module GeoCalculations
Constants
- COMPASS_POINTS
Compass point names, listed clockwise starting at North.
If you want bearings named using more, fewer, or different points override Geocoder::Calculations.COMPASS_POINTS with your own array.
- EARTH_RADIUS
Radius of the Earth, in kilometers. Value taken from: en.wikipedia.org/wiki/Earth_radius
- KM_IN_MI
Conversion factor: multiply by kilometers to get miles.
Public Instance Methods
Bearing between two points on Earth. Returns a number of degrees from due north (clockwise).
See Geocoder::Calculations.distance_between for ways of specifying the points. Also accepts an options hash:
-
:method
-:linear
(default) or:spherical
; the spherical method is “correct” in that it returns the shortest path (one along a great circle) but the linear method is the default as it is less confusing (returns due east or west when given two points with the same latitude)
Based on: www.movable-type.co.uk/scripts/latlong.html
# File lib/geo_calc/geo_calculations.rb, line 91 def bearing_between(point1, point2, options = {}) # set default options options[:method] = :linear unless options[:method] == :spherical # convert to coordinate arrays point1 = extract_coordinates(point1) point2 = extract_coordinates(point2) # convert degrees to radians point1 = to_radians(point1) point2 = to_radians(point2) # compute deltas dlat = point2[0] - point1[0] dlon = point2[1] - point1[1] case options[:method] when :linear y = dlon x = dlat when :spherical y = Math.sin(dlon) * Math.cos(point2[0]) x = Math.cos(point1[0]) * Math.sin(point2[0]) - Math.sin(point1[0]) * Math.cos(point2[0]) * Math.cos(dlon) end bearing = Math.atan2(x,y) # Answer is in radians counterclockwise from due east. # Convert to degrees clockwise from due north: (90 - to_degrees(bearing) + 360) % 360 end
Returns coordinates of the lower-left and upper-right corners of a box with the given point at its center. The radius is the shortest distance from the center point to any side of the box (the length of each side is twice the radius).
This is useful for finding corner points of a map viewport, or for roughly limiting the possible solutions in a geo-spatial search (ActiveRecord queries use it thusly).
See Geocoder::Calculations.distance_between for ways of specifying the point. Also accepts an options hash:
-
:units
-:mi
(default) or:km
# File lib/geo_calc/geo_calculations.rb, line 181 def bounding_box(point, radius, options = {}) lat,lon = extract_coordinates(point) radius = radius.to_f units = options[:units] || :mi [ lat - (radius / latitude_degree_distance(units)), lon - (radius / longitude_degree_distance(lat, units)), lat + (radius / latitude_degree_distance(units)), lon + (radius / longitude_degree_distance(lat, units)) ] end
Translate a bearing (float) into a compass direction (string, eg “North”).
# File lib/geo_calc/geo_calculations.rb, line 128 def compass_point(bearing, points = COMPASS_POINTS) seg_size = 360 / points.size points[((bearing + (seg_size / 2)) % 360) / seg_size] end
Distance between two points on Earth (Haversine formula). Takes two points and an options hash. The points are given in the same way that points are given to all Geocoder methods that accept points as arguments. They can be:
-
an array of coordinates ([lat,lon])
-
a geocodable address (string)
-
a geocoded object (one which implements a
to_coordinates
method which returns a [lat,lon] array
The options hash supports:
-
:units
-:mi
(default) or:km
# File lib/geo_calc/geo_calculations.rb, line 53 def distance_between(point1, point2, options = {}) # set default options options[:units] ||= :mi # convert to coordinate arrays point1 = extract_coordinates(point1) point2 = extract_coordinates(point2) # convert degrees to radians point1 = to_radians(point1) point2 = to_radians(point2) # compute deltas dlat = point2[0] - point1[0] dlon = point2[1] - point1[1] a = (Math.sin(dlat / 2))**2 + Math.cos(point1[0]) * (Math.sin(dlon / 2))**2 * Math.cos(point2[0]) c = 2 * Math.atan2( Math.sqrt(a), Math.sqrt(1-a)) c * earth_radius(options[:units]) end
# File lib/geo_calc/geo_calculations.rb, line 221 def distance_to_radians(distance, units = :mi) distance.to_f / earth_radius(units) end
Radius of the Earth in the given units (:mi or :km). Default is :mi.
# File lib/geo_calc/geo_calculations.rb, line 246 def earth_radius(units = :mi) units == :km ? EARTH_RADIUS : to_miles(EARTH_RADIUS) end
Takes an object which is a [lat,lon] array, a geocodable string, or an object that implements to_coordinates
and returns a
- lat,lon
-
array. Note that if a string is passed this may be a slow-
running method and may return nil.
# File lib/geo_calc/geo_calculations.rb, line 270 def extract_coordinates(point) case point when Array; point when String; Geocoder.coordinates(point) else point.to_coordinates end end
Compute the geographic center (aka geographic midpoint, center of gravity) for an array of geocoded objects and/or [lat,lon] arrays (can be mixed). Any objects missing coordinates are ignored. Follows the procedure documented at www.geomidpoint.com/calculation.html.
# File lib/geo_calc/geo_calculations.rb, line 139 def geographic_center(points) # convert objects to [lat,lon] arrays and convert degrees to radians coords = points.map{ |p| to_radians(extract_coordinates(p)) } # convert to Cartesian coordinates x = []; y = []; z = [] coords.each do |p| x << Math.cos(p[0]) * Math.cos(p[1]) y << Math.cos(p[0]) * Math.sin(p[1]) z << Math.sin(p[0]) end # compute average coordinate values xa, ya, za = [x,y,z].map do |c| c.inject(0){ |tot,i| tot += i } / c.size.to_f end # convert back to latitude/longitude lon = Math.atan2(ya, xa) hyp = Math.sqrt(xa**2 + ya**2) lat = Math.atan2(za, hyp) # return answer in degrees to_degrees [lat, lon] end
Conversion factor: km to mi.
# File lib/geo_calc/geo_calculations.rb, line 253 def km_in_mi KM_IN_MI end
Distance spanned by one degree of latitude in the given units.
# File lib/geo_calc/geo_calculations.rb, line 26 def latitude_degree_distance(units = :mi) 2 * Math::PI * earth_radius(units) / 360 end
Distance spanned by one degree of longitude at the given latitude. This ranges from around 69 miles at the equator to zero at the poles.
# File lib/geo_calc/geo_calculations.rb, line 34 def longitude_degree_distance(latitude, units = :mi) latitude_degree_distance(units) * Math.cos(to_radians(latitude)) end
Conversion factor: mi to km.
# File lib/geo_calc/geo_calculations.rb, line 260 def mi_in_km 1.0 / KM_IN_MI end
# File lib/geo_calc/geo_calculations.rb, line 225 def radians_to_distance(radians, units = :mi) radians * earth_radius(units) end
Convert radians to degrees. If an array (or multiple arguments) is passed, converts each value and returns array.
# File lib/geo_calc/geo_calculations.rb, line 212 def to_degrees(*args) args = args.first if args.first.is_a?(Array) if args.size == 1 (args.first * 180.0) / Math::PI else args.map{ |i| to_degrees(i) } end end
Convert miles to kilometers.
# File lib/geo_calc/geo_calculations.rb, line 232 def to_kilometers(mi) mi * mi_in_km end
Convert kilometers to miles.
# File lib/geo_calc/geo_calculations.rb, line 239 def to_miles(km) km * km_in_mi end
Convert degrees to radians. If an array (or multiple arguments) is passed, converts each value and returns array.
# File lib/geo_calc/geo_calculations.rb, line 198 def to_radians(*args) args = args.first if args.first.is_a?(Array) if args.size == 1 args.first * (Math::PI / 180) else args.map{ |i| to_radians(i) } end end