Is it possible to change the resolution of a circle after working with it so that it has a greater or fewer number of vertices? If this is not normally possible, but there is a workflow that keeps it editable, that also counts.
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$\begingroup$ related blender.stackexchange.com/questions/7850/… $\endgroup$ – cegaton Jul 7 '14 at 14:44
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$\begingroup$ The goal of this question was more of asking if there exists either a feature or an add-on (or if someone wants to write one) that notices that a selection forms a circle and then allows the user to change the number of vertices in that circle. That question may be related but the intents are different and not duplicates. $\endgroup$ – Keavon Jul 7 '14 at 20:03
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$\begingroup$ Related: blender.stackexchange.com/q/3259/599, blender.stackexchange.com/q/3487/599, blender.stackexchange.com/q/8157/599. $\endgroup$ – gandalf3♦ Jul 7 '14 at 21:15
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$\begingroup$ You could try the decimate modifier, it is not very controllable though. $\endgroup$ – PGmath Oct 28 '14 at 16:27
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$\begingroup$ In addition to what @david said, you can use this post to select every other edge loop. $\endgroup$ – Cole128 Aug 31 '17 at 14:56
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For the creation of a primitive
Yes, and no
You can change the settings right after creating any of the primitives, by pressing f6.
After you do anything else, (besides moving around the view) the settings are gone with no way to get back to them.
Editing loop count in a circle
To reduce the number of edges.
In edit mode, select every other loop by Alt RMB 
(use shift to add to the selection). Then press X or delete and choose Edge Loop. Do the same for the edges on the other axis.
To increase the number of edges.
Delete the bottom and top vertex (where all the loops meet). Select everything with A, then press W and choose Subdivide Smooth. The loops will get wavy, to fix that select them with Alt RMB then press S Z 0. Which will flatten them along the Z axis.
To fix the holes in the top of the circle, select the top edge loop, and extrude it along the Z axis. Then scale to 0, and remove doubles. Do the same for the bottom of the circle.
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For Mesh Circle:
While in the 3D View window, enter Edit Mode (Tab) and select all vertices (A) and click W and select "Subdivide Smooth", then open the Tool Shelf (T), and change the "Number of cuts" field to match your needs.
For Curve Circle:
While in the 3D View window, select the Circle, enter Edit Mode (Tab) and select all vertices (A) and click W and select "Subdivide", then open the Tool Shelf (T), and change the "Number of cuts" field to match your needs.
answered Jul 7 '14 at 14:00
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$\begingroup$ I edited my post to make it more clear, as I see you mistook "after creating it" to mean "directly after adding it to the scene." $\endgroup$ – Keavon Jul 7 '14 at 14:14
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$\begingroup$ For the Mesh Circle section, mention that that is for adding vertices and that you should play with the smoothness slider. $\endgroup$ – Keavon Jul 7 '14 at 14:33
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$\begingroup$ It's already set to 1, by default, if you use subdive smooth $\endgroup$ – someonewithpc Jul 7 '14 at 14:37
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$\begingroup$ Ah, I missed that you said Subdivide Smooth. Feel free to clean up comments and I'll do the same. $\endgroup$ – Keavon Jul 7 '14 at 20:18
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You could use the Loop Tools add-on that comes with Blender. It got me better results than Subdivide Smooth.
1) Add LoopTools to Blender (Ctrl-Alt-U, Add-ons tab, search LoopTools, check the checkbox and save)
2) Select your Circle Loop
3) Subdivide by pressing W and clicking in Subdivide
4) Select the number of cuts of your choosing in the Operator Panel (F6)
5) While having the loop selected, Press Circle in the Loop Tools section in the Tools menu (T)
You should have a perfectly round circle now:
The process of deleting vertices from the circle should be even easier than that. Just delete the undesired vertices, select the loop, then click the Circle button again.
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Decrease the number of vertices
Select an edge loop
Menu: Select / Checker Deselect
X Dissolve vertices
After that you could remove the vertices which only subdivide edges by selecting one and Shift-G Amount of connecting edges and dissolve again.
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$\begingroup$ Checker Deselect will not give good results on a UV sphere, thus causing the Dissolve vertices to fail. $\endgroup$ – David♦ Jul 7 '14 at 21:30
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$\begingroup$ @David I added images of what one could expect by this method, dissolve works. $\endgroup$ – stacker Jul 8 '14 at 6:09
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$\begingroup$ Rather [Del] -> Edge Loop, for a typical usage $\endgroup$ – Oskar Świerad Jul 8 '14 at 8:29
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$\begingroup$ @avvi removing an edge loop would keep the vertical edges. $\endgroup$ – stacker Jul 8 '14 at 8:34
