# How would you go about modeling this curve?

I am a beginner Rhino modeler.
Any help would be appreciated. Thanks.

No matter how many control points your curve has, just make sure itâ€™s Degree 5 (the `! _Curve` tool defaults to exactly that). If your curve has any other degree, then just convert it to Degree 5 with either the `! _ChangeDegree` command or the `! _Rebuild` command (make sure to choose the â€śDeformableâ€ť option from the Command line) if you want to have a smoother, fine control over its shape. Degree 5 will make the curve perfectly smooth and you can see this when you analyze it with the `! _CurvatureGraph` tool.

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Is it possible to have degree 5 with a control point count other than 6 or have you wanted to write â€śsingle spanâ€ť instead of â€śDegree 5â€ť?

Create only one half.

Of course, I often use Degree 5 curves with multiple control points. They are perfectly smooth no matter whatâ€™s the distribution of the control points. You can move any control point wherever you want and the curvature graph is always as smooth as a butter. This is a HUGE advantage over the basic Degree 3 curves who tend to break the smoothness as soon as you move their control points and change the ratio between their control points.
Here is an example of a Degree 5 curve with 15 control points that I used to draw today for a project:

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Depending on how the curve or surface will be used continuous curvature which degree 3 provides may be sufficient. Degree 3 curves and surfaces have the advantage of providing more direct and local control of the shape with fewer control points. A disadvantage is can be easier to create an unfair curve or surface with degree 3 curves compared to degree 5 curves and surfaces. Also as Bobbi notes the curvature graph (not the curve or surface) of a degree 3 curve or surface may have kinks if that is important. At a kink in the curvature graph the surface or curve has tangency and curvature continuity.

A new modeller may want to start with degree 3 curves as they will provide more direct feedback when moving control points.

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Thatâ€™s true. I consider the Degree 3 curves as a nice starting point, as they are good enough for basic stuff. However, for product design and especially vehicle design (or marine design) I much prefer to use Degree 5 curves, because they provide the necessary smoothness which is essential for the reflections of the body panels covered by shiny paint.
Also, due to their nature, the control points of Degree 5 curves need to be moved at considerably longer distance to visually affect those changes on the curve itself. This particular specific of the Degree 5 curves make them perfect to fine tune their shape â€śsecurelyâ€ť, in comparison to Degree 3 curves that could easily get wrong with the slightest movement of a certain control point in any direction.

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Thanks. I was so fixed about single-span curves that I have even thought it`s impossible to do degree 5 with more than 6 control points My bad. This is possible but this is not single-span curves of course because to be a single-span they should have 6 CP. Am I right?

When single-span curves are needed and when multi-span curves like your example are allowed?
Iâ€™ve heard that single-span curves in automotive are a must. When it`s allowed to omit that â€śmustâ€ť?

I have still a mess in my head with those automotive rules.

Cheers!!!

Iâ€™m just an amateur designer and engineer, meaning Iâ€™m self-taught and have no degree in neither design nor engineering. I donâ€™t follow these â€śrulesâ€ť about mandatory single-span curves, because itâ€™s very time consuming. Itâ€™s just enough for me if the curves and surfaces do their job for my purposes, despite being considered multi-span. A single surface may consist 100 spans and still be better and smoother than a bunch of single-span surfaces whose flow is not perfectly smooth and gradual. I have seen Alias models made by graduate designers using much more advanced tools than what Rhino could offer, yet they had plenty of wavy areas.

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@mdesign
le nombre de points dans les courbes Ă  travĂ©e unique ne peut pas ĂŞtre augmentĂ© sans que le degrĂ© augmente en mĂŞme temps, câ€™est la rĂ¨gle mathĂ©matique des courbes de BĂ©zier, il nâ€™y a pas autrement.
cependant on peut tricher sur les courbes multi-span, pour avoir plus de points de contrĂ´le.
en jouant sur les nĹ“uds, de sorte quâ€™on multiplie leurs valeurs pour gagner plus de points .

Il y a plusieurs moyens pour le faire.
le moyen le plus simple est dâ€™augmenter le degrĂ© dâ€™une courbe ou dâ€™une surface multi-span en choisissant lâ€™option (non-dĂ©formable dans lâ€™invite de commande).

example.

si jâ€™ai une courbe de degrĂ© 3 avec 6 points de contrĂ´le. cela signifie que jâ€™ai deux nĹ“uds dans la courbe. Ă©tant que la rĂ¨gle dâ€™Ă©valuation des courbes multi travĂ© est
N = P-(D+1)
N) est le nombre de nĹ“uds
P) est le nombre de points de contrĂ´le
si jâ€™augmente le degrĂ© Ă  4 cela crĂ©e une multiplication de la valeur des nĹ“uds, ce qui me fait gagner un point de contrĂ´le de plus pour chaque nĹ“ud,car je suis passĂ© du degrĂ© 3 au degrĂ© 4 avec une multiplication unique)

Ce qui donne au final une courbe de degrĂ© 4 avec deux nĹ“uds, mais 9 points de contrĂ´le au total !!.
ce qui nâ€™est pas conforme Ă  la rĂ¨gle de base dâ€™Ă©valuation des courbes multi-span dĂ©crite ci-dessus.

autre exemple,

si jâ€™augmente le degrĂ© de la premiĂ¨re courbe Ă  6 cette fois.
cela fait trois multiplications des valeurs des nĹ“uds.
ce qui me fait gagner 3 points de contrĂ´le supplĂ©mentaires pour chaque nĹ“ud.
puisque je suis montĂ© en degrĂ©s par trois incrĂ©ments. (de 3 Ă  6) ce qui me donne une courbe de degrĂ© 6 avec 2 nĹ“uds et 15 points de contrĂ´le, (ce qui est Ă©norme)

(lâ€™inverse nâ€™est pas possible)

Ce fil peut ĂŞtre util aussi https://discourse.mcneel.com/t/what-is-really-the-knot-of-a-nurbs-curve

La commande blendsrf utilise aussi la multiplication des nĹ“uds .mais souvent elle ne donne pas de bons rĂ©sultats.
On dirait que la surface passe de degrĂ© 2 au degrĂ© 3 dans les coulisses . Ce qui donne une contunuitĂ© interne de G1 .

Xnurbs aussi utilise la multiplication des nĹ“uds avec un passage de degrĂ© 3 Ă  5 dans ses patchs
Cela garde une contunuitĂ© interne de G2 .
Ca fait longtemps je nâ€™ai pas touchĂ© xnurbs , je ne sais pas comment il est maintenant.

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@user2682
Tu peut commencer avec une courbe de degrĂ© 2 .
Augmenter en degrĂ© au fur et Ă  mesure, jusquâ€™Ă  lâ€™obtention de la forme souhaitĂ©e.
Sinon tu peut diviser la courbe en deux pour plus control.
Mais ce nâ€™est pas la bonne solution

Le capot ou le toit ne devront pas ĂŞtre diviser pour faire des symĂ©trieâ€¦

A toi de choisir.

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Donâ€™t start trying to model a car as your first model.

Why are you even trying to draw that curve? Thatâ€™s not how any complex NURBS model is made, not even something as dull and ugly as a modern BMW. That curve is the result of an intersection of surfacesâ€¦actually maybe itâ€™s a cut line in a larger shape. Either way, that curve is irrelevant to the basic shape of the car.

Iâ€™m also self-taught. Thanks for your point of view on the topic of multi-span curves. I admire you as a PRO Rhino user who self-taught level which is my personal target so Iâ€™m interested in theory which has relation to everyday practice in production (even if it is low scale). I would like to learn Rhino more for low scale production mainly cause I`m also a freelancer who is a one-man army, so I have to know every part of the process in low scale production (I already work in that kind of production). I think I should give multi-span curves more attention especially on shapes that are long enough to be hard to do with many single-spans (f.e. car roof on side-view or belt-line which often is long and complicated, aircraft main shape profile from the nose up to the tail).

I promise to ask you more

Cheers!!!

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Thanks, Fares for the complicated theory. French is not a problem

When do you consider a multi-span curve as an acceptable way to go?

je ne suis pas tres habille en expliquant les choses thĂ©oriquement .

tous sont acceptables et utiles, cela dĂ©pend de tes projets ou de la qualitĂ© que tu veux atteindre.
les courbe multis span de degrĂ© 4 5 et 6 sont un bon compromis.
la contunuitĂ© entres leurs travĂ© est lisse et ne contiennent pas de pique de graphique.

il a la contunuitĂ© interne de G3, plus une bonne Ă©lasticitĂ© de la courbe pour une bonne manipulation.

Le seul inconvĂ©nient est que la manipulation dâ€™une courbe multis spans est un peu plus dĂ©licate. Si tu veux garder le graphique de courbure lisse est parfait. Dans certains endroits

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