Thanks for rounding 
My problem with this script is that it use only one type of handles at once (and only Vector and Auto).
That’s why script generates unwanted shape in bezier type for object type Arc, Sector, Segment.
Yellow is add-ons result, orange is my shape how does it should look like (from my opinion).
See blend - https://www.dropbox.com/s/1gaua7opjgrn6of/test-Addon-Curve-Simple.blend
Since these things has to be fixed manually the script doesn’t speed our workflow as much as it could.
Your first screen gives people feeling that object, for example “Sector”, is from three points, but object on your image use many control points for radius to be smooth.
That is not a benefit of any object as curve. Curve supposed to be as less control points as possible for object, right?.
Switch one central point to vector handle is not problem, but correct handles angle of start and end radius point is not such easy and moves speed of creation of this simple object into time nonprofit section.
That’s a shame.
Ellipse - Wouldn’t it be better to generate ellipse like stretched circle (orange on screen)?
Right now script generates the same length for each handle, that’s more oval than ellipse.
At the end - for me is this add-on (in this version) helpful for “Segment” kind of objects - to get exact angle and segment of circle in specific angle, that is terrible do manually.
And for rectangle too, that is frequently used.
(With current version of blender we need for rectangle insert circle, set to poly, rotate 45° and than finally start to change Width and Length. That is not really a speed way .
Or insert mesh plane and convert to curve.
Its like to have only a plane (mesh) on a list without cube, because cube is just extruded a plane.
At the end, it’s faster create cube from plane than rectangle from curved circle :).
So, thank you very much for that
Circle, Elipse, Rectangle, Rhomb are mostly the same, seems to me like it would be enough use only “Polygon” type with Width, Length, Angle and Rounded options.
But I can understand it could be easier for newbies …
Question:
Is there any reason why “Segment” generates for “b” part about one control point less?
Sorry for previous note about “Cyclic” option, it looks like I just didn’t notice there is a checkbox
