Class: GridRef

Inherits:
Object
  • Object
show all
Defined in:
lib/grid_ref.rb

Constant Summary collapse

OsTiles = 
{
	:a => [0,4], :b => [1,4], :c => [2,4], :d => [3,4], :e => [4,4],
	:f => [0,3], :g => [1,3], :h => [2,3], :j => [3,3], :k => [4,3],
	:l => [0,2], :m => [1,2], :n => [2,2], :o => [3,2], :p => [4,2],
	:q => [0,1], :r => [1,1], :s => [2,1], :t => [3,1], :u => [4,1],
	:v => [0,0], :w => [1,0], :x => [2,0], :y => [3,0], :z => [4,0],
}
FalseOrigin = 
[2,1]
SquareSize =

shorter grid ref = larger square.

[nil, 10000, 1000, 100, 10, 1]
@@iteration_ceiling = 
1000
@@ellipsoids = 
{
  :osgb36 => Ellipsoid.new(6377563.396, 6356256.910),
  :wgs84 => Ellipsoid.new(6378137.000, 6356752.3141),
  :ie65 => Ellipsoid.new(6377340.189, 6356034.447),
  :utm => Ellipsoid.new(6378388.000, 6356911.946)
}
@@projections = 
{
  :gb => {:scale => 0.9996012717, :Phio => 49.to_radians, :Lambdao => -2.to_radians, :Eo => 400000, :No => -100000, :ellipsoid => :osgb36},
  :ie => {:scale => 1.000035, :Phio => 53.5.to_radians, :Lambdao => -8.to_radians, :Eo => 250000, :No => 250000, :ellipsoid => :ie65},
  :utm29 => {:scale => 0.9996, :Phio => 0, :Lambdao => -9.to_radians, :Eo => 500000, :No => 0, :ellipsoid => :utm},
  :utm30 => {:scale => 0.9996, :Phio => 0, :Lambdao => -3.to_radians, :Eo => 500000, :No => 0, :ellipsoid => :utm},
  :utm31 => {:scale => 0.9996, :Phio => 0, :Lambdao => 3.to_radians, :Eo => 500000, :No => 0, :ellipsoid => :utm}
}
@@helmerts = 
{
  :wgs84 => { :tx => 446.448, :ty => -125.157, :tz => 542.060, :rx => 0.1502, :ry => 0.2470, :rz => 0.8421, :s => -20.4894 }
}
@@defaults = 
{
  :projection => :gb,   # mercator projection of input gridref. Can be any projection name: usually :ie or :gb
  :precision => 6       # decimal places in the output lat/long
}

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(string, options = {}) ⇒ GridRef

Returns a new instance of GridRef.

Raises:

  • (ArgumentError) 


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# File 'lib/grid_ref.rb', line 55

def initialize(string, options={})
  raise ArgumentError, "invalid grid reference string '#{string}'." unless string.is_gridref?
  @gridref = string.upcase
  @options = @@defaults.merge(options)
  @projection = @@projections[@options[:projection]]
  @ellipsoid = @@ellipsoids[@projection[:ellipsoid]]
  @datum = @options[:datum]
  self
end

Instance Attribute Details

#datum ⇒ Object

Returns the value of attribute datum.



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# File 'lib/grid_ref.rb', line 48

def datum
  @datum
end

#ellipsoid ⇒ Object

Returns the value of attribute ellipsoid.



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# File 'lib/grid_ref.rb', line 48

def ellipsoid
  @ellipsoid
end

#gridref ⇒ Object

Returns the value of attribute gridref.



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# File 'lib/grid_ref.rb', line 48

def gridref
  @gridref
end

#options ⇒ Object

Returns the value of attribute options.



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# File 'lib/grid_ref.rb', line 48

def options
  @options
end

#projection ⇒ Object

Returns the value of attribute projection.



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# File 'lib/grid_ref.rb', line 48

def projection
  @projection
end

Instance Method Details

#coordinates ⇒ Object 



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# File 'lib/grid_ref.rb', line 114

def coordinates
  unless @coordinates
    # variable names correspond roughly to symbols in the OS algorithm, lowercased:
    # n0 = northing of true origin 
    # e0 = easting of true origin 
    # f0 = scale factor on central meridian
    # phi0 = latitude of true origin 
    # lambda0 = longitude of true origin and central meridian.
    # e2 = eccentricity squared
    # a = length of polar axis of ellipsoid
    # b = length of equatorial axis of ellipsoid
    # ning & eing are the northings and eastings of the supplied gridref
    # phi and lambda are the discovered latitude and longitude
    
    ning = northing
    eing = easting

    n0 = projection[:No]
    e0 = projection[:Eo]
    phi0 = projection[:Phio]
    l0 = projection[:Lambdao]
    f0 = projection[:scale]
    
    a = ellipsoid.a
    b = ellipsoid.b
    e2 = ellipsoid.ecc
    
    # the rest is taken from the OS equations with help from CPAN's Geography::NationalGrid
    # and only enough understanding to transliterate it, and sometimes not even that.

    n = (a - b) / (a + b)
  	m = 0
    phi = phi0
  
    # iterate to within acceptable distance of solution
    
  	count = 0
  	while ((ning - n0 - m) >= 0.001) do
      raise RuntimeError "Demercatorising equation has not converged. Discrepancy after #{count} cycles is #{ning - n0 - m}" if count >= @@iteration_ceiling

  		phi = ((ning - n0 - m) / (a * f0)) + phi
      ma = (1 + n + (1.25 * n**2) + (1.25 * n**3)) * (phi - phi0)
      mb = ((3 * n) + (3 * n**2) + (2.625 * n**3)) * Math.sin(phi - phi0) * Math.cos(phi + phi0)
      mc = ((1.875 * n**2) + (1.875 * n**3)) * Math.sin(2 * (phi - phi0)) * Math.cos(2 * (phi + phi0))
      md = (35/24) * (n**3) * Math.sin(3 * (phi - phi0)) * Math.cos(3 * (phi + phi0))
      m = b * f0 * (ma - mb + mc - md)
  		count += 1
	  end
	  
	  # engage alphabet soup
	  
	  nu = a * f0 * ((1-(e2) * ((Math.sin(phi)**2))) ** -0.5)
  	rho = a * f0 * (1-(e2)) * ((1-(e2)*((Math.sin(phi)**2))) ** -1.5)
  	eta2 = (nu/rho - 1)
  	
  	# fire
  	
  	vii = Math.tan(phi) / (2 * rho * nu)
  	viii = (Math.tan(phi) / (24 * rho * (nu ** 3))) * (5 + (3 * (Math.tan(phi) ** 2)) + eta2 - 9 * eta2 * (Math.tan(phi) ** 2) )
  	ix = (Math.tan(phi) / (720 * rho * (nu ** 5))) * (61 + (90 * (Math.tan(phi) ** 2)) + (45 * (Math.tan(phi) ** 4)) )
  	x = sec(phi) / nu
  	xi = (sec(phi) / (6 * nu ** 3)) * ((nu/rho) + 2 * (Math.tan(phi) ** 2))
  	xii = (sec(phi) / (120 * nu ** 5)) * (5 + (28 * (Math.tan(phi) ** 2)) + (24 * (Math.tan(phi) ** 4)))
  	xiia = (sec(phi) / (5040 * nu ** 7)) * (61 + (662 * (Math.tan(phi) ** 2)) + (1320 * (Math.tan(phi) ** 4)) + (720 * (Math.tan(phi) ** 6)))

    d = eing-e0

    # all of which was just to populate these last two equations:
    
  	phi = phi - vii*(d**2) + viii*(d**4) - ix*(d**6)
    lambda = l0 + x*d - xi*(d**3) + xii*(d**5) - xiia*(d**7)

    # here coordinates are still in radians and osgb36

    @coordinates = helmerted(phi, lambda)
  end
  
  @coordinates
end

#digits ⇒ Object 



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# File 'lib/grid_ref.rb', line 69

def digits
  @digits ||= gridref[2,10]
end

#easting ⇒ Object 



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# File 'lib/grid_ref.rb', line 90

def easting
  @east ||= offsets[:e] + digits[0, resolution].to_i * SquareSize[resolution]
end

#helmerted(phi, lambda) ⇒ Object 



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# File 'lib/grid_ref.rb', line 194

def helmerted(phi, lambda)
  return {:lat => phi, :lng => lambda} unless @datum && @datum != :osgb36
  target_datum = @@ellipsoids[@datum] 
  t = @@helmerts[@datum]
  
  if t && target_datum

    # convert polar to cartesian coordinates using osgb datum

    a = @@ellipsoids[:osgb36].a
    b = @@ellipsoids[:osgb36].b
    e2 = @@ellipsoids[:osgb36].ecc
    
    nu = a / (Math.sqrt(1 - e2 * Math.sin(phi)**2))
    h = 0

    x1 = (nu + h) * Math.cos(phi) * Math.cos(lambda)
    y1 = (nu + h) * Math.cos(phi) * Math.sin(lambda)
    z1 = ((1 - e2) * nu + h) * Math.sin(phi)
    
    # parameterise helmert transformation

    tx = t[:tx]
    ty = t[:ty]
    tz = t[:tz]
    rx = (t[:rx]/3600).to_radians
    ry = (t[:ry]/3600).to_radians
    rz = (t[:rz]/3600).to_radians
    s1 = t[:s]/1e6 + 1

    # apply helmert transformation
    
    xp = tx + x1*s1 - y1*rz + z1*ry
    yp = ty + x1*rz + y1*s1 - z1*rx
    zp = tz - x1*ry + y1*rx + z1*s1
          
    # convert back to polar coordinates using target datum

    a = target_datum.a
    b = target_datum.b
    e2 = target_datum.ecc
    precision = 4 / a
    
    p = Math.sqrt(xp**2 + yp**2)
    phi = Math.atan2(zp, p*(1-e2));
    phip = 2 * Math::PI

    count = 0
    while (phi-phip).abs > precision do
      raise RuntimeError "Helmert transformation has not converged. Discrepancy after #{count} cycles is #{phi-phip}" if count >= @@iteration_ceiling
      
      nu = a / Math.sqrt(1 - e2 * Math.sin(phi)**2)
      phip = phi
      phi = Math.atan2(zp + e2 * nu * Math.sin(phi), p)
      count += 1
    end 

    lambda = Math.atan2(yp, xp)

    {:lat => phi, :lng => lambda}
    
  else
    raise RuntimeError, "Missing ellipsoid or Helmert transformation for #{@datum}"
  end
end

#lat ⇒ Object 



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# File 'lib/grid_ref.rb', line 98

def lat
  coordinates[:lat].to_degrees.round(self.options[:precision])
end

#lng ⇒ Object 



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# File 'lib/grid_ref.rb', line 102

def lng
  coordinates[:lng].to_degrees.round(self.options[:precision])
end

#northing ⇒ Object 



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# File 'lib/grid_ref.rb', line 94

def northing
  @north ||= offsets[:n] + digits[resolution, resolution].to_i * SquareSize[resolution]
end

#offsets ⇒ Object 



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# File 'lib/grid_ref.rb', line 77

def offsets
  if tile
    major = OsTiles[tile[0,1].downcase.to_sym ]
    minor = OsTiles[tile[1,1].downcase.to_sym]
  	@offset ||= {
      :e => (500000 * (major[0] - FalseOrigin[0])) + (100000 * minor[0]),
    	:n => (500000 * (major[1] - FalseOrigin[1])) + (100000 * minor[1])
  	}
  else
    { :e => 0, :n => 0 }
  end
end

#resolution ⇒ Object 



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# File 'lib/grid_ref.rb', line 73

def resolution
  digits.length / 2
end

#tile ⇒ Object 



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# File 'lib/grid_ref.rb', line 65

def tile
  @tile ||= gridref[0,2]
end

#to_latlng ⇒ Object 



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# File 'lib/grid_ref.rb', line 110

def to_latlng
  "#{lat}, #{lng}"
end

#to_s ⇒ Object 



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# File 'lib/grid_ref.rb', line 106

def to_s
  gridref.to_s
end