Sculpt workspace: How many diameter faces needed for perfect circle?

[jsejcksn]

When creating a sculpt body with "circular" geometry, like a cylinder for example, how many diameter faces are necessary to get a perfect circle?

I realize a few things here:

First, there is no such thing as a perfect circle. What I am asking is: what is the minimum number of faces needed to create, in the sculpt workspace, a cylinder at center origin with diameter 100 mm whose profile will mathematically match a circle sketched in the model workspace on the same plane at center origin with diameter 100 mm?

Further, I'm no expert in the mathematics behind Fusion's spline geometry, or I would already know how to determine this. However, I did a few tests of different numbers of diameter faces, took screenshots, and then did difference pixel analysis (black backgrounds) on the images to produce this gif:

I would really like an authoritative answer to this—ideally with an explanation and a link to documentation.

(Finally, this question is not related to this question.)

Thanks!

[Rajesh.Punniakodi]

I don't have exact number for creating perfect circle but we can inspect the curve using curvature analysis. Create a cylinder in sculpt and finish form, now you can inspect the curve by using Inspect->"Curvature Comb Analysis". Curvature is smooth when we create cylinder with 32 faces.

[PhilProcarioJr]

@jsejcksn

It can be done with 8 and setting the tolerance very low. Depending on the accuracy you need that number may need to go as high as 32, but I would only use as many as you have to to get the accuracy you need. Working with high face counts in the sculpt environment is asking for trouble. Saying you want to mathematically match the model workspace makes little sense. If that's your end goal then do the cylinder in the model workspace and just connect up the sculpt to it. The sculpt workspace has one large drawback to it, surface tension and there is currently no way to see or deal with surface tension in Fusion, so even though your sculpted cylinder might be perfect, editing your sculpt in anyway could trash that unless you freeze the edge. That too comes with it's own problems...

If you are going by the curvature comb analysis alone then no amount of faces will give you the same result as a cylinder in the model workspace. This is why I said if you want perfect you need to just model the cylinder in the model workspace. Even a 100 sided T-Spline will show small spikes in the cylindrical edge under curvature analysis although it will be a lot less apparent then an 8 sided one. This is also why I said it depends on the amount of tolerance your after.

But if you check with the measurement tool it will show the same length and diameter and radius with the 8 sided but no less.....

@Rajesh.Punniakodi

Smooth yes, completely matching a cylinder from model space no, as can be seen here in the two screen caps.

The first is a T-Spline with 32 sides, the second is a cylinder from model space.....You can clearly see a difference...

[Aaron.Magnin]

Great question, and some great answers as well! 

I think this question is more out of curiosity than anything, but if you REALLY want a perfect circle this needs to be said: use parametric design. 

[cekuhnen]

@Rajesh.Punniakodi

As long as T-Splines struggles with generating a smooth comb transition between edges I would highly suggest not promoting

the curvature graph tool to be used at all.

The internal structure of T-Splines - how it later is being also converted to BREP - has to solve that issue and behave the same

as a non-rational CV curve

Fusion:

This is similar / the same as a circle that uses spans on the surface

Non Ration CV Curve in Alias: (2 arcs making a circle)

useful in that case would rather be like in the last image a radius read out. One case see that while the comb is fine the read outs

clearly show the radius differences

also a curve with spans can have a comb with a smooth transition / shape

[cekuhnen]

@Aaron.Magnin

Better answer would be use the sketch circle because the circle in sketch is not made out of weighted CVs but uses a math function that

draws the circle shape by using radius and a center point!

[PhilProcarioJr]

@Aaron.Magnin

"but if you REALLY want a perfect circle this needs to be said: use parametric design. "

Actually parametric design has nothing to do with it, it is the nature of how splines (vs. a radius with a center point) work. A cylinder done in the model work space in DM will produce the perfect circle with no parametrics.

It's how the two geometries are being created that is different.

As Class stated "Better answer would be use the sketch circle because the circle in sketch is not made out of weighted CVs but uses a math function that

draws the circle shape by using radius and a center point!"

[cekuhnen]

@jsejcksn

Here is a quick video that explains a little what is happening under the hood.

https://drive.google.com/file/d/0Byzv_NlyKp_2ektETmVXNzRpdWc/view

[jsejcksn]

Thank you, everyone, for your responses. Especially @PhilProcarioJr for the explanation and @cekuhnen for the very detailed examples and the video—it was very insightful!

[cekuhnen]

@jsejcksn

You are welcome.