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usng2.rb
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usng2.rb
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## Library to convert between NAD83 Lat/Lon and US National Grid
## Based on the FGDC-STS-011-2001 spec at http://www.fgdc.gov/standards/projects/FGDC-standards-projects/usng/fgdc_std_011_2001_usng.pdf
## Also based on the UTM library already in GeoMOOSE
## (c) Jim Klassen 4/2008
## Not tested in southern hemisphere...
## Known to fail for USNG zones A and B
#
# License:
#
# Copyright (c) 2008-2009 James Klassen
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the 'Software'), to
# deal in the Software without restriction, including without limitation the
# rights to use, copy, modify, merge, publish, distribute, sublicense, and/or
# sell copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies of this Software or works derived from this Software.
#
# THE SOFTWARE IS PROVIDED 'AS IS', WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
# FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS
# IN THE SOFTWARE.
#
class USNG2
class LL84
attr_reader :lon, :lat
def initialize(lon, lat)
@lon = lon.to_f
@lat = lat.to_f
end
end
class UTM
attr_reader :utm_zone, :easting, :northing, :precision
private
MajorAxis = 6378137.0
MinorAxis = 6356752.3
Ecc = (MajorAxis * MajorAxis - MinorAxis * MinorAxis) / (MajorAxis * MajorAxis)
Ecc2 = Ecc / (1.0 - Ecc)
K0 = 0.9996
E4 = Ecc * Ecc
E6 = Ecc * E4
Degrees2Radians = Math::PI / 180.0
# Computes the meridian distance for the GRS-80 Spheroid.
# See equation 3-22, USGS Professional Paper 1395.
def self.meridianDist(lat)
c1 = MajorAxis * (1 - Ecc / 4 - 3 * E4 / 64 - 5 * E6 / 256)
c2 = -MajorAxis * (3 * Ecc / 8 + 3 * E4 / 32 + 45 * E6 / 1024)
c3 = MajorAxis * (15 * E4 / 256 + 45 * E6 / 1024)
c4 = -MajorAxis * 35 * E6 / 3072
return(c1 * lat + c2 * Math.sin(lat * 2) + c3 * Math.sin(lat * 4) + c4 * Math.sin(lat * 6))
end
public
def initialize(utm_zone, easting, northing, precision)
@utm_zone = utm_zone.to_i
@easting = easting.to_f
@northing = northing.to_f
@precision = precision.to_i
end
def to_ll84
zone = @utm_zone
easting = @easting
northing = @northing
centeralMeridian = -((30 - zone) * 6 + 3) * Degrees2Radians
temp1 = Math.sqrt(1.0 - Ecc)
ecc1 = (1.0 - temp1) / (1.0 + temp1)
ecc12 = ecc1 * ecc1
ecc13 = ecc1 * ecc12
ecc14 = ecc12 * ecc12
easting = easting - 500000.0
m = northing / K0
um = m / (MajorAxis * (1.0 - (Ecc / 4.0) - 3.0 * (E4 / 64.0) - 5.0 * (E6 / 256.0)))
temp8 = (1.5 * ecc1) - (27.0 / 32.0) * ecc13
temp9 = ((21.0 / 16.0) * ecc12) - ((55.0 / 32.0) * ecc14)
latrad1 = um + temp8 * Math.sin(2 * um) + temp9 * Math.sin(4 * um) + (151.0 * ecc13 / 96.0) * Math.sin(6.0 * um)
latsin1 = Math.sin(latrad1)
latcos1 = Math.cos(latrad1)
lattan1 = latsin1 / latcos1
n1 = MajorAxis / Math.sqrt(1.0 - Ecc * latsin1 * latsin1)
t2 = lattan1 * lattan1
c1 = Ecc2 * latcos1 * latcos1
temp20 = (1.0 - Ecc * latsin1 * latsin1)
r1 = MajorAxis * (1.0 - Ecc) / Math.sqrt(temp20 * temp20 * temp20)
d1 = easting / (n1*K0)
d2 = d1 * d1
d3 = d1 * d2
d4 = d2 * d2
d5 = d1 * d4
d6 = d3 * d3
t12 = t2 * t2
c12 = c1 * c1
temp1 = n1 * lattan1 / r1
temp2 = 5.0 + 3.0 * t2 + 10.0 * c1 - 4.0 * c12 - 9.0 * Ecc2
temp4 = 61.0 + 90.0 * t2 + 298.0 * c1 + 45.0 * t12 - 252.0 * Ecc2 - 3.0 * c12
temp5 = (1.0 + 2.0 * t2 + c1) * d3 / 6.0
temp6 = 5.0 - 2.0 * c1 + 28.0 * t2 - 3.0 * c12 + 8.0 * Ecc2 + 24.0 * t12
lat = (latrad1 - temp1 * (d2 / 2.0 - temp2 * (d4 / 24.0) + temp4 * d6 / 720.0)) * 180 / Math::PI
lon = (centeralMeridian + (d1 - temp5 + temp6 * d5 / 120.0) / latcos1) * 180 / Math::PI
return LL84.new(lon, lat)
end
# Convert lat/lon (given in decimal degrees) to UTM, and optionally given a particular UTM zone.
def self.from_ll84(ll84, zone = nil)
in_lon = ll84.lon.to_f
in_lat = ll84.lat.to_f
# Calculate UTM Zone number from Longitude
# -180 = 180W is grid 1... increment every 6 degrees going east
# Note [-180, -174) is in grid 1, [-174,-168) is 2, [174, 180) is 60
zone ||= ((in_lon - (-180.0)) / 6.0).floor + 1
centeralMeridian = -((30 - zone) * 6 + 3) * Degrees2Radians
lat = in_lat * Degrees2Radians
lon = in_lon * Degrees2Radians
latSin = Math.sin(lat)
latCos = Math.cos(lat)
latTan = latSin / latCos
latTan2 = latTan * latTan
latTan4 = latTan2 * latTan2
n = MajorAxis / Math.sqrt(1 - Ecc * (latSin*latSin))
c = Ecc2 * latCos*latCos
a = latCos * (lon - centeralMeridian)
m = meridianDist(lat)
temp5 = 1.0 - latTan2 + c
temp6 = 5.0 - 18.0 * latTan2 + latTan4 + 72.0 * c - 58.0 * Ecc2
temp11 = (a**5)
x = K0 * n * (a + (temp5 * (a**3)) / 6.0 + temp6 * temp11 / 120.0) + 500000
temp7 = (5.0 - latTan2 + 9.0 * c + 4.0 * (c*c)) * (a**4) / 24.0
temp8 = 61.0 - 58.0 * latTan2 + latTan4 + 600.0 * c - 330.0 * Ecc2
temp9 = temp11 * a / 720.0
y = K0 * (m + n * latTan * ((a * a) / 2.0 + temp7 + temp8 * temp9))
return UTM.new(zone, x, y, 6) # TODO: made up precision
end
end
class USNG
attr_reader :utm_zone, :grid_zone, :grid_square
attr_reader :easting, :northing, :precision
private
# Note: grid locations are the SW corner of the grid square (because easting and northing are always positive)
# 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 x 100,000m northing
NSLetters135 = ['A','B','C','D','E','F','G','H','J','K','L','M','N','P','Q','R','S','T','U','V']
NSLetters246 = ['F','G','H','J','K','L','M','N','P','Q','R','S','T','U','V','A','B','C','D','E']
# 1 2 3 4 5 6 7 8 x 100,000m easting
EWLetters14 = ['A','B','C','D','E','F','G','H']
EWLetters25 = ['J','K','L','M','N','P','Q','R']
EWLetters36 = ['S','T','U','V','W','X','Y','Z']
# -80 -72 -64 -56 -48 -40 -32 -24 -16 -08 0 8 16 24 32 40 48 56 64 72 (*Latitude)
GridZones = ['C', 'D', 'E', 'F', 'G', 'H', 'J', 'K', 'L', 'M', 'N', 'P', 'Q', 'R', 'S', 'T', 'U', 'V', 'W', 'X']
GridZonesDeg = [-80, -72, -64, -56, -48, -40, -32, -24, -16, -8 , 0, 8, 16, 24, 32, 40, 48, 58, 64, 72]
# TODO: This is approximate and actually depends on longitude too.
GridZonesNorthing = Array.new(20) { |i|
110946.259 * GridZonesDeg[i] # == 2 * PI * 6356752.3 * (latitude / 360.0)
}
# = [-8875700.72, -7988130.648, -7100560.576, -6212990.504, -5325420.432, -4437850.36, -3550280.288, -2662710.216, -1775140.144, -887570.072, 0.0, 887570.072, 1775140.144, 2662710.216, 3550280.288, 4437850.36, 5325420.432, 6434883.022, 7100560.576, 7988130.648]
# http://en.wikipedia.org/wiki/Great-circle_distance
# http://en.wikipedia.org/wiki/Vincenty%27s_formulae
def llDistance(ll_start, ll_end)
lat_s = ll_start.lat * Math.PI / 180
lat_f = ll_end.lat * Math.PI / 180
d_lon = (ll_end.lon - ll_start.lon) * Math.PI / 180
return( Math.atan2( Math.sqrt( (Math.cos(lat_f) * Math.sin(d_lon)**2) + (Math.cos(lat_s)*Math.sin(lat_f) - Math.sin(lat_s)*Math.cos(lat_f)*Math.cos(d_lon)**2)) ,
Math.sin(lat_s)*Math.sin(lat_f) + Math.cos(lat_s)*Math.cos(lat_f)*Math.cos(d_lon) )
);
end
public
def self.parse_usng(usng)
# Parse USNG into component parts
easting = 0;
northing = 0;
precision = 0;
digits = nil # don't really need this if using call to parsed...
grid_square = nil
grid_zone = nil
utm_zone = nil
# Make sure uppercase and remove whitespace (shouldn't be any)
usng = usng.upcase.gsub(/ /, "")
# Strip Coordinate values off of end, if any
# This will be any trailing digits.
re = Regexp.compile("([0-9]+)$")
fields = re.match(usng)
if(fields) then
digits = fields[0]
precision = digits.length / 2 # TODO: throw an error if #digits is odd.
easting = (digits.slice(0, precision))
northing =(digits.slice(precision, precision))
end
usng = usng.slice(0, usng.length-(precision*2))
# Get 100km Grid Designator, if any
re = Regexp.compile("([A-Z][A-Z]$)")
fields = re.match(usng)
if(fields) then
grid_square = fields[0]
end
usng = usng.slice(0, usng.length - 2)
# Get UTM and Grid Zone
re = Regexp.compile("([0-9]+)([A-Z])")
fields = re.match(usng)
if(fields) then
utm_zone = fields[1]
grid_zone = fields[2]
end
USNG.new(utm_zone, grid_zone, grid_square, easting, northing, precision)
end
# Returns a USNG String for a UTM point, and zone id's, and precision
# utm_zone => 15
# utm_easting => 491000, utm_northing => 49786000; precision => 2 (digits)
def self.from_utm(utm)
utm_zone = utm.utm_zone
utm_easting = utm.easting
utm_northing = utm.northing
precision = utm.precision
# Calculate USNG Grid Zone Designation from Latitude
# Starts at -80 degrees and is in 8 degree increments
lat = utm.to_ll84.lat
if(! ((lat > -80) && (lat < 80) )) then
throw("USNG2: Latitude must be between -80 and 80. (Zones A and B are not implemented yet.)")
end
grid_zone = GridZones[((lat - (-80.0)) / 8).floor]
# Check valid coordinate
raise("USNG2: Invalid UTM Zone") unless (0..60).include?(utm_zone.to_i)
raise("USNG2: Invalid Easting") unless (100000..9000000).include?(utm_easting)
raise("USNG2: Invalid Northing") unless (0..10000000).include?(utm_northing)
grid_square_set = utm_zone % 6;
ew_idx = (utm_easting / 100000).floor - 1 # should be [100000, 9000000]
ns_idx = ((utm_northing % 2000000) / 100000).floor # should [0, 10000000) => [0, 2000000)
grid_square = case(grid_square_set)
when 1; EWLetters14[ew_idx] + NSLetters135[ns_idx]
when 2; EWLetters25[ew_idx] + NSLetters246[ns_idx]
when 3; EWLetters36[ew_idx] + NSLetters135[ns_idx]
when 4; EWLetters14[ew_idx] + NSLetters246[ns_idx]
when 5; EWLetters25[ew_idx] + NSLetters135[ns_idx]
when 0; EWLetters36[ew_idx] + NSLetters246[ns_idx] # Calculates as zero, but is technically 6
end
# Calc Easting and Northing integer to 100,000s place
easting = (utm_easting % 100000).floor.to_s
northing = (utm_northing % 100000).floor.to_s
# Pad up to meter precision (5 digits)
while(easting.length < 5) do
easting = '0' + easting
end
while(northing.length < 5) do
northing = '0' + northing
end
if(precision > 5) then
# Calculate the fractional meter parts
digits = precision - 5
grid_easting = easting + ("%#{digits}f" % (utm_easting % 1)).slice(2,digits)
grid_northing = northing + ("%#{digits}f" % (utm_northing % 1)).slice(2,digits)
else
# Remove unnecessary digits
grid_easting = easting.slice(0, precision)
grid_northing = northing.slice(0, precision)
end
return USNG.new(utm_zone, grid_zone, grid_square, grid_easting, grid_northing, precision)
end
# Should really only be called by self.parse_usng and self.from_utm
# UTM Zone Number (15), Grid Zone ('T'), 100km Grid Square ('VK'), easting (meters), northing (meters),
# precision (significant digits per easting/northing)
def initialize(utm_zone, grid_zone, grid_square, easting, northing, precision)
@utm_zone = utm_zone.to_i
@grid_zone = grid_zone.to_s
@grid_square = grid_square.to_s
@easting = easting.to_s
@northing = northing.to_s
@precision = precision.to_i
end
def to_s
return @utm_zone.to_s + @grid_zone + @grid_square + @easting + @northing
end
def to_utm
utm_easting = 0
utm_northing = 0
grid_square_set = @utm_zone % 6
ns_grid = nil
ew_grid = nil
case(grid_square_set)
when 1 then
ns_grid = NSLetters135
ew_grid = EWLetters14
when 2 then
ns_grid = NSLetters246
ew_grid = EWLetters25
when 3 then
ns_grid = NSLetters135
ew_grid = EWLetters36
when 4 then
ns_grid = NSLetters246
ew_grid = EWLetters14
when 5 then
ns_grid = NSLetters135
ew_grid = EWLetters25
when 0 then # grid_square_set will == 0, but it is technically group 6
ns_grid = NSLetters246
ew_grid = EWLetters36
else
raise("USNG2: shouldn't get here")
end
ew_idx = ew_grid.find_index(grid_square[0])
ns_idx = ns_grid.find_index(grid_square[1])
if(ew_idx.nil? || ns_idx.nil?) then
raise("USNG2: Invalid USNG 100km grid designator.")
end
scale_factor = 10**(5 - precision) # 1 digit => 10k place, 2 digits => 1k ...
easting = @easting.to_f * scale_factor
northing = @northing.to_f * scale_factor
utm_easting = ((ew_idx + 1) * 100000) + easting # Should be [100000, 9000000]
utm_northing = ((ns_idx + 0) * 100000) + northing # Should be [0, 2000000)
# TODO: this really depends on easting too...
# At this point know UTM zone, Grid Zone (min latitude), and easting
# Right now this is lookup table returns a max number based on lon == utm zone center
min_northing = GridZonesNorthing[GridZones.find_index(grid_zone)] # Unwrap northing to ~ [0, 10000000]
p min_northing
utm_northing += 2000000 * ((min_northing - utm_northing) / 2000000).ceil
# Check that the coordinate is within the utm zone and grid zone specified:
utm = UTM.new(utm_zone, utm_easting, utm_northing, precision)
ll = utm.to_ll84
ll_utm_zone = ((ll.lon - (-180.0)) / 6.0).floor + 1
ll_grid_zone = GridZones[((ll.lat - (-80.0)) / 8).floor]
# If error from the above TODO mattered... then need to move north a grid
if( ll_grid_zone != grid_zone) then
utm_northing -= 2000000
utm = UTM.new(utm_zone, utm_easting, utm_northing, precision)
ll = utm.to_ll84
ll_utm_zone = ((ll.lon - (-180.0)) / 6.0).floor + 1
ll_grid_zone = GridZones[((ll.lat - (-80.0)) / 8).floor]
end
if(ll_utm_zone != utm_zone || ll_grid_zone != grid_zone) then
# raise("USNG2: calculated coordinate not in correct UTM or grid zone! Supplied: "+utm_zone.to_s+grid_zone+" Calculated: "+ll_utm_zone.to_s+ll_grid_zone)
# print("USNG2: calculated coordinate not in correct UTM or grid zone! Supplied: "+utm_zone.to_s+grid_zone+" Calculated: "+ll_utm_zone.to_s+ll_grid_zone)
end
return utm
end # to_utm Method
# Returns the bounding box of the USNG square represented by the coordinate
# In the CS of the USNG coordinate (even if part of the square's extent
# Happens to fall outside the 100km grid square/grid zone)
def simple_bbox
utm = self.to_utm
size = 10**(5-@precision)
minx = utm.easting
miny = utm.northing
maxx = minx + size
maxy = miny + size
srid=26900 + @utm_zone
# ex. POLYGON((654000 5191000,654000 5192000,655000 5192000,655000 5191000,654000 5191000))
"SRID=#{srid};POLYGON((#{minx} #{miny}, #{minx} #{maxy}, #{maxx} #{maxy}, #{maxx} #{miny}, #{minx} #{miny}))"
end
end # USNG Class
end # USNG2 Module