Talk:Non-uniform rational B-spline

Continuity again

I propose to remove the discussion on continuity within the article by splitting it in two distinct parts (and putting it in a separate section). The C0, C1, ... etc definitions relate to parametric continuity and require the derivatives of the curve with respect to the parameter to be continuous. G0, G1, ... definitions relate to geometric continuity, which I think is equivalent to parametric continuity provided that the parameter exactly represents the length of the curve -- which is hard to achieve in practice. In modeling, geometric continuity is usually a requirement. Parametric continuity is a bonus, e.g. if rendering can use parameter space directly for tesselation. Two separate NURBS curves which are not Cn continuous can be Gn continuous. For instance, two linear NURBS segments with different knot spans but collinear control points will show G1 continuity. Mauritsmaartendejong (talk) 15:11, 6 January 2008 (UTC)

Number of Knots per Control Point

Quote from the text (from the section on Knot Vector): The number of knots is always equal to the number of control points plus curve degree plus one.

Shouldn't it be: ...always equal to the number of control points minus curve degree plus one..

Example: A cubic NURBS curve with 4 CPs has got 2 knots: 4 – 3 + 1 = 2 —Preceding unsigned comment added by 193.170.135.17 (talk) 11:05, 2 December 2007 (UTC)

No. If a cubic curve with four control points has two knots, they have multiplicity 4, bringing the total number of knots to 8 = 4 + 3 + 1. The multiplicity of the boundary knots causes the curve to be clamped to the first and last control point. See also property P3.2 in chapter three of Piegl and Tiller Mauritsmaartendejong 12:56, 2 December 2007 (UTC)

Parameterisation ratio

Also note that the only significant factor is the ratio of the values to each other: the knot vectors [0 0 1 2 3], [0 0 2 4 6] and [1 1 2 3 4] produce the same curve.

Er, I've got a problem with the ratios (0:1 = 0:2 = 1:2) and (1:2 = 2:4 = 2:3) which is what this states. I can only conclude that the minimum value is also a significant factor. Can anyone help me out on this one?

The only significant thing is the ratio of neighboring parameter values in their ascending order, therefore the given example is correct. Minimum value has no significance. As long as a multiplier value exists to make ratio between different parameter values the same, the resulting b-spline curve will be the same.

E.g. 0 1 2 3 4 is the same as 0 2 4 6 8 (multiplier being 0.5)

or

0 3 6 9 12 is the same as 0 0.25 0.50 0.75 1.0 (multiplier being 12)

Actually for any uniformly increasing parameter values, curves with same control points position and same number of knot vectors will have the same shape (which means that all four above examples give identical curve shape provided their control points positions are the same).

For non-uniform splines:

0 0 1 3 4 5 is the same as 0 0 0.5 1.5 2.0 2.5 (multiplier is 2)

It is those differences in parameter values that determine chord length and affect the resulting curve shape. Therefore, same ratio between knot parameter values, combined with same control points positions will give the same curve. Think of it as a tension increased in one knot by any factor will not change the curve if the same factor of increased tension is applied to all the other knots.

The text doesn't make clear that changing the knot vector by a constant multiple will change the parametrization of the curve. The curve will be the same shape, but it will be different as a parametric function of u. Verdanthue (talk) 23:11, 2 April 2008 (UTC)

Uniformed circle?

Can someone explain what a "uniformed circle" is? --P3d0 03:21, 5 February 2006 (UTC)

I asked myself the same question. I think it's a typo, and should be 'uniform circle', which I think is a circle that will give equidistant points when the parameter space is uniformly traversed. As an aside, the table needs an order and a knot vector before it really defines a uniform circle. The order is three, and the knot vector something like {0,0,0,1,1,2,2,3,3,4,4,4} Mauritsmaartendejong 20:38, 19 June 2007 (UTC)

Picture

This article could do with a picture in as much as NURBS is an adjective to describe a class of shapes, particularly shapes of consumer products of recent years. —BenFrantzDale 16:46, 16 February 2006 (UTC)

---

Well, its kindoff hard and simple at the same time. See more is about the specifications of the image, i mean you could photograph any mobile telephone, or any western airplane. But more of the trouble here is to make a piucture that is MEANINGFULL for the potential viewer. See when i take a look at my telephone i know what im looking for so i can see how the patch layout is done. But the untrained person will most definetly not see it unless pointed out, and even then if the designer of the phone did a superb job there would be noothing to see. Just imaginary lines. So its definetly going to have to be a rendering.

Now to complicate this a bit, most eingeneering applications make use of as many independent pieces of trimmed nurbs surfaces that most noneingeneers wont believe. -J-

Subs versus nurbs

the following line needs editting:

Subdivision surface modeling is now preferred over NURBS modeling in major modelers because subdivision surfaces have lots of benefits.

Because it is simply untrue. Or it would be true if a modelling packge could be clearly demonstrated not to include cad packages, and/or if cad packages would be very specialized minority. But the simple truuth is that theres more cad users on nurbs out there than theres DCC visualisers with subdivision surface modellers. And yet no cad package has switched over to subds. Because theres NO 2 degree continuity... And the tools are severely lacking form engeneerig perspective. -J-

I do completely agree as this is more or less opinion. It implies that nobody uses NURBS any more and instead uses Subs. NURBS do have important advantages compared to Subs and therefor all mayor animation packages contain a NURBS engine. Opinions about Sub Division Surfaces beeing "better" belong to the appropriate page only. -R-

Miswording

When describing the alternative definitions for C0 through C2 (right after they are introducted) the following claim is made.

This definition is also valid for curves and surfaces with base functions higher than 3rd order (cubic). It requires that both the direction and the magnitude of the nth derivate of the curve/surface (d/du C(u)) are the same at a joint. The main difference to the definition above is the requirement for a same order of magnitude.

It sounds like whoever wrote this is confusing same 'order of magnitude' (roughly the same value) with having the same value. If not one of the definitions is stated incorrectly as nowhere do they require same order of magnitude. The order of magnitude bit appears in the next sentence as well.

I'm pretty confident that 'same magnitude' is what was intended from textual clues and my knowledge of the mathematical notions so I'm going to change it but I'm just learning about computer graphics so if I got it wrong please correct my error. In either case once a person who knows the facts comes along and reads this and the page over this comment will become superflous.

Logicnazi 09:17, 19 June 2006 (UTC)

Yes i changed magnitude in the first explanation to the word length, magnitude however does mean the same thing for a vector (magnitude of a vector is its exact length, so all vectors of same length have same magnitude). But for the readability its indeed better to use the word length. Because its a more understandable wording -J-

Edity, i think the entire section of C0 C1 and C2 continuity should be revised fully, indeed C0 continuity implies end points matching, C1 is matching the vector of change direction and C2 is matching vector length change. So it is NOT enough to be same length but the rate of change must also be a continuous function (remember we are talking of function continuation here)

So simply, c0 ensures that the curves continue seamlessly, c1 ensures the angles the same, c2 ensures change of rate is continuous. -J-

PS i was talking to a engineer who needed c3 continuity because of some stress calculational reason.

External links

Could someone, preferably with expertise in the subject, go through the last four (untitled) external links? Seems like a lot of duplicate information. --Ronz 00:27, 12 September 2006 (UTC)

Unverifiable History ("by linking to other websites only")

I removed the following sentence from the article and moved it here until it can be verified:

In 1993, the first interactive NURBS modeller for PCs, called NöRBS, was developed by CAS Berlin, a small startup company cooperating with the Technical University Berlin.

I did a Google search to try and verify it and found nothing of note. Dallben 22:33, 1 December 2006 (UTC)

87.123.118.104 01:39, 27 December 2006 (UTC)

As Google search is your only source for verification, you are much too daring to touch historic facts in this article. Wikipedia is not intented to be reduced to google-content only. You might have realized that 1993 was very long before Google was founded or active on the internet. If you doubt the facts here you should take a closer look at the history of this article, which includes additional information about the first NURBS modeler on the PC. And NöRBS was also listed on the 1995 published O'ReillyNew Riders Pub Book about 3D Studio Plugins. So please dont touch it again as you have nothing to offer which can be called a reason, but: >>I did not find it on a Google quicksearch.<<

87.123.118.104 01:39, 27 December 2006 (UTC)

• Well, I think it would be prudent for you to review Wikipedia's policies on verifiability (pay special attention to point three of the nutshell summary). Thus, you cannot claim that I am wrong in removing the sentence—it is unsourced and does little to add to the article's quality. So, instead of removing it, I've added a citation notice to the sentence, which you should fill out with nicely formatted sources, verifying the claim that NöRBS was indeed the first interactive NURBS modeller. (Please note that citing this article's history is patented nonsense—how on earth can that verify anything?). Finally, from your tone and from your IP address's geographic region, you've given me every reason to believe that a WP:COI is highly probable. Regardless of your motivation, cite the sources that verify this claim and the sentence will actually improve the article. Dallben 21:18, 27 December 2006 (UTC)

Hi, it seems we have a completely different reception of what is verifiability. Some editors have decided that the fact that NöRBS was published and presented first on the CeBit fare in 1994 is not an important information and therefor removed it from the article. You can find this information only in the history of the article now. I can perfectly understand people treating this information as not important enough to be part of the main article. In my reception this is a perfect source for verification: "It was developed in cooperation with the TU Berlin and presented on the biggest IT fare in the world, the CeBit 1994", as all these are verifiable facts. Not by a google search, but by researching at the place itself. Some editor added the fact that it was presented at the booth of a company called CAA Gmbh, to emphasize the credibility of the statement. This was removed too. Now you call it complete Bollocks to be directed to the history page for valuable information for verifiability?

Another - and in my view much more important - aspect is the fact that the article about the history and the use of NURBS containing the sentence you are challenging now is online since 10th3rd of July 2005. Many people have contributed and edited since then and much more have read and reviewed the content. There is not a single statement which could be regarded as doubt or even contradiction to the stated facts. Except yours, of course. Therefor the challenged informations have been steeled by the most valuable source of infomation: The Public. Everybody with access to the internet had the chance to say: Thats not true! for nearly two years now, and even more important: still has. Nobody did because it is simply the verifiable truth.

And we are not talking about some minor or even irrelevant subject, NURBS is one of the most widespread technologies in the world, even more than the PC as it is used in the industry too. Therefor it can be assumed that this article has been read by nearly anybody who has to do with NURBS on a professional level and knows about the Wikipedia.

All this is also the answer to the question: Was NöRBS really the first one on the PC? This is perfectly true until somebody comes up with some evidence saying: No, this one was earlier. Nobody knows everything in the world. I dont know if e.g. some Nepalese or Chinese climbed on the Mount Everest before Sir Edmund Hillary did so in 1953. Therefor, as long as there is no evidence for this case i will continue to say and believe: "Yes, it was Hillary who first climbed on top of this mountain".

But for those who still see any incompatibility of all the above with some *guidelines* here, the software called NöRBS was also presented (and included on CDROM) in the 1995 published book called >3D Studio Ipas Plug-In Reference<,

1. Author: Tim Forcade
2. Publisher: New Riders Pub; Bk&CD-Rom edition (July 1995)
3. Language: English
4. ISBN-10: 1562054317
5. ISBN-13: 978-1562054311

I am citing it here and not in the article itself for not making it subject of removement to the page history and in the following.... see above for details. 87.123.92.233 23:22, 3 January 2007 (UTC)

Removed the citation request as it is fullfilled here without adding unwanted overhead to the article itself. In addition the Google search cited here before shows that this page is used as a reference for other websites. Google itself judges this as a fact emphasizing the relevance of this page. 87.162.96.161 23:02, 7 February 2007 (UTC)

Removed the cleanup request too, as there has not been any noteable argument for keeping it since the request for verifiability has been answered here. 87.162.89.63 21:02, 11 April 2007 (UTC)

Request for image ?

From my point of view it does not make much sense to add an image or rendering, as this would mostly show the effect of rendering, which is not a subject of this article. Therefor it would not really help for understanding NURBS, but in opposition add to the widespread missunderstandings of NURBS by giving the impression of "this is how they look like". Instead look at any car built within the last decade, or any hairdryer, sophisticated shampoo bottle, designerphone or other industrially generated freeform object. There is a 99% chance you are looking at NURBS. 87.162.97.244 22:41, 19 April 2007 (UTC)

Violation

http://www.highend3d.com/dictionary/N/NURBS violation of rights, unauthorized copy please check dear friends After checking erase post. TNX Flaming-Balrog

This is definitely a (quite literal) copy. But, if I look at the substantial history of the wiki page, I see parts of the page gradually emerging, which suggests that the copy was made from wiki to there.

Mauritsmaartendejong 10:04, 24 June 2007 (UTC)