Module: Geocoder::Calculations

Extended by:
Calculations
Included in:
Calculations
Defined in:
lib/geocoder/calculations.rb

Constant Summary

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.

%w[N NE E SE S SW W NW]
EARTH_RADIUS =

Radius of the Earth, in kilometers. Value taken from: en.wikipedia.org/wiki/Earth_radius

6371.0
KM_IN_MI =

Conversion factor: multiply by kilometers to get miles.

0.621371192
KM_IN_NM =

Conversion factor: multiply by nautical miles to get miles.

0.539957
DEGREES_PER_RADIAN =

Conversion factor: multiply by radians to get degrees.

57.2957795
NAN =

Not a number constant

defined?(::Float::NAN) ? ::Float::NAN : 0 / 0.0

Instance Method Summary collapse

Instance Method Details

#bearing_between(point1, point2, options = {}) ⇒ Object

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



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# File 'lib/geocoder/calculations.rb', line 120

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 = {}) ⇒ Object

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. Use Geocoder.configure(:units => …) to configure default units.



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# File 'lib/geocoder/calculations.rb', line 212

def bounding_box(point, radius, options = {})
  lat,lon = extract_coordinates(point)
  radius  = radius.to_f
  units   = options[:units] || Geocoder.config.units
  [
    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) ⇒ Object

Translate a bearing (float) into a compass direction (string, eg “North”).



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# File 'lib/geocoder/calculations.rb', line 158

def compass_point(bearing, points = COMPASS_POINTS)
  seg_size = 360 / points.size
  points[((bearing + (seg_size / 2)) % 360) / seg_size]
end

#coordinates_present?(*args) ⇒ Boolean

Returns true if all given arguments are valid latitude/longitude values.

Returns:

  • (Boolean)


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# File 'lib/geocoder/calculations.rb', line 40

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 = {}) ⇒ Object

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 Use Geocoder.configure(:units => …) to configure default units.



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# File 'lib/geocoder/calculations.rb', line 82

def distance_between(point1, point2, options = {})

  # set default options
  options[:units] ||= Geocoder.config.units

  # 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) ⇒ Object



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# File 'lib/geocoder/calculations.rb', line 324

def distance_to_radians(distance, units = nil)
  units ||= Geocoder.config.units
  distance.to_f / earth_radius(units)
end

#earth_radius(units = nil) ⇒ Object

Radius of the Earth in the given units (:mi or :km). Use Geocoder.configure(:units => …) to configure default units.



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# File 'lib/geocoder/calculations.rb', line 359

def earth_radius(units = nil)
  units ||= Geocoder.config.units
  case units
    when :km; EARTH_RADIUS
    when :mi; to_miles(EARTH_RADIUS)
    when :nm; to_nautical_miles(EARTH_RADIUS)
  end
end

#endpoint(start, heading, distance, options = {}) ⇒ Object

Given a start point, distance, and heading (in degrees), 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



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# File 'lib/geocoder/calculations.rb', line 273

def endpoint(start, heading, distance, options = {})
  options[:units] ||= Geocoder.config.units
  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) ⇒ Object

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.



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# File 'lib/geocoder/calculations.rb', line 404

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) ⇒ Object

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.



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# File 'lib/geocoder/calculations.rb', line 169

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_miObject

Conversion factor: km to mi.



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# File 'lib/geocoder/calculations.rb', line 371

def km_in_mi
  KM_IN_MI
end

#km_in_nmObject

Conversion factor: km to nm.



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# File 'lib/geocoder/calculations.rb', line 378

def km_in_nm
  KM_IN_NM
end

#latitude_degree_distance(units = nil) ⇒ Object

Distance spanned by one degree of latitude in the given units.



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# File 'lib/geocoder/calculations.rb', line 52

def latitude_degree_distance(units = nil)
  units ||= Geocoder.config.units
  2 * Math::PI * earth_radius(units) / 360
end

#longitude_degree_distance(latitude, units = nil) ⇒ Object

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.



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# File 'lib/geocoder/calculations.rb', line 61

def longitude_degree_distance(latitude, units = nil)
  units ||= Geocoder.config.units
  latitude_degree_distance(units) * Math.cos(to_radians(latitude))
end

#mi_in_kmObject

Conversion factor: mi to km.



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# File 'lib/geocoder/calculations.rb', line 387

def mi_in_km
  1.0 / KM_IN_MI
end

#nm_in_kmObject

Conversion factor: nm to km.



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# File 'lib/geocoder/calculations.rb', line 394

def nm_in_km
  1.0 / KM_IN_NM
end

#radians_to_distance(radians, units = nil) ⇒ Object



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# File 'lib/geocoder/calculations.rb', line 329

def radians_to_distance(radians, units = nil)
  units ||= Geocoder.config.units
  radians * earth_radius(units)
end

#random_point_near(center, radius, options = {}) ⇒ Object

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.



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# File 'lib/geocoder/calculations.rb', line 240

def random_point_near(center, radius, options = {})

  # set default options
  options[:units] ||= Geocoder.config.units

  # 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 * rand

  # random radius, use the square root to ensure a uniform
  # distribution of points over the circle
  r = Math.sqrt(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) ⇒ Object

Convert radians to degrees. If an array (or multiple arguments) is passed, converts each value and returns array.



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# File 'lib/geocoder/calculations.rb', line 315

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) ⇒ Object

Convert miles to kilometers.



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# File 'lib/geocoder/calculations.rb', line 337

def to_kilometers(mi)
  mi * mi_in_km
end

#to_miles(km) ⇒ Object

Convert kilometers to miles.



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# File 'lib/geocoder/calculations.rb', line 344

def to_miles(km)
  km * km_in_mi
end

#to_nautical_miles(km) ⇒ Object

Convert kilometers to nautical miles.



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# File 'lib/geocoder/calculations.rb', line 351

def to_nautical_miles(km)
  km * km_in_nm
end

#to_radians(*args) ⇒ Object

Convert degrees to radians. If an array (or multiple arguments) is passed, converts each value and returns array.



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# File 'lib/geocoder/calculations.rb', line 301

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