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{"sheet":"Vincenty formulae","index":0,"n_rows":52,"n_cols":10,"rows_kept":52,"cut":false,"hidden":false,"merged":[[23,1,24,1],[31,1,32,1],[33,1,34,1]]}
[null,"Vincenty's Direct and Inverse Solution of Geodesics on the Ellipsoid"]
[null,"to calculate new coordinate based on azimuth and distance (direct)"]
[null,"or distance and azimuth based on two coordinates (inverse)"]
[]
[null,"Algorithms by Thaddeus Vincenty (1975)"]
[null,"https://en.wikipedia.org/wiki/Vincenty%27s_formulae"]
[]
[null,"Ported to VBA by © Tomasz Jastrzębski 2018-2022 MIT License"]
[null,"Version: 2022-07-03"]
[null,"Latest version available at:"]
[null,"https://github.com/tdjastrzebski/Vincenty-Excel"]
[]
[null,"Based on the implementation in Java Script by Chris Veness, ver 2.4.0"]
[null,"https://www.movable-type.co.uk/scripts/latlong-vincenty.html"]
[null,"https://github.com/chrisveness/geodesy"]
[]
[null,"This Excel workbook contains 6 functions implementing [Vincenty Direct] and [Vincenty Inverse] calculations"]
[null,"as well as 2 functions for Decimal ↔ Degrees/Minutes/Seconds format conversion using WGS84 model"]
[]
[null,"For functions description please use Excel function wizard, search in Geodesic function category."]
[]
[null,"Vincenty Direct Calculation Example"]
[null,"Input: point 1, distance, azimuth",null,null,null,null,"Result: point 2, reverse azimuth"]
[null,"Flinders Peak (point 1)","37°57′03.7203″S",null,{"$f":"ConvertDecimal(C24)","v":-37.951033416666668},null,"Point 2 - latitude",{"$f":"VincentyDirLat(E24,E25,C27,C26)","v":-37.652821138864894},null,{"$f":"ConvertDegrees(H24, FALSE)","v":"37°39'10.1561\"S"}]
[null,null,"144°25′29.5244″E",null,{"$f":"ConvertDecimal(C25)","v":144.42486788888888},null,"Point 2 - longitude",{"$f":"VincentyDirLon(E24,E25,C27,C26)","v":143.92649552774759},null,{"$f":"ConvertDegrees(H25, TRUE)","v":"143°55'35.3839\"E"}]
[null,"Distance [m]",54972.271142042664,null,null,null,"Reverse Azimuth",{"$f":"VincentyDirRevAzimuth(E24,E25,C27,C26,TRUE)","v":127.17363062946853}]
[null,"Azimuth",306.86815920330764]
[]
[]
[null,"Vincenty Inverse Calculation Example"]
[null,"Input: point 1, point 2",null,null,null,null,"Result: distance, azimuth, reverse azimuth"]
[null,"Flinders Peak (point 1)","37°57′03.7203″S",null,{"$f":"ConvertDecimal(C32)","v":-37.951033416666668},null,"Distance [m]",{"$f":"VincentyInvDistance(E32,E33,E34,E35)","v":54972.271138415599}]
[null,null,"144°25′29.5244″E",null,{"$f":"ConvertDecimal(C33)","v":144.42486788888888},null,"Forward Azimuth",{"$f":"VincentyInvFwdAzimuth(E32,E33,E34,E35)","v":306.8681592033081}]
[null,"Buninyong (point 2)","37°39′10.1561″S",null,{"$f":"ConvertDecimal(C34)","v":-37.652821138888889},null,"Reverse Azimuth",{"$f":"VincentyInvRevAzimuth(E32,E33,E34,E35, TRUE)","v":127.17363062944486}]
[null,null,"143°55′35.3839″E",null,{"$f":"ConvertDecimal(C35)","v":143.92649552777777}]
[]
[]
[null,"Calculation results have been validated using 1200 test cases generated for 6 range clusters and distance between 10 m and 30,000 km"]
[null,"against Geoscience Australia website:"]
[null,"http://www.ga.gov.au/geodesy/datums/vincenty_direct.jsp",null,null,null,null,"Geoscience Australia","GeodSolve Library"]
[null,"http://www.ga.gov.au/geodesy/datums/vincenty_inverse.jsp",null,null,null,"VincentyDirLat()",5.0000000000000001E-9,0]
[null,"and GeodSolve library by Charles Karney:",null,null,null,"VincentyDirLon()",2.0000000000000001E-9,1.0000000000000001E-9]
[null,"https://geographiclib.sourceforge.io/cgi-bin/GeodSolve",null,null,null,"VincentyDirRevAzimuth()",8.3300000000000001E-7,0]
[null,"https://geographiclib.sourceforge.io/scripts/geod-google.html",null,null,null,"VincentyInvDistance()",2.4182999999999999E-5,1.269E-6]
[null,"https://link.springer.com/article/10.1007%2Fs00190-012-0578-z",null,null,null,"VincentyInvFwdAzimuth()",8.0979999999999994E-6,3.9280000000000003E-6]
[null,null,null,null,null,"VincentyInvRevAzimuth()",5.2449999999999998E-6,3.9280000000000003E-6]
[null,"References:"]
[null,"Thaddeus Vincenty: original publication (1)"]
[null,"Thaddeus Vincenty: original publication (2)"]
[null,"Wikipedia: Vincenty's formulae"]
[null,"Wikipedia: Geodesics on an ellipsoid"]
[null,"Wikipedia: Great-circle distance"]