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Densify... Euclidean vs Geodesic

Anonymous User

Hi Dan Patterson - Do you know about projected versus geographic coordinate systems with the Densify tool? It says to pick an 'appropriate' spatial reference but I don't see more details. I want to make sure I densify a planar line and keep it planar. The densified lines come out ~30 meters apart depending on whether I use a PCS or GCS. I'm unclear on why, and if it's because one is planar or geodesic, or if something else is going on.

Thanks for any ideas.

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DanPatterson_Retired

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76,45 to -74,45 E-W defines two points on a parallel... aka a line of latitude.

The distance along a line of latitude (parallel) is going to be greater than the great circle distance between those two points. Calculate distance and bearing between two Latitude/Longitude points using haversine formula in JavaScript for an interactive example (157.3 vs 157.2 km for my examples)

So you will see deflection between the two. See Melita's answer to me.

Anonymous User

Melita Kennedy do you agree that using 'Densify' on a GCS produces an error? Or perhaps I made an error myself?

Anonymous User

I thought so too...what got me confused was some very strange behavior where the densified GCS line (assumed to be geodesic) did not match the the same GCS line densified using Geodetic Densify. And the densified PCS line matched the Geodetic Densified lines that were both GCS and PCS. Could it be that the planar and geodesic lines over this distance (~40km) are just too similar to tell the difference?

In which case the one outlier was the GCS line that was Densified...that line would just be wrong.

MelitaKennedy

If you use a PCS, it should be densifying relative to the plane. A GCS should densify the line based on the geodesic line between the two points.

DanPatterson_Retired

They can't be shifted at all points hopefully, that would imply a datum shift (ie NAD27 to NAD83). I won't address that but assume that the issues are due to the densification process.

My thoughts...

A big widths, long lengths, large spacing for example (ie E-W) :

Geodetic Densify—Help | ArcGIS for Desktop

B small (less than UTM zone width maybe) :

Densify—Help | ArcGIS for Desktop

I don't have my test results here, but I tested using the following procedure:

Locate yourself (me -75 lon, 45 lat)
make a couple of lines that span your area of interest
1. -76,44 to -74,46 a diagonal
2. -75,44 to -75,46 N-S
3. -76,45 to -74,45 E-W

densify at some appropriate increment using the methods in A and B
compare step 3

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