Thank you for your reply. Some thoughts:
RE: “How often do you want to draw a spiral? 1 out of 10 000 times probably………should have a dedicated tool.”
To introduce dedicated sketch tools (especially for such a rare requirement) would break a fundamental tenet of the interface:
that sketch elements are created via gestural input and “Tools” act upon these elements and forms derived from them.
For instance, it would be redundant to have a dedicated ellipse tool, when an ellipse is simply a non-uniform scale of a circle.
It would be better to extend functionality of Transform/Freeform/Scale by inclusion of non-uniform toggle.
Similarly, arcs could become conical section curve via the same means, and once it is no longer a neutral curve, an new option button could be attached to highlighted curve to choose between parabolic, hyperbolic, catenary etc.
RE: "as we recognize more, the recognition will be less accurate”
Getting back to spiral definition: let’s say the user needed to scribe 2 full unbroken loops with the pencil before initiating the spiral functionality, then there would be no case of a user creating a spiral when they intended to create a circle. If such an interfacing event could be captured by the software, it might be argued that it could be better assigned to something more useful, because as you say a spiral is 1/10000 requirement. But, the gesture infers that the intent is a spiral, so despite the rarity of need, it would be the logical result.
RE: "infinite number or regular geometries”
EDIT: See my new post below