What's wrong with multi span/knots?

Hi,

I am trying to figure out why bezier curve is better than multi span curve or surface…From my understanding A class curve/surface is smoother but I did a little experiment.

I build a curve with 6cps and degree 5 and then used fitcrv which produced 11cps, degree 3 and 9 knots. I run crvdeviation and it came up with 0.000239…cm. So how is it smoother? It’s almost identical

Then I made a surface from both curves to check reflections/continuity and again it looks identical.


The only difference is in curvature graph. The breaks between knots are visible at the ends but why does it even matter if the surface appear to be the same when analyzing it with zebra and emap?

Finally I moved one of the points up by 0.5cm which resulted in even bigger break in curvature graph of 8 span surface while A class srf graph remained smooth

Now the changes are visible in reflection of surface and they don’t appear to be as smooth anymore.

So to conclude, correct me if I am wrong but A class surface is easier for editing while maintaining the smoothness but if we create multi span surface and don’t move its control points it looks equally smooth so why is it bad idea to be using them? Why is it not prefered option for A class modeling?

Two points here-

  1. When using a multispan you probably will be using it to achieve greater variations than in your example. Why would you use 11 control points on a very gentle curving surface??! So therefore those curvature graph spikes will absolutely show. The goal is to model with as few control points as possible.

  2. The single span will always stay smooth and fair. Always. And be easier to work with.

If you’re not dealing with styling surfaces that are ‘customer facing’ then don’t worry yourself about single spans.

Regards,

Rob.

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If you are manufacturing this part it is unlikely to make any difference. The only possible difference would have to do with how well your part translates to other software.

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Hi Radovan - I think you’ve answered your own question. Single span surfaces ease the editing process. In your example, if you were to split the surface made from the rebuilt/degree 3 curve at the knots, you would then have class A surfaces - just smaller ones of a lower degree than the original. Managing the joins between these surfaces can become a headache if you need to ensure (curvature) continuity. Equally, you could also imagine your degree 5 surface being part of a larger set of surfaces that may also require management of continuity. It’s all a question of context.

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Thank you for reply… I understand that the goal is to model with least amount of cvs etc…but the question was why?..why is it the goal if sometimes you can achieve almost the same result using more complex geometry?..I just think that in some cases it is easier to add a knot to a surface than worry about not using it at all and thinking how to lay out surfaces because you are not allowed to use more than 1 span…maybe its just me but I find it easier in some cases

Oh, you’re absolutely correct there. It’s definitely easier to lay down multispans to start with but managing the curvature matching over different patches will be harder (as MattE has said) and you’ll end up with those non-smooth graphs somewhere.

I guess ClassA modelling is just being super-fussy. Again, only use it where you need to.

I have heard people say that if you use degree5 or 7 multispans then they should have enough internal smoothing to avoid the spikes. But I still think you loose a level of control where the knots are. Don’t know, haven’t really looked into this yet. Could be worth a try?

Regards,

Rob.

You can use InsertKnot to add knots to a single-span surface in a way that leaves the actual surface completely unchanged, so the curvature would be identical either way.

I think the main difference is that single span makes it harder to get yourself into trouble, while multispan gives you more rope. That said, it’s possible to have great multispan surfaces, and it’s possible to have crappy single span surfaces. I think some people prefer to only use single-span, as a way to help enforce discipline.

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But then you’d end up with a multispan wouldn’t you? I’m not sure just adding in knots into a single span surface and then leaving as-is would be particularly useful? I’m guessing most people would then go on to tweaking the multispan?? Or have I missed something?

Hi Rob -
No, I think the point was just that the number of spans is not in itself an indication of “quality”.

-Pascal

Ahhhh, I see now… thanks.
Apologies Tom.

Degree 2, 5, 7 or higher curves are inherently continuous.

Draw the some single span degree 2, 3 and 5 curves next to each other and look at the curvature graph, as you change the interior CPs. You will notice a degree 3 curve is not inherently continuous. If you use degree 3 for building surfaces, it won’t be inherently continuous either. Surfaces inherit the math from their boundary conditions.

You can easily create any surface, single span, by avoiding degree 3 curves in the future.

well…‘continuous’ … it is inherently G2 continuous , internally, between spans, but not G3.

-Pascal

Yep, degree 3 usage is the beginning of several troubles that are easily avoidable for the beginner Rhinoist.

Examples?

G2 continuity between single span patches is frequently said to be sufficient for many uses. If G2 continuity is sufficient between single span patches then why is it not sufficient within a multi-span surface?

Draw a degree 3 and degree 5 circle next to each other and switch on the curvature graph.

Single span degree 3 curves have only four CPs, meaning you can only achieve G1 on both ends. Often degree 3 cuves, and thus degree 3 surfaces, are troublesome in later G2 filleting or matching to a higher degree; then you’d have to rebuild. Often trim curves are too loose if you need tight tolerances, for example when passing on your data to a solid modelling software. Also G2 fillets between degree 3 surfaces can result in fillets with too many spans, far from the simple Bezier single span approach, and much clicking around and fiddling will ensue.

Most of these basic nuisances, also in SolidWorks or Catia, can simply be avoided by using degree 2, 5, etc. curves in the first place - and just forgetting about degree 3. When drawing a new curve with Curve, use the Degree option to set a “proper” degree, so there is actually no extra work involved : )

Even easier, set the degree to be 11 in the options and then the command will give you single spans until you click out a curve with over 12 control points.

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Degree 2 multi-span curves are G1 continuous at internal knots.
Degree 3 multi-span curves are G2 continuous at internal knots.
Degree 4 multi-span curves are G3 continuous at internal knots.
Degree 5 multi-span curves are G4 continuous at internal knots.
Degree 6 multi-span curves are G5 continuous at internal knots.
Degree 7 multi-span curves are G6 continuous at internal knots.
(Lower continuity occurs at multi-knots.)

Single span degree 2 curves have only three control points, so the maximum continuity which can be achieved is G1 at one end and G0 at the other end.
Single span degree 4 curves have four control points, so the maximum continuity which can be achieved is G2 at one end and G1 at the other end.
Single span degree 5 curves have five control points, so the maximum continuity which can be achieved is G2 at both ends.

This can occur with fillets between multi-span surfaces of any degree, not just degree 3 multi-span surfaces.

@Lagom It looks like you are assuming all degree 3 curves and surfaces are multi-span, while curves and surfaces of other degrees are always single span. Curves and surfaces of any degree can be single span or multi-span.

The problem is that one should not use degree 3 curves, as explained.

If all you want is some crown, use degree 2. If you want G2 on two sides, use degree 5. Both have no internal discontinuity. It’s as easy as that.

What is this “internal discontinuity” which you claim degree 3 curves have but degree 2 and degree 5 curves do not have? An example with a comparison would be helpful.