# Single Span Surface and Curves

Deal All,

I would be grateful if anyone can kindly give me a definition on what a Single Span Surface/ Curve means and the methd of achieving them when modeling.

This is a term i have heard many times but there is no clear defintion for it.
much apreciate any help at all

regards
Mori

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A single span curve or surface has one more control point then the degree of the curve or surface direction.

A degree 3 curve will have 4 points.
A degree 5 curve will have 6 points.

Single span = (degree+1)

https://www.rhino3d.com/nurbs

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Dear John
Thank you very much John.

So would that mean for example, a degree 3 curve containing more than 4 points is not single span? If so, this would be very hard to achieve in certain complex situations.

Best regards
Mori

Correct. There just isnât enough control in a single span curve to define a complicated shape. Thatâs why Rhino support more than single span curves.

If you have a general rule of modeling so you have the least number of curves with the least number of points that still accurately define your desired shape, then all of the span/knot/NURBS stuff will take care of itself.

Daer John

Got it, thank you so much for that. Yes, the mindset in the quality of curves and surfaces to look for when modeling is important.
So can I say that a Car with Class A surface means it has single spans surfaces or would it refer more to its contunity being G2.

âClass A Surfacingâ is a made up, marketing buzz-phrase.
Itâs not meaningless, but itâs not succinctly defined either.
If you model the surfaces you like that have the reflective properties you want, youâve done it.

Using single span curves and G2+ curvature continuity are just tactics.
Using single span curves and G2 curvature continuity tools do not guarantee âClass A surfacingâ.

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Great thanks, at least I dont feel too bad in not having single spans in complex models now.

Great for general modelling, bad idea if you want to achieve A-class surfaces.

I think itâs a bit more than that.

Mori,

Iâm not an A-class modeller, but my understanding of it all is the following -

If your intention is to model the highest quality surfaces on parts of a product that are visible to a customer then youâll be wanting to do A-class surfacing. Highest quality in-part refers to how the reflections pass over the surfaces.

Single span surfaces will have better âfairnessâ and greater quality of reflection than multispan.

As John says, single span surfaces have a strict relationship of Control points = Degree number +1

So you have to keep a very close eye on what each of your surface generation tools generates for you. I often find it easier to create a simple surface using the plane command first and then use the change degree command to increase the plane to the required degree (and therefore the required control points needed). After that Iâll display the control points and then manually move them into the positions I want.

This is where keeping the number of control points to an absolute minimum for the shape you want is crucial, otherwise the task of moving points becomes too complicated.

If you have a complex shape that canât be achieved using one single span surface then all you do is split the shape into multiple single span surfaces. However these do take time to match into each other and this can be time consuming. Only use them where you need to.

You also have to be careful when mixing a load of different degree surfaces, for instance a degree3 surface wonât match into a degree6 surface. Youâll have to use at least a degree6 or one degree higher than the surface youâre matching into (letâs say itâs a partial match along an edge).

âŚA-class modellers - if Iâve written any nonsense then please correct me!

Rob.

For two single span degree 3 surfaces with G2 (curvature) match along coincident edges there is an exactly equivalent degree 3 surface with a single span in one direction and two spans in the other direction.

For two single span degree 5 surfaces with G4 match along coincident edges there is an exactly equivalent to degree 5 surface with a single span in one direction and two spans in the other direction.

And so on.

David, this may well be technically correct but the two different types of surfaces seem to be parameterised differently. Itâs not just as a simple as matching up a multispan surface over the same control point locations as the two single spans. Obviously there has to be some sort of different parameterisation in order for the multispan to retain a smoothness between spans. Iâve thrown down a couple of single span surfaces in the model below, have a go at creating a multispan surface which is exactly equivalent and displays the same curvature graph.

degree3.3dm (175.2 KB)

But weâre in danger of missing the real-world benefits of using single spans here. They are easy to maintain good-looking curvature whereas multispans get wobbly very quickly. And hopefully youâll see in the above exercise that to hit the sweet spot of a multispan surface is way more work than using single spans (we are of course talking about exactly equivalent curvature between the two).

Rob.

Dear Rob, David and John,

Thank you all so much for the valuable points which is not found in the Levels 1&2 manuals (or I must have missed it).

I will do a bit of experiment as all you experts have suggested and get back to you on my findings!

Thanks a mill all!
Kind Regards
Mori

Mori,

Definitely have a play around and see where single span surfaces could be better and where they cause more trouble than theyâre worth.

In your quest to create single spans there are a few things which come in handy -

1. When you start the curve command look at the command line - itâll tell you what degree of curve itâll try to make. I think the default is 3. If you donât click enough locations for a degree3 curve then itâll automatically create the appropriate degree curve. If you click four locations then youâll get single span. If you click more locations then youâll get degree3 but itâll automatically be multispan. Keep that in mind when creating curves from scratch.

2. Rebuild curves and surfaces - this will allow you to specify the degree number and control point directly. Just remember the relationship between degree and control point number in order to get single spans.

3. Degree command - this is similar to rebuild but just asks you for a degree value for the u then v direction of the surface. Probably the quickest way to get a single span surface.

4. If you need to find out if a surface or curve is single or multispan just select it and then under the âProperties/objectâ tab just go to the bottom of the tab and click the âdetailsâŚâ button - within all the text it will tell you about the parameterisation.

5. PointsOn command - display those control points and push and pull those points around!

6. MoveUVN command - will move the selected points in relation to the U, V or N (normal) direction of the surface. Very handy.

Have fun pushing and pulling those points!!

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Dear Rob

Great practical advise thanks, that also solved my previous wonders in regards to control points and degree.
Unless I have missed it, a lot of your tips esp. on single spans were not explained in the training manual.
I will try out your advise and let you know my progress, many thanks indeed much appreciated!

Warm Regards
Mori

@davidcockey
I found this great explanation of single vs multi span on the Alias website, it explains it pretty well. Looks like if you use degree5 multispans then itâll be pretty fair as per separate single spans (and easier to edit). Seems itâs all to do with the mathematics of the knots which cause the surface continuity breaks which become less of an issue as the degree increases.

Iâll have to have a play around with some degree5 multispans, up until now Iâve only used degree3 multispans.

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very nice explanation of the span, curves, surfaces, trimmingâŚ
http://www.aliasworkbench.com/theoryBuilders/

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Thanks @Nosorozec , will have a read through that lot.

Hi. I am trying to learn the theory about NURBS.

âCurves that have more control points than 1+the degree are internally piecewise, that is they consist of more than one polynomial curve span. The points of transition between these internal curve spans are called knots.â

Can someone please explain why this single-span quadratic curve with 3 control points, showed below, have 3 knots?

Hello - how are you checking knots? It looks like you have edit points turned on - there will be three of those but they are not knots and the curve is not multi-span.

-Pascal