http://franz.com/ns/allegrograph/5.0/geo/nd#inBoundingBox

Returns the subject or subject and object of triples in the bounding box specified by the nD minimum and maximum ordinate values. 

?event nd:inBoundingBox (ex:myCartesianPredicate  
                         :x-min 30.3 :x-max 31.2  
                         :y-min 11.6 :y-max 11.9  
                         :time-min "2016-03-02T10:00:00"  
                         :time-max "2016-03-02T11:00:00"  
                         :temp-min 48 :temp-max 60 ) .

or 

(?event ?coord) nd:inBoundingBox (ex:mySphericalPredicate  
                                  :lon-min -123 :lon-max -122  
                                  :lat-min 32   :lat-max 33  
                                  :time-min "2016-03-02T10:00:00"  
                                  :time-max "2016-03-02T11:00:00"  
                                  :temp-min 48 :temp-max 60 ) .

The pairs of lower and upper bounds specifying the nD box for each ordinate in the nD literal encoding must all be bound before this magic property can be evaluated.

http://franz.com/ns/allegrograph/5.0/geo/nd#inCircle

Returns the subject or subject and object of triples within an N-Dimensional radius

The center of the region is specified by the ordinate values given for the several geo ordinates. In spherical ordinate systems exactly one ordinate of type :latitude and exactly one ordinate of type :longitude must be provided. In cartesian ordinate systems one or more ordinates of type :cartesian must be provided. A minimum and maximum ordinate value must be provided for each of the remaining ordinates, as for nd:inBoundingBox.

This can return the subject of the matching triples or the subject and the N-Dimensional literal (which is in the object). For example: 

?event nd:inCircle (ex:locationPredicate :lat 37.805 :lon -122.1217  
                                         :radius 0.1 :units :km  
                                         :time-min "2015-11-04T08:45:00Z"  
                                         :time-max "2015-11-04T09:00:00Z") .

or 

(?event ?wherewhen) nd:inCircle (ex:locationPredicate ...) .

For spherical coordinates a :units argument is accepted specifying the units of the :radius argument. It may be :km (default), :miles, or :radians of arc.

Notes

The following namespace abbreviations are used:

The SPARQL magic properties reference has additional information on using AllegroGraph magic properties and functions.