Loxodromic line
geomannie
Global Mapper UserTrusted User
I have a series of points and I am told that they define a loxdromic line, also called aRhumb line. Can GM display the line between the points such that they follow a loxodromic line, ideed is this the default behaviour?
In asking this question I am displaying my lack of knowledge on navigation. Any pointers would be greatly apreciated.
Thanks
In asking this question I am displaying my lack of knowledge on navigation. Any pointers would be greatly apreciated.
Thanks
Best Answer

geomannie said:Thanks a lot for your thoughts. I understand the definition of a loxodromic line and indeed if I plot my points using a Mercator grid, that is what I get. The joining line crosses all meridians of longitude at the same angle, thus I have a loxodrome. However, as Mykle points out changing the projection changes the joining line. For example, if I plot an intermediate point on my Mercator defined loxodrome and then change the projection, my intermediate point no longer lies on the line. The displacement is not huge and depends on the selected projection.
Does this mean that in GM a loxodromic line can only be plotted on a Mercator Projection? Logically it seems that if GM knew that a line were a loxodrome, the software could warp the line in other projections so that it crosses the exact same linear position on the ground as defined when plotted in Mercator.
GM developers, any comments?
Cheers,
Bob
Answers

A projection that has parallel lines of longitude, like Mercator, will show a straight line crossing each longitude line at the same angle/bearing. So you can load your points and draw a line between the endpoints. When displaying a Mercator projection, the line should pass through each of your points if they lie along a rhumb (loxodrome) line.
Depending upon the extent of your points, the line may look "interesting" in other projections. The points will not remain on your line when the projection does not have parallel lines of longitude. I'm just playing around with different projections, and my sample points and line are indeed interesting.

A projection that has parallel lines of longitude, like Mercator, will show a straight line crossing each longitude line at the same angle/bearing.
I had to check Snyder to make sure of this (as always).
In addition to lines of longitude being drawn parallel, lines of latitude must also be adjusted, their spacing being increased towards the poles in the same proportion as longitude at that point has been stretched.
This is special to Mercator. And the double stretching is why Mercator is such a poor projection for any purpose other than navigation (which it was designed for).

Hi Mykle & tjhb
Thanks a lot for your thoughts. I understand the definition of a loxodromic line and indeed if I plot my points using a Mercator grid, that is what I get. The joining line crosses all meridians of longitude at the same angle, thus I have a loxodrome. However, as Mykle points out changing the projection changes the joining line. For example, if I plot an intermediate point on my Mercator defined loxodrome and then change the projection, my intermediate point no longer lies on the line. The displacement is not huge and depends on the selected projection.
Does this mean that in GM a loxodromic line can only be plotted on a Mercator Projection? Logically it seems that if GM knew that a line were a loxodrome, the software could warp the line in other projections so that it crosses the exact same linear position on the ground as defined when plotted in Mercator.
GM developers, any comments?

Hi Bob
Your reply makes perfect sense and fully understood. I wonder, however, if it might be worth adding a note to the GM help file for plotting loxodromic lines, something like as follows?
Using GM for Plotting Loxodromes (Rhumb lines) in NonMercator Projections
If a loxodromic line is required in any projection other than Mercator a close representation to its location on the ground can be created by use of the following procedure. Initially create the line by plotting the defined vertices using the Mercator projection
 Resample the line line by using the Resample/Split Selected Features at Specified Spacing tool (right click on line) and select an appropriate resample value, e.g. 10100m. Closer spacing give greater accuracy.
 Reproject to desired projection

Thanks to tjhb for cleaning up my lack of precision when defining a suitable projection for a rhumb line.
I now see that Bob has said much of the same that I write below. Good Stuff. His Best Answer gets popped up under the initial question, and I didn't notice it until later.
If your line has only two endpoints, then the track of the line will change when you change your projection.
If you want to define a line that is straight when using a particular projection (mercator, for example), then you will need to select that projection and define enough points along your line so the track of the line remains constant after you change to a different projection.
The first of the attached images uses the polyconic projection. The endpoints are arbitrary (another image displayed during a google search used the same points). I simply displayed the mercator projection, then defined a number of points along the line. This image is the result when I then switched to the polyconic projection. The variation between rhumb and straight line depends upon the distance between your points, and your choice of displayed projection.
I have one line with only the two endpoints (blue), and I have a second line with several intermediate points (green). Note that it is possible in GM to add additional points along a line, but not change the line. You want to break the line into segments at each point, so look carefully at your options.
If you are displaying a lat/long grid, note that under some circumstances only the lines of longitude are displayed (second image, WinkleTriple projection as an example). Some projections show both, some appear to show only one direction. This behavior is not consistently repeatable, so it is hard to submit a bug report. Different zoom levels, no change. Different projection, sometimes no change. V17 seemed to show all, but haven't played enough to be sure. Background may be nothing, or OSM maps, hasn't mattered. I'm just using 10 degree lines, Show All Grid Lines, and NOT Extend Grid Lines. Go figger.

geomannie said:Your reply makes perfect sense and fully understood. I wonder, however, if it might be worth adding a note to the GM help file for plotting loxodromic lines, something like as follows?
Using GM for Plotting Loxodromes (Rhumb lines) in NonMercator Projections
If a loxodromic line is required in any projection other than Mercator a close representation to its location on the ground can be created by use of the following procedure. Initially create the line by plotting the defined vertices using the Mercator projection
 Resample the line line by using the Resample/Split Selected Features at Specified Spacing tool (right click on line) and select an appropriate resample value, e.g. 10100m. Closer spacing give greater accuracy.
 Reproject to desired projection
Cheers,
Bob 
Using GM for Plotting Great Circle Routes in NonMercator Projections
Hmm, this thread has got me thinking. Am I right to suppose that we can use a similar method to plot approximate great circle routes in projections other than Gnomic?
viz: Initially create the line by plotting the defined vertices using the Gnomic projection
 Resample the line by using the Resample/Split Selected Features at Specified Spacing tool (right click on line) and select an appropriate resample value, e.g. 10100m. Closer spacing give greater accuracy.
 Reproject to desired projection
Have I got this right?

That works. Suggest adding a few notes:
* Less than half of the sphere can be shown in the Gnomonic Projection. (If the center of your projection is at one of the poles, then the equator is at infinity.) The coordinates of the central point in the Gnomonic Projection must be within less than 90 degrees of all points on your line.
* Your sampling interval needs to be suitable for the length of your line. You are unlikely to need more than 100 points along your line (about 0.01 x line length).

Hello,
This additional information has been given to the documentation team as well. Thanks.
Cheers,
Bob
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