# 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

• Bearing between two points on Earth.

• Returns coordinates of the southwest and northeast corners of a box with the given point at its center.

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

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

• Distance between two points on Earth (Haversine formula).

• Radius of the Earth in the given units (:mi or :km).

• Given a start point, heading (in degrees), and distance, provides an endpoint.

• 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.

• Compute the geographic center (aka geographic midpoint, center of gravity) for an array of geocoded objects and/or [lat,lon] arrays (can be mixed).

• Conversion factor: km to mi.

• Conversion factor: km to nm.

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

• Distance spanned by one degree of longitude at the given latitude.

• Conversion factor: mi to km.

• Conversion factor: nm to km.

• Random point within a circle of provided radius centered around the provided point Takes one point, one radius, and an options hash.

• Convert radians to degrees.

• Convert miles to kilometers.

• Convert kilometers to miles.

• Convert kilometers to nautical miles.

• Convert degrees to radians.

## 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.

 ``` 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 - point1 dlon = point2 - point1 case options[:method] when :linear y = dlon x = dlat when :spherical y = Math.sin(dlon) * Math.cos(point2) x = Math.cos(point1) * Math.sin(point2) - Math.sin(point1) * Math.cos(point2) * 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 - point1 dlon = point2 - point1 a = (Math.sin(dlat / 2))**2 + Math.cos(point1) * (Math.sin(dlon / 2))**2 * Math.cos(point2) 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 lon = start 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) * Math.cos(p) y << Math.cos(p) * Math.sin(p) z << Math.sin(p) 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 ⇒ Object

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_nm ⇒ Object

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_km ⇒ Object

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_km ⇒ Object

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 + delta_lat, center + 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```