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# https://raw.github.com/LambethCouncil/OSGB36_Converter/master/OSGB36.rb |
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module OSGB36 |
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extend self |
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# Takes OSGB36 Easting/Northing coords |
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# and returns WGS84 Latitude and Longitude |
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def en_to_ll(easting, northing) |
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@OSGB36_ll = to_OSGB36(easting, northing) |
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to_WGS84(@OSGB36_ll[:latitude], @OSGB36_ll[:longitude]) |
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end |
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# Takes OSGB36 Easting/Northing coords and returns |
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# OSGB36 Latitude and Longitude |
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def to_OSGB36(easting, northing) |
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@OSGB_F0 = 0.9996012717 |
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@N0 = -100000.0 |
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@E0 = 400000.0 |
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@phi0 = deg_to_rad(49.0) |
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@lambda0 = deg_to_rad(-2.0) |
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@a = 6377563.396 |
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@b = 6356256.909 |
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@eSquared = ((@a * @a) - (@b * @b)) / (@a * @a) |
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@phi = 0.0 |
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@lambda = 0.0 |
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@E = easting |
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@N = northing |
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@n = (@a - @b) / (@a + @b) |
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@M = 0.0 |
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@phiPrime = ((@N - @N0) / (@a * @OSGB_F0)) + @phi0 |
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begin |
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@M = |
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(@b * @OSGB_F0)\ |
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* (((1 + @n + ((5.0 / 4.0) * @n * @n) + ((5.0 / 4.0) * @n * @n * @n))\ |
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* (@phiPrime - @phi0))\ |
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- (((3 * @n) + (3 * @n * @n) + ((21.0 / 8.0) * @n * @n * @n))\ |
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* Math.sin(@phiPrime - @phi0)\ |
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* Math.cos(@phiPrime + @phi0))\ |
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+ ((((15.0 / 8.0) * @n * @n) + ((15.0 / 8.0) * @n * @n * @n))\ |
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* Math.sin(2.0 * (@phiPrime - @phi0))\ |
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* Math.cos(2.0 * (@phiPrime + @phi0)))\ |
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- (((35.0 / 24.0) * @n * @n * @n)\ |
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* Math.sin(3.0 * (@phiPrime - @phi0))\ |
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* Math.cos(3.0 * (@phiPrime + @phi0)))) |
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@phiPrime += (@N - @N0 - @M) / (@a * @OSGB_F0) |
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end while ((@N - @N0 - @M) >= 0.001) |
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@v = @a * @OSGB_F0 * ((1.0 - @eSquared * sin_pow_2(@phiPrime)) ** -0.5) |
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@rho = |
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@a\ |
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* @OSGB_F0\ |
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* (1.0 - @eSquared)\ |
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* ((1.0 - @eSquared * sin_pow_2(@phiPrime)) ** -1.5) |
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@etaSquared = (@v / @rho) - 1.0 |
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@VII = Math.tan(@phiPrime) / (2 * @rho * @v) |
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@VIII = |
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(Math.tan(@phiPrime) / (24.0 * @rho * (@v ** 3.0)))\ |
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* (5.0\ |
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+ (3.0 * tan_pow_2(@phiPrime))\ |
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+ @etaSquared\ |
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- (9.0 * tan_pow_2(@phiPrime) * @etaSquared)) |
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@IX = |
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(Math.tan(@phiPrime) / (720.0 * @rho * (@v ** 5.0)))\ |
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* (61.0\ |
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+ (90.0 * tan_pow_2(@phiPrime))\ |
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+ (45.0 * tan_pow_2(@phiPrime) * tan_pow_2(@phiPrime))) |
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@X = sec(@phiPrime) / @v |
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@XI = |
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(sec(@phiPrime) / (6.0 * @v * @v * @v))\ |
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* ((@v / @rho) + (2 * tan_pow_2(@phiPrime))) |
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@XII = |
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(sec(@phiPrime) / (120.0 * (@v ** 5.0)))\ |
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* (5.0\ |
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+ (28.0 * tan_pow_2(@phiPrime))\ |
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+ (24.0 * tan_pow_2(@phiPrime) * tan_pow_2(@phiPrime))) |
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@XIIA = |
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(sec(@phiPrime) / (5040.0 * (@v ** 7.0)))\ |
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* (61.0\ |
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+ (662.0 * tan_pow_2(@phiPrime))\ |
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+ (1320.0 * tan_pow_2(@phiPrime) * tan_pow_2(@phiPrime))\ |
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+ (720.0\ |
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* tan_pow_2(@phiPrime)\ |
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* tan_pow_2(@phiPrime)\ |
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* tan_pow_2(@phiPrime))) |
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@phi = |
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@phiPrime\ |
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- (@VII * ((@E - @E0) ** 2.0))\ |
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+ (@VIII * ((@E - @E0) ** 4.0))\ |
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- (@IX * ((@E - @E0) ** 6.0)) |
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@lambda = |
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@lambda0\ |
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+ (@X * (@E - @E0))\ |
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- (@XI * ((@E - @E0) ** 3.0))\ |
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+ (@XII * ((@E - @E0) ** 5.0))\ |
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- (@XIIA * ((@E - @E0) ** 7.0)) |
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{ :latitude => rad_to_deg(@phi), :longitude => rad_to_deg(@lambda) } |
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end |
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# Takes OSGB36 Latitude and Longitude coords |
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# and returns WGS84 Latitude and Longitude |
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def to_WGS84(latitude,longitude) |
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@a = 6377563.396 |
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@b = 6356256.909 |
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@eSquared = ((@a * @a) - (@b * @b)) / (@a * @a) |
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@phi = deg_to_rad(latitude) |
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@lambda = deg_to_rad(longitude) |
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@v = @a / (Math.sqrt(1 - @eSquared * sin_pow_2(@phi))) |
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@H = 0 |
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@x = (@v + @H) * Math.cos(@phi) * Math.cos(@lambda) |
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@y = (@v + @H) * Math.cos(@phi) * Math.sin(@lambda) |
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@z = ((1 - @eSquared) * @v + @H) * Math.sin(@phi) |
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@tx = 446.448 |
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@ty = -124.157 |
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@tz = 542.060 |
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@s = -0.0000204894 |
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@rx = deg_to_rad( 0.00004172222) |
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@ry = deg_to_rad( 0.00006861111) |
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@rz = deg_to_rad( 0.00023391666) |
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@xB = @tx + (@x * (1 + @s)) + (-@rx * @y) + (@ry * @z) |
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@yB = @ty + (@rz * @x) + (@y * (1 + @s)) + (-@rx * @z) |
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@zB = @tz + (-@ry * @x) + (@rx * @y) + (@z * (1 + @s)) |
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@a = 6378137.000 |
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@b = 6356752.3141 |
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@eSquared = ((@a * @a) - (@b * @b)) / (@a * @a) |
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@lambdaB = rad_to_deg(Math.atan(@yB / @xB)) |
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@p = Math.sqrt((@xB * @xB) + (@yB * @yB)) |
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@phiN = Math.atan(@zB / (@p * (1 - @eSquared))) |
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(1..10).each do |i| |
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@v = @a / (Math.sqrt(1 - @eSquared * sin_pow_2(@phiN))) |
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@phiN1 = Math.atan((@zB + (@eSquared * @v * Math.sin(@phiN))) / @p) |
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@phiN = @phiN1 |
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end |
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@phiB = rad_to_deg(@phiN) |
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{ :latitude => @phiB, :longitude => @lambdaB } |
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end |
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private # Some Math |
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def deg_to_rad(degrees) |
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degrees / 180.0 * Math::PI |
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end |
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def rad_to_deg(r) |
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(r/Math::PI)*180 |
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end |
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def sin_pow_2(x) |
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Math.sin(x) * Math.sin(x) |
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end |
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def cos_pow_2(x) |
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Math.cos(x) * Math.cos(x) |
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end |
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def tan_pow_2(x) |
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Math.tan(x) * Math.tan(x) |
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end |
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def sec(x) |
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1.0 / Math.cos(x) |
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end |
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end |