Geodesic for measuring; Planar for analysis

[Craig_Eissler_Iceman]

Measure tool: Geodesic vs. Planar: The Help page indicates "Geodesic" is always more accurate.

OK, but, why do they also indicate that projected coordinate systems are more suited for analysis -- which includes measuring, of course?

In fact, in the Calculate Geometry menu tool (but NOT the ArcGIS toolbox tool) is grayed out, when attempting to measure in geographic coordinates ..this, I understand. How it relates to the other observations, I do not.

Thanks, CCE

[Leo_Liu_WA]

I think it because there are many 'analysis' tools are based on raster datasets.

I.E. Sometimes counting cell numbers are much easier and faster than calculating area of a complex polygon.

Especially when you need to transfer coordinates and units.

[Craig_Eissler_Iceman]

OK sure, but let me restate my question another way: If I'm using geoprocessing/analysis tools with a 'vector' dataset in a projected coordinate system, aren't the calculations using planar measurements?

If so, "why". if geodesic measurements are more accurate?
Or, are geodesic measurements only more accurate when specifically calculating "distance"..?

[Leo_Liu_WA]

Hi Craig,

If I'm using geoprocessing/analysis tools with a 'vector' dataset in a projected coordinate system, aren't the calculations using planar measurements?

Yes, my understanding is that the calculations in the analysis tool SHOULD use planar measurements to respect the coordinate system, unless the programmer didn't consider this.

If so, "why". if geodesic measurements are more accurate?

I think it is the natural drawback of the projection coordinate system: the earth is an 'epileptoid' other than 'cubic'.

If you look into the transformation of those projection coordinate systems, you will see that only certain areas (I.E. close to the tangential point/line) can have very accurate locations transferred from spheroid surface to planar surface. Most of other areas are calculated by certain algorithms, with distortions.

[Craig_Eissler_Iceman]

Thanks Leo; yeah, that's how I understand things also.

...What made me re-think this is when I read this in the Distance tool Help page (see below):

And then I opened that tool and saw the Distance measurement mode option (see below that):

And, now I see -- for example -- that for the vector equivalent, Proximity tools -- some of them provide the option (Geodesic or Planar) and some don't.  So, then I started wondering what the "default" is for the tools that do not offer the option..? Like you, my assumption is also "Planar", but this has certainly raised my eyebrow 😉

[Craig_Eissler_Iceman]

Hello again, Leo -- please see previous Reply, but I also thought of something else relevant to this.

...Back to the Measure tool:
If measure distance or area using a projected coordinate system in geodesic mode, can I expect to get the same result if I used a geographic coordinate system in geodesic mode, so long as the spheroid/datum are the same? ...In other words, if the projected coordinate system I'm using is based on the same underlying geographic coordinate system.

I tried this with a couple of examples and this held true. However, I'm wondering if I was just lucky with my samples and whether this is the expected behavior regardless of the results..?

[DanPatterson]

Think large area/ long distance vs small area/short distance then add latitude to the equation.

If your data are already projected then you can use it or convert back to geographic coordinates.

Some points to consider from a variety of links such as ...

Geodesic versus planar distance—ArcGIS Pro | Documentation

•  Although some map projections preserve some characteristics accurately, none preserve all distances correctly. 
• The difference between planar and geodesic calculations of distance and direction varies with map projection and size of the study area.
• areas are defined by edges/line segments forming the border, hence area will depend on the accurate determination of distance between them
• etc

A good example of showing this is to use 4 points of long/lat to define a "square" at some latitude of some size ( keep it less than 3 degrees in E/W and N/S extent for now). 

Project those points to something like UTM.

Calculate the distance  between points and the area for both, using geodesic calculations for both options and planar for the projected set.

The distances along the meridians won't be too bad, but along the parallels they will differ.  Now a bunch of points will form distance errors that can vary with location, hence areas bounded by the segments will result in values differing from geodesic calculations.

Tissot's indicatrix - Wikipedia

Tissot's indicatrix helps illustrate map projection distortion (esri.com)

sums it up pretty well so geodesic calculations will be better than planar but planar can be pretty good if the projection chosen is an area preserving projection.  Most projections used by government maps are "compromise" meaning they are not perfect at anything but as good as they can be for the area they cover and their intent.

I am sure you know all this, but don't get hung up on how "accurate" calculations are since the measurement of location is inherently influenced by precision/accuracy issues.

Lastly location is based on a proper model of earth whose "shape" has "changed" over time as technology has advanced (eg. NAD27 vs NAD83 issues of many decades ago)... 

let's leave 3D area vs 2D area out of the question for now ... 

[Craig_Eissler_Iceman]

Thanks, Dan, but yes this is the information I had already read. ...For me, I then usually have very pointed questions I'm seeking answers for, like:

1) Why does that Help page say, "Geodesic distance always produces a more accurate result and is the recommended method, unless speed is more important than accuracy". Do note that this was referring to  the Raster > Distance tool, but makes me wonder about other other tools or vector analysis, like my other question:

2) Which measurement mode (geodesic or planar) is used in vector-based analysis?
If planar, why, if geodesic is ALWAYS more accurate? (see Question 1)

[DanPatterson]

It isn't just raster, vector as well, and yes geodesic will be more "accurate" but to what degree depends on all I listed above.  As I said,

• take two points in UTM, MTM or State Plane (not Web Mercator), spaced 50 km or so apart. 
• they have scale factors of 0.9996 and 0.9999 respectively so they are pretty good compromise projections.
• The planar distance between them doesn't account for curvature associated with Earth (eg horizon has a vanish point)
• convert to decimal degrees using the same datum, and calculate the geodesic distance
• To have fun, calculate the mid-point of your UTM line, convert it to decimal degrees  (it won't be the mid-point of your line in decimal degrees.

How accurate!  As I said, it is all relative...  

Remember Web Mercator is the most widely used Projection in gis now (thanks to google, esri etc) and it has to be the worst projection that you can use for distance and area calculations!

Has that stopped anyone?  No. Check the Community feeds, there are dozens of of threads dealing with bad distance and area questions.

I would strongly advise against stating that there is a "rule" that geodesic is better than planar... it all depends by what you mean by "accurate". perhaps "best" for the current application at this time and in this space would be a nice alternative

[Craig_Eissler_Iceman]

Thanks, Dan ...of course I'm just pointing out a Help page that Esri says geodesic always more accurate...

...which led me to my question (which I'm still not sure is answered), but I'll re-post again: "What measurement mode is used in the geoprocessing analysis tools?" Geodesic or Planar? 

And if it matters, I'm asking from the vector-based, projected coordinate system perspective.

So, my assumption has always been that it is using 'Planar' measurements

...But, reading that Esri Help page is what had me question this...