Is it possbile for a perfect circle with 6 control points?

[lmnoc1]

The default Rhino circle has 8 control point in 3 degrees.
Is it possible to create a perfect circle with 6 or 12 control points?

This is for a hex grid based project. I tried rebuild circle but it seems off (if the default Circle command is considered perfect), not trying to approximate it with a certain tolerance. I do know some basic nurbs theory. Just wondering is this possible?

Or what’s the best possbile way to create the most perfect form of this 3-fold periodic sine curve (the black line)? Thanks

[John_Brock]

No.
A deformable NURBS “circle” can be made with more points, but a perfect NURBS circle requires 8 and the corners have their “weight” tweaked.

[lmnoc1]

ok sounds good

[lmnoc1]

I also just edit the question about a perfect 3-fold sine wave. Do you might have any suggestion for that?

[davidcockey]

A perfect circular arc of 90 degrees or less can be made with 3 control points. Use the Arc command.

[pascal (Pascal Golay)]

Hello- yes - like so, degree 2 from 3 3 point arcs joined:

Is it possible to create a perfect circle with 6 or 12 control points?

ChangeDegree to 4 to get 12 points.

weight = radius / distance from middle control point to arc center

-Pascal