# Perfect circle in ArcGIS, why I get a multiside polygone (plurigone)?

Using ArcGIS basic (10.3), I tried to make perfect circles in ArcGIS with the buffer tool. As you can see on the two print screens, the circle is not perfect when I use a radius of 7,5 meters in a MTM projection project. The circle is composed of small lines (see arrows in the 2nd image). If I calculate a surface area of that circle, I get 175.81878 m² (area normal) and 175.846927 m² (geodesic area). At least, I should get 176.71458676 m² using 7.5 m x 7.5 m x ∏ formula (∏xR²) Why I get that? How can I have perfect circle with a radius of 176.71458676 m²?

• Are the buffers being written to a geodatabase? Shapefiles don't store curves. Jul 7, 2016 at 14:24
• These are shapefiles. That's explain everything. Thank Kirk!
– Doum
Jul 7, 2016 at 15:44
• I think the buffer wizard doesn't produce curves even when stored in a geodatabase.
– John
Jul 8, 2016 at 12:39
• @johns the examples in my answer below were tested with both the editor buffer wizard and the arctoolbox tool. Both produced curves.
– Midavalo
Jul 8, 2016 at 19:34
• II was using the buffer wizard that can be found in the Tools. You can find it by going into Customize mode and then searching Commands for Buffer Wizard or just go to the Tools category. I just tested this buffer wizard again and I get a 99 vertice circle using a 33 foot buffer in it around a point.
– John
Jul 11, 2016 at 12:02

## 2 Answers

As commented by @Kirk Kuykendall, it appears your buffer is being saved into a Shapefile. Shapefiles do not support true arcs/curves, so saves the features with multiple segments.

Shapefiles do not support true parametric curves, including circular arcs, ellipses, and Bézier curves, so these shapes are stored as straight segments. True curves are fully supported in geodatabase feature classes.

(from About editing shapefiles)

Geodatabase feature classes do store arcs/curves, so setting your buffer output to a geodatabase will produce the output you require.

In the screenshot below, the stars highlight the vertices for the two buffer circles. The buffer on the left is stored in a geodatabase, the one on the right in a shapefile. Both are 7.5m buffers.

The buffer areas - top is geodatabase, bottom is shapefile:

Below are the same buffers without the stars highlighting the vertices

I haven't looked at this in a long while, but as far as I know it hasn't changed.

ArcGIS draws the buffers at a fixed graphical resolution, so they appear smooth when viewed at that zoom level but if you zoom in you see the straight lines as you observe. If you zoom in the layer to buffer and then run the buffer tool you should see that these straight lines do not appear until you zoom in again to a yet finer scale. Its a weird limitation and can be quite significant if interested in detailed buffers over very large areas.

MapInfo allows direct control of the number of segments (at least it did last I checked 15 years ago!).

As to why.. well all vector data boils down to points and straight lines, so its a question of how accurately one wishes to describe an arc. Why ArcGIS uses such an obscure method to determine it.. good question!

• ArcGIS doesn't have the limitation, it comes down to the features being stored in Shapefile rather than geodatabase. Shapefile does not support true arcs while geodatabase feature classes do. A buffer into a GDB feature class will produce the curve.
– Midavalo
Jul 8, 2016 at 4:59
• That is good to know, when I last looked at this it was pre GDB. thanks! Jul 8, 2016 at 8:15
• I was curious as to how ArcGIS GDB managed true curves so Ive googled abit. It seems to me a little more complex. The true curve needs to be a mathematically tractable shape. So a circle, as above, will buffer exactly. A more complex shape will require more vertices to fit the curves to the buffer. So the question is whether these inflection points still depended on the graphical scale? I can't find an answer. However it seems GDB store both true and segment versions, and which display depends if the former are supported. support.esri.com/technical-article/000003578 Jul 8, 2016 at 8:49