How to do an intersection or overlap query in mongo shell - what circles overlap my search region? Within relate only to the center position but doesn't include radius of the other circles in searched scope.

Mongo:

# My bad conception:
var search = [[30, 30], 10]
db.places.find({circle : {"$within" : {"$center" : [search]}}})

Now I can obtain only this circles within central point lies in searched area of circle:

Ruby:

# field :circle, type: Circle # eg. [ [ 30, 30 ], 10 ]
field :radius, type: Integer
field :location, :type => Array, :spatial => true
spatial_index :location

Places.within_circle(location: [ [ 30, 30 ], 10 ])

# {"$query"=>{"location"=>{"$within"=>{"$center"=>[[30, 30], 10]}}}

I created example data with additional location (special index) and radius instead circle because circle isn't supported by mongodb geo index:

{ "_id" : 1, "name" : "a", "circle" : [ [ 5, 5 ], 40 ], "latlng" : [ 5, 5 ], "radius" : 40 }
{ "_id" : 2, "name" : "b", "circle" : [ [ 10, 10 ], 5 ], "latlng" : [ 10, 10 ], "radius" : 5 }
{ "_id" : 3, "name" : "c", "circle" : [ [ 20, 20 ], 5 ], "latlng" : [ 20, 20 ], "radius" : 5 }
{ "_id" : 4, "name" : "d", "circle" : [ [ 30, 30 ], 50 ], "latlng" : [ 30, 30 ], "radius" : 50}
{ "_id" : 5, "name" : "e", "circle" : [ [ 80, 80 ], 30 ], "latlng" : [ 80, 80 ], "radius" : 30}
{ "_id" : 6, "name" : "f", "circle" : [ [ 80, 80 ], 20 ], "latlng" : [ 80, 80 ], "radius" : 20}

Desired query result:

{ "_id" : 1, "name" : "a", "circle" : [ [ 5, 5 ], 40 ], "latlng" : [ 5, 5 ], "radius" : 40 }
{ "_id" : 3, "name" : "c", "circle" : [ [ 20, 20 ], 5 ], "latlng" : [ 20, 20 ], "radius" : 5 }
{ "_id" : 4, "name" : "d", "circle" : [ [ 30, 30 ], 50 ], "latlng" : [ 30, 30 ], "radius" : 50}
{ "_id" : 5, "name" : "e", "circle" : [ [ 80, 80 ], 30 ], "latlng" : [ 80, 80 ], "radius" : 30}

Solution below assumes that I get all rows and then filter on the ruby side my radius but it returns only:

{ "_id" : 4, "name" : "d", "circle" : [ [ 30, 30 ], 50 ], "latlng" : [ 30, 30 ], "radius" : 50}