about the option under the interpolate curve

I have been wondering what is the difference between different curve degree, and what do sub options of the interpolate mean, I have experiment with it for a while, but i cannot really see some obvious difference, and feel very confused about how they function. If anyone can help thanks alot!.

Replies to This Discussion

Permalink Reply by Tian on June 22, 2016 at 1:57am

thanks !!! i am going to experiment more on u said.

Permalink Reply by David Rutten on June 22, 2016 at 2:12am

In addition to Tom's and Marcus' answers, it is indeed true that for freeform curves degree=-3 is the most common. However not all curves are freeform. The following degrees occur often:

1 = straight segments (ie. polylines)

2 = conic section (ie. arcs, circles, ellipses, parabolas, hyperbolas)

3 = standard freeform curve

5 = smoother freeform curve

The higher the degree, the less effect a single control-point has on the curve, but the further that weak effect reaches. Degree=5 curves are smoother, but it's also harder to add local details to it without adding a lot of control points. Rhino supports curves up to degree=11, but you almost never need more than 5.

Permalink Reply by David Rutten on June 22, 2016 at 3:54am

Absolutely. The degree of a nurbs curve and the degree of a polynomial are very similar kinds of thing, and polynomials with higher degrees have many more derivatives before you end up at f(x)=0. The more derivatives you have the smoother you can make your geometry.

Nurbs curves and surfaces are piece-wise objects, meaning that they consist of one or more consecutive elements that are -at the very least- positionally continuous. Ie. the next piece starts where the previous piece ends. If this is all the continuity you have then it means you have a kink/crease in your geometry and the first derivatives of your pieces are different on either side of that kink.

If the first derivatives are identical, but the second derives are not, then you have positional and tangential continuity, but no curvature continuity. If the second derivatives line up as well, then the curvature on either side of the piece boundary is the same. And so on and so forth.

As you mentioned many objects, especially cars, require higher levels of continuity than that, because they are shiny objects that tend to move. Thus, at the very least, we'd like the rate-of-change-of-the-reflected-environment-across-the-surface to be smooth, which means I think third or fourth degree continuity. As far as I know there are no universally accepted terms for these higher kinds of continuity, in Rhino core we call them 'Jerk' and 'Yank' respectively, but in the Rhino UI they are just called G3, G4, ..., GInfinity.

RSS