Module: Geocoder::Calculations

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

Constant Summary collapse

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]
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
EARTH_RADII =

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

{km: 6371.0}
EARTH_RADIUS =

TODO: deprecate this constant (use `EARTH_RADII`)

EARTH_RADII[:km]
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


118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
# 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 = {}) ⇒ 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.


210
211
212
213
214
215
216
217
218
219
# 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) ⇒ Object

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


156
157
158
159
# 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) ⇒ Boolean

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

Returns:

  • (Boolean)

44
45
46
47
48
49
50
51
# 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 = {}) ⇒ 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.


84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
# 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) ⇒ Object


319
320
321
# 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) ⇒ Object

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


355
356
357
# File 'lib/geocoder/calculations.rb', line 355

def earth_radius(units = nil)
  EARTH_RADII[units || Geocoder.config.units]
end

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

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


269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
# 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) ⇒ 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.


397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
# 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) ⇒ 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.


167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
# 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_miObject

Conversion factor: km to mi.


362
363
364
365
# 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_nmObject

Conversion factor: km to nm.


370
371
372
373
# 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) ⇒ Object

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


56
57
58
# 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) ⇒ 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.


64
65
66
# 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_kmObject

Conversion factor: mi to km.


378
379
380
381
# 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_kmObject

Conversion factor: nm to km.


386
387
388
389
# 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) ⇒ Object


323
324
325
# 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 = {}) ⇒ 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.

  • :seed - The seed for the random number generator


238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
# 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) ⇒ Object

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


310
311
312
313
314
315
316
317
# 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) ⇒ Object

Convert miles to kilometers.


330
331
332
333
# 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) ⇒ Object

Convert kilometers to miles.


338
339
340
341
# 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) ⇒ Object

Convert kilometers to nautical miles.


346
347
348
349
# 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) ⇒ Object

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


296
297
298
299
300
301
302
303
# 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