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

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

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(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:

  • :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
distance_to_radians(distance, units = :mi) click to toggle source
# File lib/geo_calc/geo_calculations.rb, line 221
def distance_to_radians(distance, units = :mi)
  distance.to_f / earth_radius(units)
end
earth_radius(units = :mi) click to toggle source

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
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/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
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/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
km_in_mi() click to toggle source

Conversion factor: km to mi.

# File lib/geo_calc/geo_calculations.rb, line 253
def km_in_mi
  KM_IN_MI
end
latitude_degree_distance(units = :mi) click to toggle source

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
longitude_degree_distance(latitude, units = :mi) 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/geo_calc/geo_calculations.rb, line 34
def longitude_degree_distance(latitude, units = :mi)
  latitude_degree_distance(units) * Math.cos(to_radians(latitude))
end
mi_in_km() click to toggle source

Conversion factor: mi to km.

# File lib/geo_calc/geo_calculations.rb, line 260
def mi_in_km
  1.0 / KM_IN_MI
end
radians_to_distance(radians, units = :mi) click to toggle source
# File lib/geo_calc/geo_calculations.rb, line 225
def radians_to_distance(radians, units = :mi)
  radians * earth_radius(units)
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/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
to_kilometers(mi) click to toggle source

Convert miles to kilometers.

# File lib/geo_calc/geo_calculations.rb, line 232
def to_kilometers(mi)
  mi * mi_in_km
end
to_miles(km) click to toggle source

Convert kilometers to miles.

# File lib/geo_calc/geo_calculations.rb, line 239
def to_miles(km)
  km * km_in_mi
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/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