1. A great compass makes perfect circles
A great compass is one that does what it promises. It draws perfect circles. Everything beyond that basic feature is just a bonus. It is of no use if a compass has all kinds of accessoires like extra lead fillers or a extra extension leg but fails to deliver consistency in drawing perfectly round circles.
That is to me the most important feature a compass needs to have; consistency. Always. No matter how fast I turn my compass it should arrive at the exact same point as it started from. I emphasize this important feature of any compass because I’ve had cheap compasses in the past and tried to draw all kinds of geometric artworks and failed miserably because the compass would not do what it was suppossed to. It would start off from a certain point and arrive on a different point as where it started from. That was because the hinge was of such bad quality that the hinge would not hold steady causing the distance between the legs to change while drawing a circle.
2. A great compass is adaptable
A great compass has adaptability. It needs to hold different kinds of pencils and markers. Because when you start drawing and creating art forms based on geometric diagrams which need precision to look good then there are two distinct phases that define the creation process. First part of the creation process is the setup phase when you lay out the grid. These function as guidelines, intended to be guides for the latter phase; the tracing phase. So usually during both phases you need the compass to do the work precisely. But at the same time the type of pencils are different in each phase. In the primary phase your lines are only guides and need not to be permanent. The goal usually is to have them replaced by permanent lines that you want to emphasize and bring out in the design. Therefore you need a compass that can have a holder for different type of pens.
3. The compass that is extendable
A good compass needs to be extendable. Especially when drawing and creating geometric art you will sometimes want to draw complex geometric forms with lots of details. And you want to be able to see those details and that’s why your geometric art sometimes needs to be bigger then you normally could on A4 paper. So your ideal compass must have the ability to make bigger circles. Instead of having several sized compasses, a good compass has the ability to interchange the legs that would make it possible to draw bigger circles.