Class: SVY21

Inherits:

Object

Object
SVY21

Defined in:: lib/svy21.rb

Overview

The SVY21 class provides functionality to convert between the SVY21 and Lat/Lon coordinate systems.

Internally, the class uses the equations specified in the following web page to perform the conversion. www.linz.govt.nz/geodetic/conversion-coordinates/projection-conversions/transverse-mercator-preliminary-computations/index.aspx

Constant Summary collapse

RAD_RATIO = Ratio to convert degrees to radians.

Math::PI / 180.0

A = Semi-major axis of reference ellipsoid.

6378137.0

F = Ellipsoidal flattening

1.0 / 298.257223563

ORIGIN_LATITUDE = Origin latitude (degrees).

1.366666

ORIGIN_LONGITUDE = Origin longitude (degrees).

103.833333

FALSE_NORTHING = False Northing.

38744.572

FALSE_EASTING = False Easting.

28001.642

K = Central meridian scale factor.

1.0

B = Semi-minor axis of reference ellipsoid.

A * (1.0 - F)

E2 = Squared eccentricity of reference ellipsoid.

(2.0 * F) - (F * F)

E4 =

E2 * E2

E6 =

E4 * E2

A0 = Naming convention: A0..6 are terms in an expression, not powers.

1.0 - (E2 / 4.0) - (3.0 * E4 / 64.0) - (5.0 * E6 / 256.0)

A2 =

(3.0 / 8.0) * (E2 + (E4 / 4.0) + (15.0 * E6 / 128.0))

A4 =

(15.0 / 256.0) * (E4 + (3.0 * E6 / 4.0))

A6 =

35.0 * E6 / 3072.0

N = Naming convention: the trailing number is the power of the variable.

(A - B) / (A + B)

N2 =

N * N

N3 =

N2 * N

N4 =

N2 * N2

G =

A * (1.0 - N) * (1.0 - N2) * (1.0 + (9.0 * N2 / 4.0) + (225.0 * N4 / 64.0)) * RAD_RATIO

Class Method Summary collapse

.calc_m(lat) ⇒ Object

M: meridian distance.
.calc_rho(sin_2_lat) ⇒ Object

Rho: radius of curvature of meridian.
.calc_v(sin_2_lat) ⇒ Object

v: radius of curvature in the prime vertical.
.lat_lon_to_svy21(latitude, longitude) ⇒ Object

Computes SVY21 Northing and Easting based on a Latitude and Longitude coordinate.
.svy21_to_lat_lon(northing, easting) ⇒ Object

The conversion result as an array, [lat, lon].

Class Method Details

.calc_m(lat) ⇒ `Object`

M: meridian distance.

# File 'lib/svy21.rb', line 54

def self.calc_m(lat)
  lat_r = lat * RAD_RATIO
  
  A * ((A0 * lat_r) - (A2 * Math.sin(2.0 * lat_r)) + (A4 * Math.sin(4.0 * lat_r)) - (A6 * Math.sin(6.0 * lat_r)))
end

.calc_rho(sin_2_lat) ⇒ `Object`

Rho: radius of curvature of meridian.

# File 'lib/svy21.rb', line 61

def self.calc_rho(sin_2_lat)
  num = A * (1.0 - E2)
  denom = (1.0 - E2 * sin_2_lat) ** (3.0 / 2.0)
  
  num / denom
end

.calc_v(sin_2_lat) ⇒ `Object`

v: radius of curvature in the prime vertical.

# File 'lib/svy21.rb', line 69

def self.calc_v(sin_2_lat)
  poly = 1.0 - E2 * sin_2_lat
  
  A / Math.sqrt(poly)
end

.lat_lon_to_svy21(latitude, longitude) ⇒ `Object`

Computes SVY21 Northing and Easting based on a Latitude and Longitude coordinate.

This method returns an array object that contains two numbers, northing, accessible with [0], and easting, accessible with [1].

Parameters:

latitude —

latitude in degrees.
longitude —

longitude in degrees.

Returns:

the conversion result as an array, [northing, easting].

# File 'lib/svy21.rb', line 151

def self.lat_lon_to_svy21(latitude, longitude)
  # Naming convention: sin_2_lat = "square of sin(lat)" = sin(lat) ** 2.0
  lat_r = latitude * RAD_RATIO
  sin_lat = Math.sin(lat_r)
  sin_2_lat = sin_lat * sin_lat
  cos_lat = Math.cos(lat_r)
  cos_2_lat = cos_lat * cos_lat
  cos_3_lat = cos_2_lat * cos_lat
  cos_4_lat = cos_3_lat * cos_lat
  cos_5_lat = cos_3_lat * cos_2_lat
  cos_6_lat = cos_5_lat * cos_lat
  cos_7_lat = cos_5_lat * cos_2_lat
  
  rho = calc_rho(sin_2_lat)
  v = calc_v(sin_2_lat)
  psi = v / rho
  t = Math.tan(lat_r)
  w = (longitude - ORIGIN_LONGITUDE) * RAD_RATIO
  m = calc_m(latitude)
  origin_m = calc_m(ORIGIN_LATITUDE)
  
  # Naming convention: the trailing number is the power of the variable.
  w2 = w * w
  w4 = w2 * w2
  w6 = w4 * w2
  w8 = w6 * w2
  psi2 = psi * psi
  psi3 = psi2 * psi
  psi4 = psi2 * psi2
  t2 = t * t
  t4 = t2 * t2
  t6 = t4 * t2
  
  # Compute Northing.
  # Naming convention: n_term_1..4 are terms in an expression, not powers.
  n_term_1 = w2 / 2.0 * v * sin_lat * cos_lat
  n_term_2 = w4 / 24.0 * v * sin_lat * cos_3_lat * (4.0 * psi2 + psi - t2)
  n_term_3 = w6 / 720.0 * v * sin_lat * cos_5_lat * ((8.0 * psi4) * (11.0 - 24.0 * t2) - (28.0 * psi3) * (1.0 - 6.0 * t2) + psi2 * (1.0 - 32.0 * t2) - psi * 2.0 * t2 + t4)
  n_term_4 = w8 / 40320.0 * v * sin_lat * cos_7_lat * (1385.0 - 3111.0 * t2 + 543.0 * t4 - t6)
  northing = FALSE_NORTHING + K * (m - origin_m + n_term_1 + n_term_2 + n_term_3 + n_term_4)
  
  # Compute Easting.
  # Naming convention: e_term_1..3 are terms in an expression, not powers.
  e_term_1 = w2 / 6.0 * cos_2_lat * (psi - t2)
  e_term_2 = w4 / 120.0 * cos_4_lat * ((4.0 * psi3) * (1.0 - 6.0 * t2) + psi2 * (1.0 + 8.0 * t2) - psi * 2.0 * t2 + t4)
  e_term_3 = w6 / 5040.0 * cos_6_lat * (61.0 - 479.0 * t2 + 179.0 * t4 - t6)
  easting = FALSE_EASTING + K * v * w * cos_lat * (1 + e_term_1 + e_term_2 + e_term_3)
  
  [northing, easting]
end

.svy21_to_lat_lon(northing, easting) ⇒ `Object`

Returns the conversion result as an array, [lat, lon].