# 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]`

`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`
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).

• 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 miles to kilometers.

• Convert kilometers to miles.

• Convert kilometers to nautical miles.

## 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.

 ``` 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148``` ```# File 'lib/geocoder/calculations.rb', line 115 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.

 ``` 207 208 209 210 211 212 213 214 215 216 217``` ```# File 'lib/geocoder/calculations.rb', line 207 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”).

 ``` 153 154 155 156``` ```# File 'lib/geocoder/calculations.rb', line 153 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)
 ``` 35 36 37 38 39 40 41 42``` ```# File 'lib/geocoder/calculations.rb', line 35 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 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.

 ``` 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98``` ```# File 'lib/geocoder/calculations.rb', line 77 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

 ``` 285 286 287 288``` ```# File 'lib/geocoder/calculations.rb', line 285 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.

 ``` 320 321 322 323 324 325 326 327``` ```# File 'lib/geocoder/calculations.rb', line 320 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```

### #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.

 ``` 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386``` ```# File 'lib/geocoder/calculations.rb', line 365 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.

 ``` 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189``` ```# File 'lib/geocoder/calculations.rb', line 164 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 ⇒ Object

Conversion factor: km to mi.

 ``` 332 333 334``` ```# File 'lib/geocoder/calculations.rb', line 332 def km_in_mi KM_IN_MI end```

### #km_in_nm ⇒ Object

Conversion factor: km to nm.

 ``` 339 340 341``` ```# File 'lib/geocoder/calculations.rb', line 339 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.

 ``` 47 48 49 50``` ```# File 'lib/geocoder/calculations.rb', line 47 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.

 ``` 56 57 58 59``` ```# File 'lib/geocoder/calculations.rb', line 56 def longitude_degree_distance(latitude, units = nil) units ||= Geocoder.config.units latitude_degree_distance(units) * Math.cos(to_radians(latitude)) end```

### #mi_in_km ⇒ Object

Conversion factor: mi to km.

 ``` 348 349 350``` ```# File 'lib/geocoder/calculations.rb', line 348 def mi_in_km 1.0 / KM_IN_MI end```

### #nm_in_km ⇒ Object

Conversion factor: nm to km.

 ``` 355 356 357``` ```# File 'lib/geocoder/calculations.rb', line 355 def nm_in_km 1.0 / KM_IN_NM end```

 ``` 290 291 292 293``` ```# File 'lib/geocoder/calculations.rb', line 290 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 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.

 ``` 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255``` ```# File 'lib/geocoder/calculations.rb', line 235 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.

 ``` 276 277 278 279 280 281 282 283``` ```# File 'lib/geocoder/calculations.rb', line 276 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.

 ``` 298 299 300``` ```# File 'lib/geocoder/calculations.rb', line 298 def to_kilometers(mi) mi * mi_in_km end```

### #to_miles(km) ⇒ Object

Convert kilometers to miles.

 ``` 305 306 307``` ```# File 'lib/geocoder/calculations.rb', line 305 def to_miles(km) km * km_in_mi end```

### #to_nautical_miles(km) ⇒ Object

Convert kilometers to nautical miles.

 ``` 312 313 314``` ```# File 'lib/geocoder/calculations.rb', line 312 def to_nautical_miles(km) km * km_in_nm end```

 ``` 262 263 264 265 266 267 268 269``` ```# File 'lib/geocoder/calculations.rb', line 262 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```