Circular vs. Octagonal Cost Distance

[DarrenWiens2]

Is there an ArcGIS tool that will make circular, rather than octagonal, cost distance rasters? Refer to the raster below, made with the Cost Distance tool, symbolized by arbitrary distance classes.

[DanPatterson_Retired]

never seen this behaviour before...what does your cost surface look like?

[DarrenWiens2]

It's flat - all ones.

[DanPatterson_Retired]

hmmm I would have to sit down and do the math by hand but it seems to be related to the square root 2 used in the calculations... ArcGIS Help (10.2, 10.2.1, and 10.2.2)‌  which is going against what I think it should be (ie circular)

[AndrewWilson99]

This octagonal artifact is standard in Cost Path calculations.  In the cost distance calculations, there are only 8 directions of travel (the eight neighboring cells) and eight weightings.   When there is a variable cost surface, these artifacts are not as noticeable.   With a fixed cost surface, it can get pretty obvious.

The square root of two is an artifact of using square rather than rectangular cells (which also have eight sided cost contour polygons). 

For alternate and possibly more eloquent explanations of this phenomenon, refer to Li, Larson and Rex ( http://geo.appstate.edu/sites/geo.appstate.edu/files/Creating%20buffers%20on%20surfaces%20_revised%2...‌ ) or Huber over on Stack Exchange ( terminology - Correct use of the terms geographic, path, and Euclidean distance - Geographic Informa...‌ ).

SInce you are looking at a constant cost surface, is there a reason why you can't use Euclidean distance functions?

[DarrenWiens2]

Thanks for these explanations, Andrew Wilson‌.

I don't believe I can use Euclidean distance because I want to consider barriers (i.e. constrain the distance to water pixels). For example, in the original image (a lake), I want to know the distance by water (not as the crow flies) to the nearest point. My understanding of Euclidean Distance is that it always results in concentric circles around points, although I haven't tried it with a Mask environment.