# Points along geodesic do not fall on straight line in Gnomonic projection

Jake
Global Mapper UserPosts:

**269**Trusted User
Windows 7

GM 13.2.2 5 October 2012 64 bit

I am trying to figure out why points along a geodesic do not fall on the line. I may be doing something wrong so I have attached the GMW so you can see for yourself.

The Problem

Draw a geodesic line from "A" at 45N, 75W 200 nautical miles along an azimuth of 90° to point "C".

Project the workspace to Gnomonic with lat0 = 45N and lon0 = 72.5W.

The 1/3, 1/2 and 2/3 points of the line I have computed with matlab and pctrans. They agree within 1mm of each other. However, the Global Mapper AC line is about 9 m south of these points.

After a little testing it would seem that the gnomonic line

I realize GM V14 is out but I suspect the same issue is present there as well. I am in the process of getting the V14 upgrade.

GM 13.2.2 5 October 2012 64 bit

I am trying to figure out why points along a geodesic do not fall on the line. I may be doing something wrong so I have attached the GMW so you can see for yourself.

The Problem

Draw a geodesic line from "A" at 45N, 75W 200 nautical miles along an azimuth of 90° to point "C".

Project the workspace to Gnomonic with lat0 = 45N and lon0 = 72.5W.

The 1/3, 1/2 and 2/3 points of the line I have computed with matlab and pctrans. They agree within 1mm of each other. However, the Global Mapper AC line is about 9 m south of these points.

After a little testing it would seem that the gnomonic line

__is based on a spherical earth. Can you confirm this?__**AC**I realize GM V14 is out but I suspect the same issue is present there as well. I am in the process of getting the V14 upgrade.

## Comments

17,238The projection that you are in doesn't really matter for calculating the end point projected some distance in great circle mode. Those calculations are always done on the ellipsoid with lat/lon values, then reprojected as necessary. Do keep in mind that if you calculate 2 points in lat/lon, then reproject, only the vertices themselves and reprojected, so the line between the vertices will always be straight in the current view projection. If you want it to curve you would need to add more vertices along the line before reprojecting so that each vertex can be reprojected.

Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

269Trusted UserI calculated points along the geodesic in matlab and pctrans. However, they do not match Global Mapper's straight geodesic line. As you mentioned the GM COGO points match matlab and pctrans. However, I want the line to match the points.

Let me put it this way. When I am starting at a point with a fixed initial azimuth there is only one path I can take if I am to follow a geodesic. Whether the distance is 10 NM or 1000NM, the first 10NM will follow exactly the same path. If I did not specify an azimuth then I would have to specify the end of the path. That would then dictate my initial azimuth.

What I found is if I use a spherical model in matlab for the earth, the geodesic points fall on the GM line. So this would seem to indicate GM is not using the reference ellipsoid but instead a spherical model.

I have one other software that can produce points along the geodesic. I will add that to the comparison tomorrow.

Thanks for looking into this.

17,238Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

269Trusted UserI have tried to use the "Create Point Features Spaced Along the Selected Feature" function but that unfortunately resulted in the points being the same 9 metres off. So it is using a sphere as well.

Is there any way you know of in GM to add points or vertices on a geodesic (ellipsoid) path? Or is the great circle (spheroid) path the only option? COGO is not always an option since the lines are defined by end points and not start point plus azimuth.

Regards.

17,238Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

269Trusted UserI made sure the layer that containing the line was gnomonic, then I added 5 points via the "Create Point Features Spaced Along the Selected Feature". The result at the middle is the point GNO_3 that you can see. I can also see that the segment distance is slightly shorter too and that is why it is shifted slightly to the left.

Regards.

17,238So it may not be possible to generate the geodesic directly. To get the points you would have to do the trick with projecting the point some distance/bearing from the start point, then keep going from that start point out the distance and bearing. Then you would connect those points into a line (there is a tool to connect points into a line in the Digitizer Tool).

Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

269Trusted UserRegards.

17,238I have placed a new build at http://www.bluemarblegeo.com/downloads/global-mapper/global_mapper14.zip with the latest changes for you to try. Simply download that file and extract the contents into your existing v14.xx installation folder to give it a try. If you are using the 64-bit v14 version there is a new build at http://www.bluemarblegeo.com/downloads/global-mapper/global_mapper14_64bit.zip .

Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

269Trusted UserYour changes are done with such speed and efficiency it boggles the mind. I hope other people appreciate this (and find the functionality useful) as much I do.

269Trusted UserI am going to test again just to make sure.

269Trusted UserGM 14.1.3 B032113 64 bit

OK so retesting shows the same 9 meter offset at point MATLAB2. I tested using the,

Resample/Split Select Feature at Specified Spacing functionand

Create Point Features Spaced Along Selected FeatureThey both gave the same answer. About 9 m south of MATLAB2 and PCTRANS2. The GM COGO solution is much closer and it only 0.15 m away from MATLAB2 and PCTRANS2.

17,238Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

269Trusted UserA line in the gnomonic projection should follow the same path as the measure tool.

Thanks.

17,238Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/

454Trusted UserIn New Zealand we like to think we can fix anything with No.8 wire. My suggestion has very much that flavour. Brits might call it a Heath Robinson suggestion.

If you need to find exact intersections between great circle paths over an ellipsoid, rather than a sphere, would there be anything wrong in practice with pre-stretching the source data in the latitudinal axis [I first though pre-shrinking], at a guess by cos(90 - |φ|) * 1/f for each vertex, before projecting to Gnomonic?

Since we are using geodetic latitude, I think the mapping between spherical and ellipsoidal latitude will be linear.

Would this work, thus remapping positions over the ellipsoid into positions over the sphere, exactly?

I think Snyder would elegantly term this kludge the use of an "aposphere".

(BTW Snyder does say that the Gnomonic is "used only in the spherical form", and gives only a set of spherical formulae.)

Tim Baigent

17,238I would hesitate to say for sure if that will work, the math makes my head hurt I imagine if it was that simple to get right then the Gnomonic formulas would have just incorporated that and been ellipsoidal to start with, so there is probably more to it than that.

Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/products/global-mapper.php

454Trusted UserI'm certain you're right. I was being much too naïve.

A great circle path on a sphere is a circle (an embedded straight line), while a great circle path on an ellipsoid is a complex curve.

These are two different things. I wouldn't be surprised if there's only an approximate, iterative translation between the two.

Mapping latitudes in spherical space to latitudes in ellipsoidal space is neither here nor there, irrelevant to that relationship.

Thanks for even thinking about it at all.

Tim

269Trusted UserAlso, I have been skimming information on an ellipsoidal implementation of the gnomonic projection. If you are interested you can find the article by Karney it in the Journal of Geodesy, January 2013, Volume 87, Issue 1, pp 43-55.

17,238Thanks,

Mike

Global Mapper Guru

gmsupport@bluemarblegeo.com

http://www.bluemarblegeo.com/products/global-mapper.php

454Trusted UserI thought I'd just add a direct link to the volume: here.

269Trusted UserHere is a direct link to the article in the volume.

http://link.springer.com/article/10.1007%2Fs00190-012-0578-z