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# Why is "light math" important for free-form surface quality?

Siemens Phenom

I have worked with numerous designers at many companies over the past few decades, and I have never quite understood the view that "few poles = good surface". Seems like people are often striving to produce curves and surfaces with "light math" (i.e. as few poles as possible). Why is that??

If you're going to be editing the surface by moving its poles around, I can see that it's important to have as few poles as possible. But if you're building some sort of sweep surface, and you'll always be editing it by modifying its defining curves, why do you care how many poles it has?  Or, if you're building an aesthetic blend surface, you'll be editing its shape parameters (radius, rho, etc.), not its poles; so, again, why does it matter that the surface has "light math"?

Do people think that the number of poles is somehow an indicator of some sort of surface "quality"? I don't see much correlation, myself -- it's easy to produce a horrible surface with a dozen poles, or a beautiful one that has hundreds of poles. Puzzled.

11 REPLIES 11

# Re: Why is "light math" important for free-form surface quality?

Genius
Hi @Yamada, I learnt quite a lot of math and coding from you. The knowledge is really important for my work. Thank you!

Your question seems to be about the core issue in free-form surfacing. From my very very limited experience and knowledge, I come to catch two points about the issue: (1) Heavy math almost surely means hidden aesthetic faults, and it's often too late when they are discovered, (2) Heavy math makes the extending trend of an object difficult to predict (e.g. the extension is easy to predict for a 2-degree curve, but almost impossible for a 5-degree one.), (3) For a highly complicated model, heavy math is often not only an issue about aesthetics, but might lead to the failure of the model.

# Re: Why is "light math" important for free-form surface quality?

Siemens Phenom

> (1) Heavy math almost surely means hidden aesthetic flaws

I don't see any intrinsic reason why this would be the case. Sweeping and blending functions often produce surfaces with very "heavy" math. Are you saying that these functions usually produce surfaces with aesthetic flaws?

And if there are aesthetic flaws, don't you think you can detect them using the numerous NX shape analysis functions?  Are you saying that some aethetic flaws don't get detected until late in the process, after you've done some physical NC machining?

> (2) Heavy math makes the extending trend of an object difficult to predict

OK, I can see that. But you don't often extend blends, do you? And if you want to extend a sweep surface, you do it by extending the defining curves, don't you?

# Re: Why is "light math" important for free-form surface quality?

Genius

And if there are aesthetic flaws, don't you think you can detect them using the numerous NX shape analysis functions?  Are you saying that some aethetic flaws don't get detected until late in the process, after you've done some physical NC machining?

Yes, even with light math, NX analysis is needed for detecting aesthetic flaws, for example inflection points. But at least for myself, to analyze a heavy surface is really a nightmare. Currently I don't have good knowledge about CNC machining.

OK, I can see that. But you don't often extend blends, do you? And if you want to extend a sweep surface, you do it by extending the defining curves, don't you?

If a model is highly parameterized and adjustable, predictability of an object seems to be a must.

# Re: Why is "light math" important for free-form surface quality?

Siemens Phenom

> to analyze a heavy surface is really a nightmare

I don't understand why. If you're doing class A work, I assume you analyze using reflections, highlight lines, section analysis, etc. Why does heavy math make these functions harder to use?

If you're judging surface quality by looking at the "flow" of the poles, then I can see that this would be very difficult if you had hundreds of them. But I would say that this is not a good assessment method, anyway, though I know that it's often used.

# Re: Why is "light math" important for free-form surface quality?

Genius

If you're doing class A work, I assume you analyze using reflections, highlight lines, section analysis, etc. Why does heavy math make these functions harder to use?

Sometimes TCM gives a heavy surface, which gives good analytical results, e.g. relfection. But I just doubt that there might be defects buried in the jungle of poles. Experience shows that a light surface is safe and reliable. It's diffucult for me to give out  an example.

If you're judging surface quality by looking at the "flow" of the poles, then I can see that this would be very difficult if you had hundreds of them. But I would say that this is not a good assessment method, anyway, though I know that it's often used.

Yes it's difficult to know why good flow of poles gives good results. But it does in most cases. That also requires the surface to be as light as possible.

If you make more challenges, I think my knowledge and experience is far from good enough to deal with them

# Re: Why is "light math" important for free-form surface quality?

Gears Phenom

One reason fewer control points and fewer patches are desired with Class A is the belief that it’s easier to modify a surface with the minimum number of poles needed for continuity. More often than not, stylists run into situations where they have to manually adjust either the pole distribution or individual pole positions. The fewer the poles, the easier this is to do.

Another reason is the belief that fewer poles helps make a smoother surface with better transitions into adjacent surfaces.

It’s a very specialized type of modeling and I feel that there are sacrifices made with model tolerances in order to achieve the results the stylist desires.

That all being said, I personally feel most of the strict requirements and practices are allowed to deviate much more than would ever be admitted by those types of modelers.

Tim
NX 11.0.2.7 MP11 Rev. A
GM TcE v11.2.3.1
GM GPDL v11-A.3.6

# Re: Why is "light math" important for free-form surface quality?

Siemens Phenom

@TimF

Thanks for the response.

If you're going to edit a surface by moving poles, then I understand why you want their number to be small. But with sweeps, and TCM, and blends, you wouldn't edit the poles, would you? So it doesn't matter if there are hundreds of poles, does it?

> Another reason is the belief that fewer poles helps make a smoother surface

I can believe that few poles implies good surface shape (much of the time, anyway).

I don't see why many poles automatically implies bad surface shape.

Blend surfaces and swept surfaces often have hundreds of poles, and their shapes are usually OK, aren't they? But I see people spending hours rebuilding them to make them "lighter", and I don't see the point of this unless you see some flaws in the original  "heavy" surface.

Please note: these are not rhetorical questions, or "challenges". I'm not trying to push any opinion; I just would like to understand better. Thanks again.

# Re: Why is "light math" important for free-form surface quality?

Genius

But with sweeps, and TCM, and blends, you wouldn't edit the poles, would you? So it doesn't matter if there are hundreds of poles, does it?

If a Swept edge is used as input for highly picky Studio Surface, the result might be difficult to imagine.

# Re: Why is "light math" important for free-form surface quality?

Pioneer

This is common sense. To create a perfect, clean surface, you should never have more poles than necessary to produce the shape you require. This is surfacing rule number one. If you have more poles than that, it means the surface at some location deviates from the shape you intended. The more poles you have, the more things can go wrong (more cooks in the kitchen). Those designers you've worked with probably used surfacing software like Alias or Rhinoceros where this is an important consideration when creating shapes. However, for the most part NX does a very good job with the regular surface tools like sweep and mesh, so if you create regular product exteriors in NX, you don't need to think about it. However, the requirements for car body styling is obviously much higher, which requires a different surface construction technique using patches. Here, ICEM Surf has always been the gold standard, as it strictly uses single patch Bezier math (which is simpler than NURBS) with pole manipulation only, allowing the modeler to work "close to the metal" so to speak. An analogy to this is writing code in assembly instead of Python where you need the fastest execution.

However, even for regular product exteriors it's important to pay attention to the number of poles. If they are evenly spread out, it's usually OK. But if they are concentrated around a small area, you can be assured the surface is not "healthy" there. This could cause a number of problems: wrinkly surface, modeling problems downstream within NX, usually with the shell tool, and with translation to other formats. When I see this situation I will correct it by changing the way the surface is constructed, even if it means slightly modifying the geometry.