Option Explicit

Private Const PI = 3.14159265358979
Private Const EPSILON As Double = 0.000000000001

Public Function distVincenty(ByVal lat1 As Double, ByVal lon1 As Double, ByVal lat2 As Double, ByVal lon2 As Double) As Double
'INPUTS: Latitude and Longitude of initial and destination points in decimal format.
'OUTPUT: Distance between the two points in Meters.
'
'=================================================================================
' Calculate geodesic distance (in m) between two points specified by latitude/longitude (in numeric [decimal] degrees)
' using Vincenty inverse formula for ellipsoids
'=================================================================================
' Code has been ported by lost_species from www.aliencoffee.co.uk to VBA from javascript published at:
' http://www.movable-type.co.uk/scripts/latlong-vincenty.html
' * from: Vincenty inverse formula - T Vincenty, "Direct and Inverse Solutions of Geodesics on the
' *       Ellipsoid with application of nested equations", Survey Review, vol XXII no 176, 1975
' *       http://www.ngs.noaa.gov/PUBS_LIB/inverse.pdf
'Additional Reference: http://en.wikipedia.org/wiki/Vincenty%27s_formulae
'=================================================================================
' Copyright lost_species 2008 LGPL http://www.fsf.org/licensing/licenses/lgpl.html
'=================================================================================
' Code modifications to prevent "Formula Too Complex" errors in Excel (2010) VBA implementation
' provided by Jerry Latham, Microsoft MVP Excel Group, 2005-2011
' July 23 2011
'=================================================================================

  Dim low_a As Double
  Dim low_b As Double
  Dim f As Double
  Dim L As Double
  Dim U1 As Double
  Dim U2 As Double
  Dim sinU1 As Double
  Dim sinU2 As Double
  Dim cosU1 As Double
  Dim cosU2 As Double
  Dim lambda As Double
  Dim lambdaP As Double
  Dim iterLimit As Integer
  Dim sinLambda As Double
  Dim cosLambda As Double
  Dim sinSigma As Double
  Dim cosSigma As Double
  Dim sigma As Double
  Dim sinAlpha As Double
  Dim cosSqAlpha As Double
  Dim cos2SigmaM As Double
  Dim C As Double
  Dim uSq As Double
  Dim upper_A As Double
  Dim upper_B As Double
  Dim deltaSigma As Double
  Dim s As Double ' final result, will be returned rounded to 3 decimals (mm).
'added by JLatham to break up "Too Complex" formulas
'into pieces to properly calculate those formulas as noted below
'and to prevent overflow errors when using Excel 2010 x64 on Windows 7 x64 systems
  Dim P1 As Double ' used to calculate a portion of a complex formula
  Dim P2 As Double ' used to calculate a portion of a complex formula
  Dim P3 As Double ' used to calculate a portion of a complex formula

'See http://en.wikipedia.org/wiki/World_Geodetic_System
'for information on various Ellipsoid parameters for other standards.
'low_a and low_b in meters
' === GRS-80 ===
' low_a = 6378137
' low_b = 6356752.314245
' f = 1 / 298.257223563
'
' === Airy 1830 ===  Reported best accuracy for England and Northern Europe.
' low_a = 6377563.396
' low_b = 6356256.910
' f = 1 / 299.3249646
'
' === International 1924 ===
' low_a = 6378388
' low_b = 6356911.946
' f = 1 / 297
'
' === Clarke Model 1880 ===
' low_a = 6378249.145
' low_b = 6356514.86955
' f = 1 / 293.465
'
' === GRS-67 ===
' low_a = 6378160
' low_b = 6356774.719
' f = 1 / 298.247167

'=== WGS-84 Ellipsoid Parameters ===
  low_a = 6378137       ' +/- 2m
  low_b = 6356752.3142
  f = 1 / 298.257223563
'====================================
  L = toRad(lon2 - lon1)
  U1 = Atn((1 - f) * Tan(toRad(lat1)))
  U2 = Atn((1 - f) * Tan(toRad(lat2)))
  sinU1 = Sin(U1)
  cosU1 = Cos(U1)
  sinU2 = Sin(U2)
  cosU2 = Cos(U2)

  lambda = L
  lambdaP = 2 * PI
  iterLimit = 100 ' can be set as low as 20 if desired.

  While (Abs(lambda - lambdaP) > EPSILON) And (iterLimit > 0)
    iterLimit = iterLimit - 1

    sinLambda = Sin(lambda)
    cosLambda = Cos(lambda)
    sinSigma = Sqr(((cosU2 * sinLambda) ^ 2) + ((cosU1 * sinU2 - sinU1 * cosU2 * cosLambda) ^ 2))
    If sinSigma = 0 Then
      distVincenty = 0  'co-incident points
      Exit Function
    End If
    cosSigma = sinU1 * sinU2 + cosU1 * cosU2 * cosLambda
    sigma = Atan2(cosSigma, sinSigma)
    sinAlpha = cosU1 * cosU2 * sinLambda / sinSigma
    cosSqAlpha = 1 - sinAlpha * sinAlpha

    If cosSqAlpha = 0 Then 'check for a divide by zero
      cos2SigmaM = 0 '2 points on the equator
    Else
      cos2SigmaM = cosSigma - 2 * sinU1 * sinU2 / cosSqAlpha
    End If

    C = f / 16 * cosSqAlpha * (4 + f * (4 - 3 * cosSqAlpha))
    lambdaP = lambda

'the original calculation is "Too Complex" for Excel VBA to deal with
'so it is broken into segments to calculate without that issue
'the original implementation to calculate lambda
'lambda = L + (1 - C) * f * sinAlpha * _
  (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * (-1 + 2 * (cos2SigmaM ^ 2))))
      'calculate portions
    P1 = -1 + 2 * (cos2SigmaM ^ 2)
    P2 = (sigma + C * sinSigma * (cos2SigmaM + C * cosSigma * P1))
    'complete the calculation
    lambda = L + (1 - C) * f * sinAlpha * P2

  Wend

  If iterLimit < 1 Then
    MsgBox "iteration limit has been reached, something didn't work."
    Exit Function
  End If

  uSq = cosSqAlpha * (low_a ^ 2 - low_b ^ 2) / (low_b ^ 2)

'the original calculation is "Too Complex" for Excel VBA to deal with
'so it is broken into segments to calculate without that issue
  'the original implementation to calculate upper_A
  'upper_A = 1 + uSq / 16384 * (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)))
  'calculate one piece of the equation
  P1 = (4096 + uSq * (-768 + uSq * (320 - 175 * uSq)))
  'complete the calculation
  upper_A = 1 + uSq / 16384 * P1

  'oddly enough, upper_B calculates without any issues - JLatham
  upper_B = uSq / 1024 * (256 + uSq * (-128 + uSq * (74 - 47 * uSq)))

'the original calculation is "Too Complex" for Excel VBA to deal with
'so it is broken into segments to calculate without that issue
  'the original implementation to calculate deltaSigma
  'deltaSigma = upper_B * sinSigma * (cos2SigmaM + upper_B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM ^ 2) _
      - upper_B / 6 * cos2SigmaM * (-3 + 4 * sinSigma ^ 2) * (-3 + 4 * cos2SigmaM ^ 2)))
  'calculate pieces of the deltaSigma formula
  'broken into 3 pieces to prevent overflow error that may occur in
  'Excel 2010 64-bit version.
  P1 = (-3 + 4 * sinSigma ^ 2) * (-3 + 4 * cos2SigmaM ^ 2)
  P2 = upper_B * sinSigma
  P3 = (cos2SigmaM + upper_B / 4 * (cosSigma * (-1 + 2 * cos2SigmaM ^ 2) - upper_B / 6 * cos2SigmaM * P1))
  'complete the deltaSigma calculation
  deltaSigma = P2 * P3

  'calculate the distance
  s = low_b * upper_A * (sigma - deltaSigma)
  'round distance to millimeters
  distVincenty = Round(s, 3)

End Function

Function SignIt(Degree_Dec As String) As Double
'Input:   a string representation of a lat or long in the
'         format of 10° 27' 36" S/N  or 10~ 27' 36" E/W
'OUTPUT:  signed decimal value ready to convert to radians
'
  Dim decimalValue As Double
  Dim tempString As String
  tempString = UCase(Trim(Degree_Dec))
  decimalValue = Convert_Decimal(tempString)
  If Right(tempString, 1) = "S" Or Right(tempString, 1) = "W" Then
    decimalValue = decimalValue * -1
  End If
  SignIt = decimalValue
End Function

Function Convert_Degree(Decimal_Deg) As Variant
'source: http://support.microsoft.com/kb/213449
'
'converts a decimal degree representation to deg min sec
'as 10.46 returns 10° 27' 36"
'
  Dim degrees As Variant
  Dim minutes As Variant
  Dim seconds As Variant
  With Application
     'Set degree to Integer of Argument Passed
     degrees = Int(Decimal_Deg)
     'Set minutes to 60 times the number to the right
     'of the decimal for the variable Decimal_Deg
     minutes = (Decimal_Deg - degrees) * 60
     'Set seconds to 60 times the number to the right of the
     'decimal for the variable Minute
     seconds = Format(((minutes - Int(minutes)) * 60), "0")
     'Returns the Result of degree conversion
    '(for example, 10.46 = 10° 27' 36")
     Convert_Degree = " " & degrees & "° " & Int(minutes) & "' " _
         & seconds + Chr(34)
  End With
End Function

Function Convert_Decimal(Degree_Deg As String) As Double
'source: http://support.microsoft.com/kb/213449
   ' Declare the variables to be double precision floating-point.
   ' Converts text angular entry to decimal equivalent, as:
   ' 10° 27' 36" returns 10.46
   ' alternative to ° is permitted: Use ~ instead, as:
   ' 10~ 27' 36" also returns 10.46
   Dim degrees As Double
   Dim minutes As Double
   Dim seconds As Double
   '
   'modification by JLatham
   'allow the user to use the ~ symbol instead of ° to denote degrees
   'since ~ is available from the keyboard and ° has to be entered
   'through [Alt] [0] [1] [7] [6] on the number pad.
   Degree_Deg = Replace(Degree_Deg, "~", "°")

   ' Set degree to value before "°" of Argument Passed.
   degrees = Val(Left(Degree_Deg, InStr(1, Degree_Deg, "°") - 1))
   ' Set minutes to the value between the "°" and the "'"
   ' of the text string for the variable Degree_Deg divided by
   ' 60. The Val function converts the text string to a number.
   minutes = Val(Mid(Degree_Deg, InStr(1, Degree_Deg, "°") + 2, _
             InStr(1, Degree_Deg, "'") - InStr(1, Degree_Deg, "°") - 2)) / 60
   ' Set seconds to the number to the right of "'" that is
   ' converted to a value and then divided by 3600.
   seconds = Val(Mid(Degree_Deg, InStr(1, Degree_Deg, "'") + _
           2, Len(Degree_Deg) - InStr(1, Degree_Deg, "'") - 2)) / 3600
   Convert_Decimal = degrees + minutes + seconds
End Function

Private Function toRad(ByVal degrees As Double) As Double
    toRad = degrees * (PI / 180)
End Function

Private Function Atan2(ByVal X As Double, ByVal Y As Double) As Double
 ' code nicked from:
 ' http://en.wikibooks.org/wiki/Programming:Visual_Basic_Classic/Simple_Arithmetic#Trigonometrical_Functions
 ' If you re-use this watch out: the x and y have been reversed from typical use.
    If Y > 0 Then
        If X >= Y Then
            Atan2 = Atn(Y / X)
        ElseIf X <= -Y Then
            Atan2 = Atn(Y / X) + PI
        Else
        Atan2 = PI / 2 - Atn(X / Y)
    End If
        Else
            If X >= -Y Then
            Atan2 = Atn(Y / X)
        ElseIf X <= Y Then
            Atan2 = Atn(Y / X) - PI
        Else
            Atan2 = -Atn(X / Y) - PI / 2
        End If
    End If
End Function