nurbs surface's knot vector

hello my friends I have two different question.

1st: with (n) as count of control point and (d) as degree of curve and (p) as periodic I can obtain (k) as Nurbs knot vector for example {0,0,0,1,2,3,4,4,4}... but this is sequence for Nurbs curve . I want finding a Nurbs surface.for example in 2 direction u{0,0,0,1,1,1,2.3..} and v{0.0.0.1,2} what's the proper action ?

2-in rhino >>>properties of object>>>detail for Nurbs surfaces somewhere demonstrated : "U": degree =3 CV count = 5 (0.0605688 <= U <= 0.954948)

"V": degree =3 CV count = 14 (0.503634 <= V <= 1.00363)

whats a meaning of this phrase in the Parenthesis ? and is it important for (u&v) that value of them be between 0 and 1 ? thank you for your consideration about the issue. With best regards.

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Permalink Reply by David Rutten on November 10, 2013 at 10:02am

Periodic knot vectors do not repeat the start and end numbers (that's the whole point of periodic). Nurbs surface vectors are basically the same, except you need 2 of them (one for u, one for v).

The numbers in the parenthesis refer to the domain of the surface. The U domain of your surface is from 0.06 to 0.95 and V goes from 0.50 to 1.00

Domains do not have to be between 0.0 and 1.0, in fact we recommend that the domain is roughly the same as the actual physical size of the object, but domains can be anything provided they are not zero-length.

Normalising the domains of geometry (i.e. set the domain to 0.0~1.0) makes it easier to write certain algorithms, but it also causes some operations (intersections and and closest-point searches most notably) to take longer to converge.

David Rutten

david@mcneel.com

Tirol, Austria

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