPoint) {
    var sw = new google.maps.LatLng(centerPoint.lat() - 0.005, centerPoint.lng() - 0.005);
    var ne = new google.maps.LatLng(centerPoint.lat() + 0.005, centerPoint.lng() + 0.005);
    var bounds = new google.maps.LatLngBounds(sw, ne);
    if (bounds.contains (checkPoint)){
        return true;
    }
    return false;
}

Any help will be great.. thanks in advance!!

Answer 1

For such short distances, and when the accuracy doesn't have to be exact to the centimeter, you can treat the surface of the earth as flat. Calculate a conversion from degrees to kilometers at the latitude of the center point, then the Pythagorean theorem can be used to get the distance:

function arePointsNear(checkPoint, centerPoint, km) {
  var ky = 40000 / 360;
  var kx = Math.cos(Math.PI * centerPoint.lat / 180.0) * ky;
  var dx = Math.abs(centerPoint.lng - checkPoint.lng) * kx;
  var dy = Math.abs(centerPoint.lat - checkPoint.lat) * ky;
  return Math.sqrt(dx * dx + dy * dy) <= km;
}

Demo: http://jsfiddle.net/Guffa/57gQa/

Note: The code doesn't take into consideration if you are passing the 0/360 longitude. If that is the case, you would have to normalize the longitudes first.

Answer 2

All you need is a little spherical trig

First you need the central angle theta of the arc subtended by your distance (L = 10 km).

L = theta*r

where r is the radius of the earth (6378.135 km)

Now, if the central angle between the point of interest and your center point is < theta, it is inside your circle. Call this angle theta_p.

Here's a diagram illustrating a spherical triangle: spherical triangle image http://en.wikipedia.org/wiki/File:Spherical_trigonometry_basic_triangle.svg

edit - sorry, apparently I don't know how to link to an image?? Here's the URL: http://en.wikipedia.org/wiki/File:Spherical_trigonometry_basic_triangle.svg

In this case, two of the sides of the spherical triangle (call them a, b ) are the difference in longitude and difference in latitude of the points respectively. The included angle C is 90 degrees (angle between lines of longitude and lines of latitude.

The spherical trig law of cosines is:

cos(c) = cos(a)*cos(b) + sin(a)*sin(b)*cos(C)

c is the central angle between your points, which we earlier called theta_p

edit - this solution isn't limited to small distance WRT the radius of the earth, as the other suggestions are.

Answer 3

Use the Pythagorean theorem to validate. The distance from your center to the point you want to validate can be calculated as the hypotenuse of a triangle.