Alias Tutorial – NURBS Curve Geometry deg. 3 v deg. 4

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Thinking about upping that degree? please, think twice.

Consider the situation: you have a degree 3×3 surface and you decide you need more cv’s to work with, so you go to that control panel and reach out to up that degree.

That is perfectly alright, but think twice, do you really need that extra row of cv’s? consider the mathematics at work for a second.

(IMAGES COURTESY WIKIPEDIA)

This is a degree 2 curve

It interpolates between the three control vertices. At the start and end it is absolute so it touches, while the middle cv acts like a magnet influencing the curve towards it.

As we know the middle cv’s of bezier/nurbs geometry do not lie on the surface or curve, they hover over like the center-of-mass of the old “ducks” used before the computer. This is, without doubt, one of the trickiest parts of nurbs/bezier modeling.

Now consider a higher degree curve, degree 4

Mama mia! what a ballet. this is getting pretty complex.

I wish to leave you with this one, a degree 5 curve, and this is pretty common. I conjure it up to your own imagination to imagine the interpolation of still higher degree geometry!

and no… weighting cv’s or spans are not the solution! sound surfacing judgement is.

By Kevin De Smet
Advanced student at

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