# 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]

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

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

• 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, distance, and heading (in degrees), 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 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.

 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 # 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.

 212 213 214 215 216 217 218 219 220 221 222 # 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”).

 158 159 160 161 # 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)
 40 41 42 43 44 45 46 47 # 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 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.

 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 # 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

 324 325 326 327 # 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.

 359 360 361 362 363 364 365 366 # 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 geocoded object (one which implements a to_coordinates method which returns a [lat,lon] array

### #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.

 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 # 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.

 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 # 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_mi ⇒ Object

Conversion factor: km to mi.

 371 372 373 # File 'lib/geocoder/calculations.rb', line 371 def km_in_mi KM_IN_MI end

### #km_in_nm ⇒ Object

Conversion factor: km to nm.

 378 379 380 # 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.

 52 53 54 55 # 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.

 61 62 63 64 # 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_km ⇒ Object

Conversion factor: mi to km.

 387 388 389 # File 'lib/geocoder/calculations.rb', line 387 def mi_in_km 1.0 / KM_IN_MI end

### #nm_in_km ⇒ Object

Conversion factor: nm to km.

 394 395 396 # File 'lib/geocoder/calculations.rb', line 394 def nm_in_km 1.0 / KM_IN_NM 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.

 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 # 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.

 315 316 317 318 319 320 321 322 # 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.

 337 338 339 # File 'lib/geocoder/calculations.rb', line 337 def to_kilometers(mi) mi * mi_in_km end

### #to_miles(km) ⇒ Object

Convert kilometers to miles.

 344 345 346 # 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.

 351 352 353 # File 'lib/geocoder/calculations.rb', line 351 def to_nautical_miles(km) km * km_in_nm end