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(point1, point2, options = {}) click to toggle source

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). Use Geocoder.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
bounding_box(point, radius, options = {}) click to toggle source

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:

# 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
compass_point(bearing, points = COMPASS_POINTS) click to toggle source

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
coordinates_present?(*args) click to toggle source

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(point1, point2, options = {}) click to toggle source

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:

# 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
distance_to_radians(distance, units = nil) click to toggle source
# File lib/geocoder/calculations.rb, line 319
def distance_to_radians(distance, units = nil)
  distance.to_f / earth_radius(units)
end
earth_radius(units = nil) click to toggle source

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
endpoint(start, heading, distance, options = {}) click to toggle source

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
extract_coordinates(point) click to toggle source

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
geographic_center(points) click to toggle source

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
km_in_mi() click to toggle source

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
km_in_nm() click to toggle source

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
latitude_degree_distance(units = nil) click to toggle source

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
longitude_degree_distance(latitude, units = nil) click to toggle source

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
mi_in_km() click to toggle source

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
nm_in_km() click to toggle source

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
radians_to_distance(radians, units = nil) click to toggle source
# File lib/geocoder/calculations.rb, line 323
def radians_to_distance(radians, units = nil)
  radians * earth_radius(units)
end
random_point_near(center, radius, options = {}) click to toggle source

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 Use Geocoder.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
to_degrees(*args) click to toggle source

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
to_kilometers(mi) click to toggle source

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
to_miles(km) click to toggle source

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
to_nautical_miles(km) click to toggle source

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
to_radians(*args) click to toggle source

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