Knot vector question - RealWorld forums

Hi,
I just bought realworld icon editor especially for its 3D capabilities. I also want to take the time to learn a bit more about NURBS. When I want to model a new surface I can design a curve that I can rotate. Designing the curve is done by adding new knot vectors and manipulating the control points. I do not understand that I have only two knots when I create a quadratic or even cubic curve. In documentation I read that the number of knots in the knot vector should be equal to the number of controlpoints + curve degree + 1.
Can someone help me out here (I know this information is not really necessary to create icons, but I can't help trying to figure out how things work)

Many thanks in advance.

Wilke

The application does not show all the knots at the ends of the knot vector. A true knot vector for a cubic NURBS without any extras would be:
0 0 0 0 1 1 1 1

8 (knots) = 4 (control points) + 3 (degree) + 1.

Since showing all these boundary knots in user interface would bring (almost) no benefit, the 3 (degree) knots at each end are hidden. (The questionable benefit would be the ability to change them, which would result in a NURBS curve that does not intersect the end control points.)

Hello Vlasta,

Thanks for your swift reply. If the focus is more on the control points, why do we have to add them then via the intermediary of a knot. Wouldn't 'add control point' then not be a more intuitive way of extending the curve?
This is in no way a point of critique, I'm merely trying to understand some basic 3d terminology as I'm a total beginner.

Thanks in advance

Wilke

I am aware of the fact that using NURBS directly is not a great thing from a user's perspective, especially for people learning 3D. In future versions, the focus will be more on simplicity and intuitiveness than on technical conformance.

To answer your question: Each knot internally splits the curve into two parts and defines a level of continuity at the split point. Knot can be inserted multiple times at the same position and each insertion reduces the continuity and adds one control point. For example, by inserting 3 knots to the same position into a cubic curve (0 0 0 0 0.5 0.5 0.5 1 1 1 1), the curve will have a sharp edge in the middle. By inserting one more 0.5 knot, the curve will not be continuous anymore (after moving the control points).

If there only were a "insert point" operation and no knot vector, this kind of control would not be possible. Not necessarily a bad thing, but it would not be a NURBS anymore.

[url=NURBS]Here is a bit of info about NURBS.[/url]

Hello Vlasta,

I think I would find it more intuitive to be able to add a control point from either the list of control points or the curve itself (following your explanation on knots in knot vectors a knot could then be added automlatically)

Anyway, your explanation helped me to somewhat better understand nurbs.

Thanks,

Wilke