' Paul B. Anderson's collection of
' Cylindrical map projection formulas
' in Visual Basic syntax
' Date: 02/07/2000
'
' e-mail: pbander@yahoo.com
' or: pbander@series2000.com
' or: pbander@picusnet.com
'
' Constructive comments, corrections,
' and enhancements appreciated.
'
' ================================
' Function used by some of the Map
' projection subroutines.
' ================================

Static Function LN#(n#)
'
  Dim Title As String
  Dim Msg As String
  Dim DgDef
  Dim Response
'
  If n# > 0# Then
    LN# = Log(n#)
  Else
    Title = "Function LN Error"
'  
    Msg = " Input Number <= 0 "
    Msg = Msg + Chr$(10) + Chr$(10)
    Msg = Msg + " Program will End! "
'  
    DgDef = 0 + 16 + 0
    Response = MsgBox(Msg, DgDef, Title)
'
    END
  End If
'
End Function ' { LN#. }
'
' ======================================================
' The function below is used compute the correct Lambda 
' value prior to calling the map projection subroutine.
' Both LambdaVal# and Lambda0Val# must be in Radians.
' ======================================================

Static Function Normalize#(LambdaVal#, Lambda0Val#)
'
' This subroutine is responsible for placing the Longitude (Lambda)
' value into the correct part of the map in relation to the selected
' Central Longitude (Lambda0) of the map.
'

' Local Variables Used
' --------------------
  Dim LambdaDiff As Double ' Stores the difference between
                           ' the current Lambda Value and
                           ' the central Longitude.

' --------------------
'
  LambdaDiff = LambdaVal# - Lambda0Val#
'
  Do While Abs(LambdaDiff) > PI
    If LambdaDiff < 0 Then
      LambdaDiff = LambdaDiff + (PI * 2)
    Else
      LambdaDiff = LambdaDiff - (PI * 2)
    End If
  Loop
'
  Normalize# = LambdaDiff
'
End Function ' { Normalize#. }
'
' ==========================
  General Notes:
' ==========================
' 1> All formulas in this text file are for the Sphere
' 2> The # symbol indicates Double Precision, Floating Point
' 3> All standard parallels values (Phi0#) must be converted to Radians
' 4> An Example: In Basic 'Phi# ^ 3' means raise Phi# value to the 3rd power
' 5> SQR is Basic's Square Root function
' 6> PI - Global Constant - 3.1415926535898
' 7> DEG2RAD - Global Constant - 1.74532925199433E-02 ' PI / 180
' 8> RAD2DEG - Global Constant - 57.2957795130822 ' 180 / PI

' Some of the unreferenced formulas (will fix soon) contained
' here are from:
' 1) "An Album of Map Projections"
'  - by Snyder & Voxland, 1987 & 1994
'  - U.S. Geological Survey Professional Paper 1453
' 
' 2) "Flattening the Earth: two thousand years of map projections"
'  - by Snyder, 1993 & 1997
' 
' 3) "Coordinate Systems and Map Projections"
'  - by Maling, 1992
'
' 4) Dr. Waldo Tobler's published work
'
' 5) Snyder's personal software
'
' 6) Voxland's 'World' program documentation
'
' ======================================
' Cylindrical map projection subroutines
' ======================================
'
Static Sub ArdenCloseCyl(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Arden-Close Cylindrical (1947)
'
' Note:
' Brief description in "Geographical By-ways and some other Geographical Essays"
' - by Col. Sir Charles Arden-Close
'
  Dim LocalPhi0#
  Dim MillerConst#
  Dim XOut1#
  Dim XOut2#
  Dim YOut1#
  Dim YOut2#
'
' Mercator Projection
  MillerConst# = 1#
  LocalPhi0# = 0
'
  XOut1# = Radius# * Lambda#
  YOut1# = Radius# * MillerConst# * LN#(TAN(PI / 4# + Phi# / (2# * MillerConst#)))
'
' Lambert's Cylindrical Equal-Area Projection
  XOut2# = Radius# * Lambda# * COS(LocalPhi0#)
  YOut2# = Radius# * (1# / COS(LocalPhi0#)) * SIN(Phi#)
'
  XCoord# = (XOut1# + XOut2#) / 2#
  YCoord# = (YOut1# + YOut2#) / 2#
'
End Sub ' { ArdenCloseCyl. }
'
' =========================
'
Static Sub Braun2(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Braun's Second (or Braun's Perspective) Cylindrical projection (1867)
'
' Note:
' Formulas from "Flattening the Earth: two thousand years of map projections"
' - by Snyder, 1993 & 1997
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * (1.4# * SIN(Phi#) / (0.4# + COS(Phi#)))
'
End Sub ' { Braun2. }
'
' ===================
'
Static Sub CentralCyl(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Central (or Perspective) Cylindrical projection
'
' Notes:
' - Both inventer and creation date lost to history
' - Useful only as comparison to Mercator
' - Transverse aspect developed by Wetch
'
' Formulas from "An Album of Map Projections" by Snyder & Voxland, 1987
' U.S. Geological Survey Professional Paper 1453
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * TAN(Phi#)
'
End Sub ' { CentralCyl. }
'
' =========================
'
Static Sub CylEqualArea(Radius#, Lambda#, Phi#, Phi0#, XCoord#, YCoord#)
' Cylindrical Equal-Area Projection
'
' - Standard Parallels (Phi0#) - convert to radians
' -----
' 1) Phi0# = 0 Deg N&S (Tangent)
' Lambert's Cylindrical Equal-area projection (1772)
' Inventor
' -----
' 2) Phi0# = 30 Deg N&S (Secant)
' Behrmann's projection (1910)
' Least mean maximum angular distortion for entire map
' -----
' 3) Phi0# = 37.06667 Deg N&S (Secant)
' Limiting case of Hyperbolic Equal-area (Craster)
' -----
' 4) Phi0# = 37.4 Deg N&S (Secant)
' Trystan Edwards, math corrected by Snyder
' -----
'  a) Phi0# = 50.8667 Deg N&S (Secant)
'  Trystan Edwards original value, 1953 (Snyder)**
'  -----
'  b) Phi0# = 37.38333 Deg N&S (Secant)
'  Trystan Edwards projection, (Maling)**
' -----
' 5) Phi0# = 45 Deg N&S (Secant)
' Gall's Orthographic/peters projection (Snyder & Maling)
' -----
'  a) Phi0# = 44.138 Deg N&S (Secant)
'  peters projection (Voxland)
'  -----
'  b) Phi0# = 46.03333 Deg N&S (Secant)
'  Original error by Peters (Maling)**
' -----
' 6) Phi0# = 55 Deg N&S (Secant)
' M. Balthasart's projection (Snyder)
' 1935
' -----
'  a) Phi0# = 50 Deg N&S (Secant)
'  M. Balthasart's projection (Maling)
' -----
' ** No longer Equal-area
'
' Notes:
' - Lambert developed its transverse aspect (1772)
' - Behrmann also published in transverse & oblique aspects (1926)
'
' Formulas from "The World in Perspective" by Canters and Decleir, 1989
' Published by John Wiley and Sons
'
  XCoord# = Radius# * Lambda# * COS(Phi0#)
  YCoord# = Radius# * (1# / COS(Phi0#)) * SIN(Phi#)
'
End Sub ' { CylEqualArea. }
'
' ========================
'
Static Sub Equidistant(Radius#, Lambda#, Phi#, Phi0#, XCoord#, YCoord#)
' Cylindrical Equidistant (or Equirectangular, or Equi-rectangular) projection
' 
' - Standard Parallels (Phi0#) - convert to radians
' -----
' 1) Phi0# = 0 Deg N&S (Tangent)
' Plate Carrée
' Other names: a) Plane Chart
'              b) Simple Cylindrical projection
'              c) Geographic
'              d) Unprojected
' -----
' 2) Phi0# = 37.5 Deg N&S (Secant)
' Ronald Miller - Minimum overall scale distortion
' -----
' 3) Phi0# = 42 Deg N&S (Secant)
' E. Grafarend and A. Niermann
' Minimum 'linear distortion' using Airy-Kavrayskiy criteria
' -----
' 4) Phi0# = 43 Deg N&S (Secant)
' Ronald Miller - Minimum continental scale distortion
' -----
' 5) Phi0# = 45 Deg N&S (Secant)
' Gall Isographic
' -----
' 6) Phi0# = 50.5 Deg N&S (Secant)
' Ronald Miller's Equi-rectangular projection
' -----
' 7) Phi0# = 61.7 Deg N&S (Secant)
' E. Grafarend and A. Niermann
' Minimum 'linear distortion' using Airy criteria
' -----
'
' Notes:
' Transverse aspect of Plate Carrée developed by Cassini
'
' Formulas from "The World in Perspective" by Canters and Decleir, 1989
' Published by John Wiley and Sons
'
  XCoord# = Radius# * Lambda# * COS(Phi0#)
  YCoord# = Radius# * Phi#
'
End Sub ' { Equidistant. }
'
' =========================
'
Static Sub CylStereographic(Radius#, Lambda#, Phi#, Phi0#, XCoord#, YCoord#)
' Cylindrical Stereographic projection
'
' Note:
' This is a type of 'Perspective Cylindrical'
'
' - Standard Parallels (Phi0#) - convert to radians
' -----
' 1) Phi0# = 0 Deg N&S (Tangent)
' Braun's Cylindrical Stereographic projection
' -----
' 2) Phi0# = 30 Deg N&S (Secant)
' Bol'shoy sovetskiy atlas mira (BSAM) projection
' or Kamenetskiy's 2nd projection
' -----
' 3) Phi0# = 45 Deg N&S (Secant)
' Gall's (Stereographic) projection
' Originator
' -----
' 4) Phi0# = 55 Deg N&S (Secant)
' Kamenetskiy's 1st projection
' -----
' 5) Phi0# = 66.1594674 Deg N&S (Secant)
' (O. M. Miller's) Modified Gall (Stereographic) projection
' - Use 'Phi0# = (2# / SQR(3#))' for this variation to get
' - the correct math precision for your software; don't
' - convert it to radians - it's already in the proper form!
' -----
'
' Note:
' Formulas from "The World in Perspective" by Canters and Decleir, 1989
' Published by John Wiley and Sons
'
  XCoord# = Radius# * Lambda# * COS(Phi0#)
  YCoord# = Radius# * (1# + COS(Phi0#)) * TAN(Phi# / 2#)
'
End Sub ' { CylStereographic. }
'
' ============================
'
Static Sub KharchenkoShab(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Kharchenko-Shabanova Cylindrical projection
'
  XCoord# = Radius# * Lambda# * COS(10# * DEG2RAD)
  YCoord# = Radius# * (0.99 * Phi# + (0.0026263 * Phi# ^ 3) + (0.10734 * Phi# ^ 5))
'
End Sub ' { KharchenkoShab. }
'
' ==========================
'
Static Sub Mercator(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Cylindrical Conformal projection, or Mercator (1569)
'
' Notes:
' Transverse aspect of Mercator developed by J. H. Lambert (1772)
' Oblique aspect of Mercator developed by Charles Sanders Peirce (1894)
'
' Formulas from "The World in Perspective" by Canters and Decleir, 1989
' Published by John Wiley and Sons
'
  Dim MaxLat#
  Dim NotVisible
'
  NotVisible = 9999
  MaxLat# <90 Deg
'  
  If ABS(Phi# * RAD2DEG) <= MaxLat# Then
    XCoord# = Radius# * Lambda#
    YCoord# = Radius# * LN#(TAN(PI / 4 + Phi# / 2#))
  Else
    XCoord# = NotVisible ' Out of range numeric value to force a NO PLOT
  End If
'
End Sub ' { Mercator. }
'
' ========================
'
Static Sub Miller1(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' (O. M.) Miller (Cylindrical) Projection
' Other Names:
' - Miller 1 projection
' - Modified Mercator (b)  
'
  XCoord# = Radius# * Lambda#
'
' Snyder version:
  YCoord# = (Radius# / .8#) * LN#(TAN((PI / 4#) + ((.8# * Phi#) / 2# )))
'
' Canters and Decleir version:
  YCoord# = Radius# * 1.25# * LN#(TAN((PI / 4#) + (Phi# / (2# * 1.25#))))
'
End Sub ' { Miller1. }
'
' ====================
'
Static Sub Miller2(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' (O. M.) Miller 2 projection, or Modified Mercator (a)
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * 1.5# * LN#(TAN((PI/4) + (Phi# / 3#)))
'
End Sub ' { Miller2. }
'
' ====================
'
Static Sub Pavlov(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Pavlov's (Cylindrical) projection 
'
' Note:
' Formulas from "The World in Perspective" by Canters and Decleir, 1989
' Published by John Wiley and Sons
'
  Dim A0#
  Dim A2#
  Dim A4#
  Dim Phi3#
  Dim Phi5#
'
  A0# = 1#
  A2# = -0.1531
  A4# = -0.0267
  Phi3# = Phi# ^ 3#
  Phi5# = Phi# ^ 5#
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * (A0# * Phi# + (A2# / 3#) * Phi3# + (A4# / 5#) * Phi5#)
'
End Sub ' { Pavlov. }
'
' ==================
'
Static Sub PerspectiveCompromise(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' (O. M. Miller's) Perspective Compromise
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * (SIN(Phi# / 2#) + TAN(Phi# / 2#))
'
' ==================================
'
Static Sub ToblerVar1(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Tobler's alternate #1 to (O. M.) Miller 1 Cylindrical projection
'  
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * (Phi# + 1 / 6 * Phi# ^ 3)
'
End Sub ' { ToblerVar1. }
'
' ======================
'
Static Sub ToblerVar2(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Tobler's alternate #2 to (O. M.) Miller 1 Cylindrical projection
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * (Phi# + 1 / 6 * Phi# ^ 3 + 1 / 24 * Phi# ^ 5)
'
End Sub ' { ToblerVar2. }
'
' =====================
'
Static Sub ToblerWorldinSqr(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Tobler's World in a Square projection
'
  XCoord# = Radius# * (Lambda# / SQR(PI))
  YCoord# = Radius# * SQR(PI) * SIN(Phi#)
'
End Sub ' { ToblerWorldinSqr. }
'
' ============================
'
Static Sub Urmayev2(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Urmayev Cylindrical II projection
'
' Note:
' Formulas from John Parr Synder's personal software
'
  Dim P10#
  Dim P10SQ#
'
  P10# = Phi# / 10 / DEG2RAD
  P10SQ# = P10# * P10#
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * Phi# * (1 + P10SQ# * (188 / 48384 + P10SQ# / 80640))
'
End Sub ' { Urmayev2. }
'
' ====================
'
Static Sub Urmayev3(Radius#, Lambda#, Phi#, XCoord#, YCoord#)
' Urmayev Cylindrical III projection
'
' Note:
' Formulas from "The World in Perspective" by Canters and Decleir, 1989
' Published by John Wiley and Sons
'
  Dim A0#
  Dim A2#
  Dim Phi3#
'
  A0# = 0.9281
  A2# = 1.1143
  Phi3# = Phi# ^ 3#
'
  XCoord# = Radius# * Lambda#
  YCoord# = Radius# * (A0# * Phi# + (A2# / 3#) * Phi3#)
'
End Sub ' { Urmayev3. }