Page Base Line: Reply to Bill93

Haven't yet mastered replying to threads, so I'll try it this way. The basic formulas that I use for calculating coordinates of points on a geodetic line are found in a 2005 paper by Thomas and Featherstone. The formulas are fairly easy to derive, but the paper summarizes them very well. I downloaded it for free years ago, but things are more complicated now.

You can read it here: http://www.researchgate.net/publication/242252855_Validation_of_Vincentys_Formulas_for_the_Geodesic_Using_a_New_Fourth-Order_Extension_of_Kiviojas_Formula
or you may be able to find a free pdf by searching the title or a piece of the title.

The relevant equations are (3), (4), (5), and (6). Equations (4) and (5) are differential equations where ds is the incremental change to the length of the line for each iteration. Solving equations (4) and (5) for d phi and d lambda and substituting the increment chosen for ds gives the latitude and longitude, respectively, of each new point. Equation (6) gives the new azimuth. These are all in radians, so they have to be converted to decimal degrees and then to degrees, minutes and seconds.

It's not sophisticated at all, just brute computing force. I input the coordinates of the beginning point, the azimuth from NGS Inverse, and an elevation factor if I'm not working directly with the ellipsoid. For a 10,000-meter line with 1/5th meter increments, the spreadsheet generates 50,000 rows. I just choose the ones I want and copy the coordinates to another worksheet, or just write them down. I'm not concerned with efficiency and elegance, I just want to see the coordinates along whatever line I'm playing with at the time. I'm confident of the intermediate points if the spreadsheet duplicates the end coordinates for the line.

This is kind of arcane stuff, but it's great entertainment for a nerdy old math guy.