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 it’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 “Deformable” 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.

2 Likes

Is it possible to have degree 5 with a control point count other than 6 or have you wanted to write “single span” instead of “Degree 5”?

Create only one half.

Of course, I often use Degree 5 curves with multiple control points. They are perfectly smooth no matter what’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:

3 Likes

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.

1 Like

That’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 “securely”, in comparison to Degree 3 curves that could easily get wrong with the slightest movement of a certain control point in any direction.

1 Like

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 :slight_smile: 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?
I’ve heard that single-span curves in automotive are a must. When it`s allowed to omit that “must”?

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

Cheers!!!

I’m just an amateur designer and engineer, meaning I’m self-taught and have no degree in neither design nor engineering. I don’t follow these “rules” about mandatory single-span curves, because it’s very time consuming. It’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. :slight_smile: 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.

1 Like

@mdesign
le nombre de points dans les courbes à travée unique ne peut pas être augmenté sans que le degré augmente en même temps, c’est la règle mathématique des courbes de Bézier, il n’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 nœuds, de sorte qu’on multiplie leurs valeurs pour gagner plus de points .

Il y a plusieurs moyens pour le faire.
le moyen le plus simple est d’augmenter le degré d’une courbe ou d’une surface multi-span en choisissant l’option (non-déformable dans l’invite de commande).

example.

si j’ai une courbe de degré 3 avec 6 points de contrôle. cela signifie que j’ai deux nœuds dans la courbe. étant que la règle d’évaluation des courbes multi travé est
N = P-(D+1)
N) est le nombre de nœuds
P) est le nombre de points de contrĂ´le
D) est le degré.
si j’augmente le degré à 4 cela crée une multiplication de la valeur des nœuds, ce qui me fait gagner un point de contrôle de plus pour chaque nœud,car je suis passé du degré 3 au degré 4 avec une multiplication unique)

Ce qui donne au final une courbe de degré 4 avec deux nœuds, mais 9 points de contrôle au total !!.
ce qui n’est pas conforme à la règle de base d’évaluation des courbes multi-span décrite ci-dessus.

autre exemple,

si j’augmente le degré de la première courbe à 6 cette fois.
cela fait trois multiplications des valeurs des nœuds.
ce qui me fait gagner 3 points de contrôle supplémentaires pour chaque nœud.
puisque je suis monté en degrés par trois incréments. (de 3 à 6) ce qui me donne une courbe de degré 6 avec 2 nœuds et 15 points de contrôle, (ce qui est énorme)

en résumé
pour une bonne compréhension d’un point de vu désign.
la multiplication des valeurs des nœuds, nous permet d’utiliser les propriétés des nœuds d’une courbe de degré inférieur sur une courbe de degré supérieur.
(l’inverse n’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 nœuds .mais souvent elle ne donne pas de bons résultats.
On dirait que la surface passe de degré 2 au degré 3 dans les coulisses . Ce qui donne une contunuité interne de G1 .

Xnurbs aussi utilise la multiplication des nœuds avec un passage de degré 3 à 5 dans ses patchs
Cela garde une contunuité interne de G2 .
Ca fait longtemps je n’ai pas touché xnurbs , je ne sais pas comment il est maintenant.

1 Like

@user2682
Tu peut commencer avec une courbe de degré 2 .
Augmenter en degré au fur et à mesure, jusqu’à l’obtention de la forme souhaitée.
Sinon tu peut diviser la courbe en deux pour plus control.
Mais ce n’est pas la bonne solution

( C’est mieux de créer des géométries uniques au milieu de la voiture.
Le capot ou le toit ne devront pas être diviser pour faire des symétrie…

A toi de choisir.

Désolé pour la réponse en français. J’ai du mal a écrire en anglais .
(Google traduction est le meilleure ami)

1 Like

Don’t start trying to model a car as your first model.

Why are you even trying to draw that curve? That’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 surfaces…actually maybe it’s a cut line in a larger shape. Either way, that curve is irrelevant to the basic shape of the car.

I’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 :slight_smile: so I’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 :slight_smile:

Cheers!!!

1 Like

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

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

je ne suis pas tres habille en expliquant les choses théoriquement . :ghost:

tous sont acceptables et utiles, cela dépend de tes projets ou de la qualité que tu veux atteindre.
les courbe multis span de degré 4 5 et 6 sont un bon compromis.
la contunuité entres leurs travé est lisse et ne contiennent pas de pique de graphique.

personnellement je préfère le degré 4 .
il a la contunuité interne de G3, plus une bonne élasticité de la courbe pour une bonne manipulation.

Le seul inconvénient est que la manipulation d’une courbe multis spans est un peu plus délicate. Si tu veux garder le graphique de courbure lisse est parfait. Dans certains endroits

1 Like