G0 ; G1 ; G2 ??? All  1-4  5-14

 From: Schbeurd 14 Jan 2007  (5 of 14)
 Hi Michael and Jonah, Thanks for the info. It's quite clear now (apart the terms "rate of change" in the explanation - from Rhino - for G3 and G4 which remain "obscure"). The comments on Bezier curves here and in another thread are very useful too. Now, just for a better understanding of NURBS in general... Very often I see mention of a degree for NURBS. Could you explain what that is ? Is there a relation between the "G value" of a curve and its degree or is this totally different stuff ? No need for a deep technical explanation there but I think understanding what's "behing the engine" always permits a better understanding of the software and generally speaking why sometimes the results are not exactly what the user expected. Thx

 From: tyglik 14 Jan 2007  (6 of 14)
 290.6 In reply to 290.5 Hi Bernard, I have been browsing a integrityware and npowersoftware websites for one hours. There is an astonishing gallery and video tutorial section about NURBS modeling. Considering that it might be a MoI's future, because the geometric kernel is the same.... whew... The tutorial can be looked through this and this. One of them is about G1,G2,G3 continuity. Don't remember to switch on your speakers! Petr

 From: Michael Gibson 14 Jan 2007  (7 of 14)

 From: Michael Gibson 14 Jan 2007  (8 of 14)
 290.8 In reply to 290.5 > Very often I see mention of a degree for NURBS. Could you explain what that is ? This one is a bit more difficult to explain. Basically, the math behind NURBS curves uses a type of polynomial equation to blend between control points. The way curves work, a point on the curve is calculated by blending together the values of a set of control points. So for example the curve above is what is called a degree 2 or "quadratic" bezier curve. Every point on this curve is calculated by a blending equation that takes in all 3 points as part of the equation and produces a point on the curve. But the blending is continuously shifting as you slide along the curve - at the very beginning of the curve the second and third points are contributing 0 (this is why the curve touches the first point), but as you move towards the middle of the curve, the blending is more of an average of all 3 points, then shifting to finally only the 3rd point at the end. Anyway, I mention this blending-together of points because the degree of a curve has to do with how many points are used to calculate one section of the curve. A degree 1 curve (linear) blends together 2 points. A degree 2 curve (quadratic) blends together 3 points. A degree 3 curve (cubic) blends together 4 points. etc... That's how bezier equations work. NURBS are similar, except NURBS provides a way to have a curve with more than just degree+1 points in it. Your curve is still made up of different sections, but each shares an overlapping set of points with each other. This sharing provides smoothness between each section. Here is a cubic (degree 3) NURBS curve with 6 control points. This makes a curve that actually has 3 internal segments to it - every 4 points defines a segment which I have illustrated here: So a higher degree means that more points are used to make a single polynomial segment of the curve. > Is there a relation between the "G value" of a curve and its degree or is this > totally different stuff ? There is a relation because the degree determines how many internal segments the curve will have, and there is a G value where segments meet (just as there is where 2 separate curves meet). Also the degree of the curve can limit the maximum G value - for instance the common cubic curve will only have inherently G2 smoothness, but if you go to a higher degree curve it means that there are a larger number of points shared in common between different sections and this means that there is a higher amount of built-in continuity between the segments (the segments are often referred to as "spans" of a curve). There are some other effects of high degree - the greater averaging makes a kind of slightly more melted effect. By which I mean that a higher degree curve kind of gradually melts a bit farther and farther away from its control points as you go to higher and higher degree. Some specialized applications want to reduce the number of internal spans to a curve, which is one effect of increasing the degree. I have thought a little bit about maybe changing the curve tool to draw curves of degree 5 instead of degree 3 as it currently does - the slightly-more-melty effect of degree 5 is kind of nice. It's not too practical to go too high in degree since a lot of processes go through loops of work depending on the degree, so there is also an increased calculation time issue with very high degree - that's why everything doesn't just go up to degree 100 or something like that. - Michael Attachments:

 From: Schbeurd 19 Jan 2007  (9 of 14)
 @ Michael : Thanks for the explanations. Limpid as usual and very interesting ! @ Petr : There seems to be a lot of informations there. Thanks for posting the links.

 From: dej (DEJULE) 1 May 2009  (10 of 14)
 Is it important to build surfaces with single span curves?..because it can introduce knots or added isoparms? Is this important when creating surface that are attached together to maintain good curvature?

 From: dej (DEJULE) 1 May 2009  (11 of 14)
 290.11 In reply to 290.10 What was confusing to me using Alias..was if I ensure all my curves g1...why do I have to set, through another option box that the surfaces are g1 also. Shouldn't this be automatic or simplified? Maybe Moi could be more intuitive that way.