Random question here, but is it possible to draw a perfect circle without using the circle command?
I’ve tried tracing the control points of a circle made using the circle command, with a rugular NURBS curve, and the resulting curve is not a perfect circle. (Looks like it has corners)
I was wondering:
Why this is?
Is there a way to create a circle without the “Circle” Command?
Hi -
Does this help?
https://discourse.mcneel.com/t/unroll-geometry-as-texture/90612/11?u=wim
-wim
My post from 2019 which Wim quoted above is not quite correct. It is possible for a degree 3 curve/surface to be a perfect circle/cylinder BUT it will be a rational degree 3 circle/surface with non-unity weights. (I will revise the post.)
One way to obtain an exact rational degree 3 circle is to use the Circle command to create a rational degree 2 curve. Then use ChangeDegree with Deformable=No to change to a rational degree 3 curve.
Draw a 3 point Curve with
_curve Degree = 2
where the 3 points form a isosceles triangle.
then use
_weight
to assign a weight of the point in the middle.
the weight is equal to cosine of the angle at the base.
Example
for a quater arc
weight = cos(45d) = 1/sqrt(2)
- Is there a way to create a circle without the “Circle” Command?
Create a plane, points
-2,-2,0
2,2,0
Create a sphere, center and radius,
0,0,0
1
Intersect.
I’m not positive of what the internal representation is, but it appears to be a second order curve without a large number of segments indicating approximation. The area also looks good. The center has some tiny tiny roundoff, on the order of 10^-17. Rhino appears to do better on that last part with the native Circle command.
Does that meet your definition of ‘perfect’?
Yes it does, however I should of mentioned I wanted to only use a Curve command.
Thanks all the same 
