module Geocoder::Calculations
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.
- DEGREES_PER_RADIAN
Conversion factor: multiply by radians to get degrees.
- EARTH_RADII
Radius of the Earth, in kilometers. Value taken from: en.wikipedia.org/wiki/Earth_radius
- EARTH_RADIUS
- KM_IN_MI
Conversion factor: multiply by kilometers to get miles.
- KM_IN_NM
Conversion factor: multiply by nautical miles to get miles.
- NAN
Not a number constant
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
or:spherical
; the spherical method is “correct” in that it returns the shortest path (one along a great circle) but the linear method is less confusing (returns due east or west when given two points with the same latitude). UseGeocoder.configure
(:distances => …) to configure calculation method.
Based on: www.movable-type.co.uk/scripts/latlong.html
# File lib/geocoder/calculations.rb, line 118 def bearing_between(point1, point2, options = {}) # set default options options[:method] ||= Geocoder.config.distances 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 southwest and northeast 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
or:km
. UseGeocoder.configure
(:units => …) to configure default units.
# File lib/geocoder/calculations.rb, line 210 def bounding_box(point, radius, options = {}) lat,lon = extract_coordinates(point) radius = radius.to_f [ lat - (radius / latitude_degree_distance(options[:units])), lon - (radius / longitude_degree_distance(lat, options[:units])), lat + (radius / latitude_degree_distance(options[:units])), lon + (radius / longitude_degree_distance(lat, options[:units])) ] end
Translate a bearing (float) into a compass direction (string, eg “North”).
# File lib/geocoder/calculations.rb, line 156 def compass_point(bearing, points = COMPASS_POINTS) seg_size = 360.0 / points.size points[((bearing + (seg_size / 2)) % 360) / seg_size] end
Returns true if all given arguments are valid latitude/longitude values.
# File lib/geocoder/calculations.rb, line 44 def coordinates_present?(*args) args.each do |a| # note that Float::NAN != Float::NAN # still, this could probably be improved: return false if (!a.is_a?(Numeric) or a.to_s == "NaN") end true 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
or:km
UseGeocoder.configure
(:units => …) to configure default units.
# File lib/geocoder/calculations.rb, line 84 def distance_between(point1, point2, options = {}) # 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/geocoder/calculations.rb, line 319 def distance_to_radians(distance, units = nil) distance.to_f / earth_radius(units) end
Radius of the Earth in the given units (:mi or :km). Use Geocoder.configure
(:units => …) to configure default units.
# File lib/geocoder/calculations.rb, line 355 def earth_radius(units = nil) EARTH_RADII[units || Geocoder.config.units] end
Given a start point, heading (in degrees), and distance, provides an endpoint. The starting point is given in the same way that points are given to all Geocoder
methods that accept points as arguments. It 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
# File lib/geocoder/calculations.rb, line 269 def endpoint(start, heading, distance, options = {}) radius = earth_radius(options[:units]) start = extract_coordinates(start) # convert degrees to radians start = to_radians(start) lat = start[0] lon = start[1] heading = to_radians(heading) distance = distance.to_f end_lat = Math.asin(Math.sin(lat)*Math.cos(distance/radius) + Math.cos(lat)*Math.sin(distance/radius)*Math.cos(heading)) end_lon = lon+Math.atan2(Math.sin(heading)*Math.sin(distance/radius)*Math.cos(lat), Math.cos(distance/radius)-Math.sin(lat)*Math.sin(end_lat)) to_degrees [end_lat, end_lon] 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/geocoder/calculations.rb, line 397 def extract_coordinates(point) case point when Array if point.size == 2 lat, lon = point if !lat.nil? && lat.respond_to?(:to_f) and !lon.nil? && lon.respond_to?(:to_f) then return [ lat.to_f, lon.to_f ] end end when String point = Geocoder.coordinates(point) and return point else if point.respond_to?(:to_coordinates) if Array === array = point.to_coordinates return extract_coordinates(array) end end end [ NAN, NAN ] 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/geocoder/calculations.rb, line 167 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/geocoder/calculations.rb, line 362 def km_in_mi Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.km_in_mi is deprecated and will be removed in Geocoder 1.5.0. Please use the constant KM_IN_MI instead.") KM_IN_MI end
Conversion factor: km to nm.
# File lib/geocoder/calculations.rb, line 370 def km_in_nm Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.km_in_nm is deprecated and will be removed in Geocoder 1.5.0. Please use the constant KM_IN_NM instead.") KM_IN_NM end
Distance spanned by one degree of latitude in the given units.
# File lib/geocoder/calculations.rb, line 56 def latitude_degree_distance(units = nil) 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/geocoder/calculations.rb, line 64 def longitude_degree_distance(latitude, units = nil) latitude_degree_distance(units) * Math.cos(to_radians(latitude)) end
Conversion factor: mi to km.
# File lib/geocoder/calculations.rb, line 378 def mi_in_km Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.mi_in_km is deprecated and will be removed in Geocoder 1.5.0. Please use 1.0 / KM_IN_MI instead.") 1.0 / KM_IN_MI end
Conversion factor: nm to km.
# File lib/geocoder/calculations.rb, line 386 def nm_in_km Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.nm_in_km is deprecated and will be removed in Geocoder 1.5.0. Please use 1.0 / KM_IN_NM instead.") 1.0 / KM_IN_NM end
# File lib/geocoder/calculations.rb, line 323 def radians_to_distance(radians, units = nil) radians * earth_radius(units) end
Random point within a circle of provided radius centered around the provided point Takes one point, one radius, 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
or:km
UseGeocoder.configure
(:units => …) to configure default units. -
:seed
- The seed for the random number generator
# File lib/geocoder/calculations.rb, line 238 def random_point_near(center, radius, options = {}) random = Random.new(options[:seed] || Random.new_seed) # convert to coordinate arrays center = extract_coordinates(center) earth_circumference = 2 * Math::PI * earth_radius(options[:units]) max_degree_delta = 360.0 * (radius / earth_circumference) # random bearing in radians theta = 2 * Math::PI * random.rand # random radius, use the square root to ensure a uniform # distribution of points over the circle r = Math.sqrt(random.rand) * max_degree_delta delta_lat, delta_long = [r * Math.cos(theta), r * Math.sin(theta)] [center[0] + delta_lat, center[1] + delta_long] end
Convert radians to degrees. If an array (or multiple arguments) is passed, converts each value and returns array.
# File lib/geocoder/calculations.rb, line 310 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/geocoder/calculations.rb, line 330 def to_kilometers(mi) Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.to_kilometers is deprecated and will be removed in Geocoder 1.5.0. Please multiply by MI_IN_KM instead.") mi * mi_in_km end
Convert kilometers to miles.
# File lib/geocoder/calculations.rb, line 338 def to_miles(km) Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.to_miles is deprecated and will be removed in Geocoder 1.5.0. Please multiply by KM_IN_MI instead.") km * KM_IN_MI end
Convert kilometers to nautical miles.
# File lib/geocoder/calculations.rb, line 346 def to_nautical_miles(km) Geocoder.log(:warn, "DEPRECATION WARNING: Geocoder::Calculations.to_nautical_miles is deprecated and will be removed in Geocoder 1.5.0. Please multiply by KM_IN_NM instead.") km * KM_IN_NM end
Convert degrees to radians. If an array (or multiple arguments) is passed, converts each value and returns array.
# File lib/geocoder/calculations.rb, line 296 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