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OK, I'm still trying to come to terms with the concepts. I was under the impression that number of degree, cv's, and knots were all dependent on each other.
You just said it. instead of seamanly adding an edit point in a spline increase the curve order from y=x^3 to y=x^5 or higher.We don't have that control in Pro/ENGINEER Edited by: design-engine
heres a great tool called designmentor to experiment with CVs,knots,degrees (up to 10 !!) . and also other curve types like: bezier, rational bezier, bspline in addition to nurbs.
(the right panel shows knot values, you can change knot values unlike any commercial cad tool!)
the interface need a little getting used to tho. as i don't have time to look for the link, i upload the program itself. you can find the help at: http://www.cs.mtu.edu/~shene/COURSES/cs3621/LAB/curve/curve. html
the software should be there too. but i upload it anyway.
playing with mentor, i can see thoes yellow dots on proe sketch splines correspond to knots. create a degree 3 nurbs curve in mentor (with clamped condition), take a snapshot, import to proE and put the CV's on the curve points you created in mentor. you'll see knot positions approximatly match yellow dots in pro. manupulating the knot values the two curves will match closely. try yourself...
"So when you talk about adding cv's without adding knots"
may have been inaccurate. I'm assuming it had to do with
elevating bezier curve degree(? G2 constraints Alias vs. Pro/E).
Any statement to the effect of "adds CVs vs. knots" should have
said "internal" or "mid span" knots. More below ...
> degree, cv's, and knots were all dependent on each other.
They are, but it can be confusing.
> "control points are a list of
> at least degree+1 points"
It is important to focus on "at least" and know that describes a bezier curve,
i.e. four CVs for a degree 3, five CVs degree six, etc. It must be remembered
that a bezier has no 'internal knots', e.g. all of the knots are are at either
end of the curve (see 'multiplicity' below).
(It may be worth noting ...
. the "order" of the curve is degree + 1 as well and
. the CV 'count' for a bezier is 0 -> degree, i.e. degree 3 is 0,1,2,3.
If that confuses more than clarifies; forget it.)
> "knots are a list of degree+N-1 numbers,
> where N is the number of control points"
What might be missing to make the whole comprehensible is the term 'full
muliplicity' or 'fully multiple' knots. The typical NURBS curve, to include
beziers and b-splines, as used in typical(?) CAD has fully multiple knots at
each end.*
So for a degree 3 bezier the expression would be; [3 + 4 - 1] or 6, three on
each end.
[*
I don't know how 'accurate' that statement is and it should be noted
that not all splines have fully multiple knots at each end.
(This is a very informative treatment of basic concepts and definitions
if you don't have a copy)
NURB Curves: A Guide for the Uninitiated, P.J. Schneider [url]http://devworld.apple.com/dev/techsupport/develop/issue25/sc hneider.html[/url]
Look at fig. 9 & 13 for quick ref, note the ends of the curve relative CVs.
I think I've also seen something similar in CADDS NURBS manual, but would
have to search.
Some older systems(?) placed degree + 1 knots on each end of a curve. IGES
uses that convention for compatibility. Newer systems add on write or
disregard on read the extra knot, should you ever come across that confusing
little bit of trivia.
]
If we create a b-spline (by 'picking' points between start and end) or if a
bezier is converted to b-spline (to satisfy imposed Constraint conditions)
a CV is added in conjunction with each knot. So ...
_ For a degree three b-spline defined by picking three points
[degree + N - 1] = 3 + 5 - 1 = 7 = three each end and one in the middle.
_ For a degree 4 b-spline defined by picking three points
[degree + n - 1] = 4 + 6 - 1 = 9 = four each end and one in the middle.
And so forth.
_ _ _ _
If that doesn't seem to make sense, holler back. I may have, again, confused
something in the telling.
> suspect all I'm learning so far I what I still don't know.
I can definitely relate to that. ;^)
_ _ _ _
Solidworm,
The interactive curve program should be a big help. Seeing and playing
in Rhino is how I wrapped my head around a lot of this. Graphics help.
(Rhino does give a user to access to CV weights, tho' not a straight up
graphics 'display' which would be much handier for comprehension. Similarly,
playing with conic arc Rho in Pro/E, which is adjusting CV weight.)
Thanks for the explanations. This is the best post ever - I've gotten more information in here then all others combined.Jeff - you should write a book. Ithink I need to see more ofthesecurves in these other programs because where I'mgetting stuckis trying to imagine what's happening in Pro/E.
I've takena week and a half total now. I learned a lot. No more tri-patches, zebra striping is always good now, and my models are easily modifiable with lattice dimension framework. Let me know when that ISDX surface edit class is.
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