Ruby script to convert ECEF to WGS84(BLH) coordinate.

ecef2blh.rb

#! /usr/local/bin/ruby
#---------------------------------------------------------------------------------
# ECEF -> BLH 変換
# : ECEF（Earth Centered Earth Fixed; 地球中心・地球固定直交座標系）座標を
#   WGS84 の緯度(Latitude)／経度(Longitude)／楕円体高(Height)に変換する。
#
# Date          Author          Version
# 2019.02.19    mk-mode.com     1.00 新規作成
#
# Copyright(C) 2019 mk-mode.com All Rights Reserved.
#---------------------------------------------------------------------------------
#
class ConvEcef2Blh
  USAGE = "[USAGE] ./ecef2blh.rb X Y Z"
  PI_180 = Math::PI / 180.0
  # WGS84 座標パラメータ
  A      = 6378137.0                # a(地球楕円体長半径(赤道面平均半径))
  ONE_F  = 298.257223563            # 1 / f(地球楕円体扁平率=(a - b) / a)
  B      = A * (1.0 - 1.0 / ONE_F)  # b(地球楕円体短半径)
  E2     = (1.0 / ONE_F) * (2 - (1.0 / ONE_F))
                                    # e^2 = 2 * f - f * f
                                    #     = (a^2 - b^2) / a^2
  ED2    = E2 * A * A / (B * B)     # e'^2= (a^2 - b^2) / b^2

  # Initialization
  # * コマンドライン引数の取得
  def initialize
    if ARGV.size < 3
      puts USAGE
      exit
    end
    @ecef = ARGV[0, 3].map(&:to_f)
  end

  # Execution
  def exec
    puts "ECEF: X = %12.3fm" % @ecef[0]
    puts "      Y = %12.3fm" % @ecef[1]
    puts "      Z = %12.3fm" % @ecef[2]
    blh = ecef2blh(@ecef)
    puts "--->"
    puts "BLH: LATITUDE(BETA) = %12.8f°" % blh[0]
    puts "  LONGITUDE(LAMBDA) = %12.8f°" % blh[1]
    puts "             HEIGHT = %12.3fm"  % blh[2]
  rescue => e
    msg = "[#{e.class}] #{e.message}\n"
    e.backtrace.each { |tr| msg << "\t#{tr}\n" }
    $stderr.puts msg
    exit 1
  end

  private

  # ECEF -> BLH  変換
  #
  # @param ecef: ECEF 座標 [x, y, z]
  # @return blh: BLH  座標 [latitude, longitude, height]
  def ecef2blh(ecef)
    x, y, z = ecef
    n = lambda do |x|
      s = Math.sin(x * PI_180)
      A / Math.sqrt(1.0 - E2 * s * s)
    end
    p = Math.sqrt(x * x + y * y)
    theta = Math.atan2(z * A, p * B) / PI_180
    lat = Math.atan2(
      z + ED2 * B * Math.sin(theta * PI_180)**3,
      p - E2  * A * Math.cos(theta * PI_180)**3
    ) / PI_180
    lon = Math.atan2(y, x) / PI_180
    ht = (p / Math.cos(lat * PI_180)) - n.call(lat)
    return [lat, lon, ht]
  rescue => e
    raise
  end
end

ConvEcef2Blh.new.exec if __FILE__ == $0