What curve monster is created by a 3-point control point spline ?

[TrippyLighting]

The lowest degree curve that can be chosen for a control point spline is 3-degree.

According to the math of NURBS a 3-degree NURBS requires 4 control points. One each for the beginning and start of the spline and two intermediate points.

However Fusion 360 perfectly fine accepts three spline points ?

That same applies to 5 degree spline, which needs at least 6 points, but one can perfectly fine create a 5-degree curve with fewer than that in Fusion 360.

So the question is what kind of contorted monster does Fusion 360 create in tis case ?

The one on the left is a 5-degree curve with three points and the right curve is a 3 degree curve with 3 points ?

[MichaelT_123]

Hi, Mr.TrippyLighting,

Hooo, hoooo, hooo,.... feeling young ... and being still curious... peeping under a skit. Good On You, Mr.TrippyLighting,

Perhaps the best answer would be to touch the issue directly by extracting its constitution parameters vi API.

propertyValue = nurbsCurve3D_var.knots,  ... etc. And comparing them.

With Regards

MichaelT

[TrippyLighting]

LOL

I conceptually understand what you are saying, alas, my programming skills are fairly basic and my knowledge of the Fusion 360 API approximates zero 😉

You, on the other hand appear to possess quite formidable programming skills and understanding of the Fusion 360 API, soooo ... would you be interested in attempting to solve this riddle ?

[MichaelT_123]

send the file

[TrippyLighting]

Awesome! File is attached.

[Johnc911]

If you only use 3 control points it must be a 2 degree (quadratic) curve. It must be. Same if you use 5 control points but you select 5 degree spline, Fusion must be downgrading the degrees of the NURBs curve to 4. 

It's frustrating that they don't explain this, and there is no documentation.

[jiang_peng]

Hi Peter,

You are right, this is a degree 2 spline. If you are creating a degree 5 spline and only create 5 points, we will create a degree 4 spline instead. To covert the degree 2 spline to the degree 3 spline, please use "Insert Control Point" from context menu of spline. Basically, the rule is if the spline is created as degree 3(or degree 5), by "Insert Control Point" we will convert the spline to degree 3(or degree 5).

To check the degree, simply select the spline, the bottom righ corner:

thanks

[TrippyLighting]

@Johnc911 Yes, I had figured that out yesterday after posting here. makes sense too, but isn’t really explained anywhere.

I extruded surfaces surfaces and looked at those in the other CAD software I use at the moment. It provides more information about surfaces amongst that the degree.

To a degree I can understand that Fusion 360 isn’t too overly informative about this. The general audience of Fusion 360 isn’t educated enough to understand what that means. The vast majority of mechanical engineers whom unfortunately Fusion 360 seems to be aimed at exclusively never leave the solid modeling world and it’s narrow confines. It mostly works and thus the question is never asked how it works under the hood.

@jiang_peng  Thanks for the feedback. Another surprise was that Fusion 350 actually also creates 5-degree surfaces. As I understand it, that hasn’t always been the case . Is that correct ?

Is that an upgrade that came somewhat hidden along with the fairly recent introduction of CV splines ?

[MichaelT_123]

Hi, Mr.TrippyLighting.

Please find referenced additional body of data describing the curves' properties in detail.

The file attached is in Excel format. I hope it is verbose enough to allow you to grasp with its content.

I am sure some will find a lecture of it very boring,... will you?

The link is: https://a360.co/38HsaYy

Regards

MichaelT

[TrippyLighting]

@MichaelT_123 thank you very much. No it's not boring!

I find it indeed interesting that the API allows a skilled user to extract so much information from the geometry.

[TrippyLighting]

@jiang_peng I still would like to have an answer to my question:

"... Fusion 350 actually also creates 5-degree surfaces. As I understand it, that hasn’t always been the case . Is that correct ?

Is that an upgrade that came somewhat hidden along with the fairly recent introduction of CV splines ? "

@jeff_strater would you be able to answer this ?

[jiang_peng]

Hi Peter,

If the source spline is degree 5, the surface of the solid body is also degree 5 in that direction. If the degree of spline is 3, we will have a degree-3 surface in that direction. Please note fit point spline is always degree 5. Also I think T-spline is always degree 3.

@jeff_strater Please correct me if I am wrong.

thanks

[TrippyLighting]

Hi Jiang,

Thanks, i was aware of those things. The question was if Fusion 360 has always been able to create 5 degree surfaces or was that an ability that came along with the recent introduction of CV splines ?

[chrisplyler]

I logically deduce from @jiang_peng 's post that 5-deg surfaces predate the introduction of CV splines, since CP splines were the only choice then, and they are all 5-deg.

[TrippyLighting]

---

@chrisplyler wrote:

I logically deduce from @jiang_peng 's post that 5-deg surfaces predate the introduction of CV splines, since CP splines were the only choice then, and they are all 5-deg.

---

That would be correct, but it could also be incorrect for a number fo reasons.

One of he reasons I am asking is that I can now create pretty decent surface quality in Fusion 360 in cases where that was previously (2-3 years back) unattainable. So somewhere along the lines "some. code" has gotten better. The question is which code 😉

I've not been able to track down what degree surfaces the ACIS kernel is able to represent.

[chrisplyler]

I logically deduce that if it IS CORRECT, then any other COULD BE scenarios are nothing more than fodder for your imagination. 😁

[jean.flower]

This is an interesting thread!  Understood that the original post is quite specific about the type of curve or surface involved, and I think the question is answered. 

I was prompted to post because I wondered if some people reading through might think that, in Fusion, all surfaces have a "degree".  Indeed, some surfaces are splines and do have a degree.  But many surfaces are not defined as splines, and do not have a degree.  There are analytics; sphere, cones, torus shapes.  But, more interestingly, there are "procedural surfaces" which may look like splines, but are not splines.   I created an example to explore the difference between a red loft (procedural) and a blue spline (a close approximation to the same shape).

One difference becomes evident when we consider how these two surfaces extend.  The red loft is defined to follow a circular section.  Its procedural definition makes the extension follow that input shape.  In contrast, the extension of the blue spline follows a different path; it's still a valid extension but the extension is inferred from the spline control points, it's not procedurally connected to the circle.

This difference in extension shape could seem just a curiosity but it's significant when we have neighbouring geometry that we want to remain coherent through modeling operations.  Here's a view of the two extensions again when there’s a neighbouring cylinder.  It's much more useful to have the extension match up with neighbouring surfaces (as in the red procedural loft) rather than diverge (like the blue spline).

These kinds of surface extensions can happen during other Fusion operations (filleting, thickening, direct-edit of a model, replacing or healing up missing faces,…).   That's why procedural geometry works well for Fusion and, for many surfaces, there's no notion of "degree".

If you export a Fusion surface into another CAD package, the data translation work may need to convert the procedural surface into a spline.  What you see in the other CAD package might not reflect exactly the definition that was in Fusion.

Hope that gives some interesting "under the hood" insight!

[TrippyLighting]

@jean.flower I cannot thank you enough for this post.

It is indeed very interested what is going on under the hood.

Are these procedural surfaces also handled in the geometric modeling kernel.

I had done some googling just to find out what degree of surface the kernel can deal with. ASM is related to ACIS, but the only thing I could find is this document and while very interesting, it did not answer that question.

[jean.flower]

Glad you liked the post.  I enjoyed thinking about how to express it.  Yes, the geometric modeling kernel can handle procedural surfaces and also splines of degree 5 (and higher or lower).  In a Fusion design, different surfaces can be represented in different ways depending on context (extruded surfaces, lofted surfaces, imported geometry, etc).

I'd very much value an opportunity to learn more about the back-story.  What's behind the question about spline degree? (some modeling challenge?  some workflow?)  If it's easier than exchanging posts here, feel free to message me (jean dot flower at autodesk dot com).

[chrisplyler]

Thanks Jean.

Unfortunately, I do understand the difference between a curvature of degrees and one that is procedural. Well, at a basic level anyway. But not so well that nobody will invite me to a party. I want to learn more, but am afraid it would hinder my social life.