Nurbs Curve Domain


I had the understanding that the domain of a curve, is based on the length of the degree 1 curve of that curve, just to realise that by changing the degree of the curve in Grasshopper the domain changes (I am using the Nurbs Curve component) we no longer have that relationship

Where does the domain number come from?

Why did you think so? Is there a theoretical background?

These blog posts from Mr Rutten explain curve domains. They are well worth a read.


That seems about right :wink:

What do you mean? Where can you find the correlation between curve domain and curve length?

only in degree 1 :wink: as he pointed out.

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I don’t really understand the correlation between curve domain and it’s length even in the degree1.

Hi @HS_Kim,

Remember from Calculus, The domain of a function is the set of inputs allowed for the function, i.e., the set of values that can be fed into the function to give a valid output.

In general, Rhino tries to have parameterization match the length of a curve or some measure of the width of the surface. Derivative information is better if we do it this way.

When curves and surfaces are paramterized with a [0,1] domain, both the accuracy and the precision of geometric calculations like intersections and closest points are reduced, sometimes dramatically.

Hope this helps.

– Dale

Thank you for the explanation.
So, in the case of degree 1 curve, does Rhino try to set a domain that matches the length behind the scene, but not always? Is it possible to have less accuracy if you have a different domain than the length? Is the curve domain a completely random configuration?

Hi @HS_Kim,

You’ve basically rephrased what I said. And no, Rhino does not paramterized randomly…

– Dale

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