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Curve and Surface Analysis

Alias can convert a curve order from a 3 degree curve to four five to seven degree curves. Ill take time out of learning RSD to describe that.
Edited by: design-engine
 
Related reading ...
[url]http://aliasdesign.autodesk.com/learning/tutorials/details/C urvature_Continuity_In_Surface/ [/url]
[url]http://catiatutor.com/Basic/CATIA-Handbook/CLASS-A-SURFACING .html[/url]
_ _ _ _


Seems someone asked about higher order constraints somewhere in the
previous pages...


I believe that in theory each degree (or order) of continuity simply
manipulates consecutive CVs; e.g. (for a curve defined CV0, 1, 2, ...)
G1 = CV1, G2 = CV2, G3 = CV3, etc.


In practice, considering G3 (rate) continuity, for instance,
(1) How do we measure rate of the reference curve?
(2) How do we calculate the position of CV3 to obtain a specific
rate at CV0?
(3) What programs might roll it all up in a neat 'contraint' function?
I don't know any of the answers.
_ _ _ _


Re higher degree splines, I just learned something about b-spline continuity.
Continuity at a knot position is curve degree - knot multiplicity. What that
means is that for a 'mid curve' knot (i.e. in Pro/E a spline created by
defining three points; end, mid, end, resulting in a degree 3 b-spline) the
continuity is C2 (I think in this instance rather than G2). I've never seen
that stated anywhere and put in those terms it makes observed phenomena
(radical changes in curvature graphs) more compehensible somehow.
( [url]http://www.rzg.mpg.de/~sa2728/CADDS5-Doku/NURBS-v12-englisch .pdf[/url])
 
design-engine said:
Don't try to force continuity in a sketch curve! ... its a bad technique.
Click to expand...

Why is it bad? Unstable? Hard to redefine?

We were talking about this technique, as described by Jeff, about adding curvature constant constraints in sketcher:

jeff4136 said:
CC constraint like the tangent constraint off an existing feature


That is the equal (=) contraint. It works with (circular) arcs and lines only.
Sketch an arc and disjoint line. Bridge the two with a spline. Apply the (=)
constraints. You'll notice that two constraints (T & C) are actually added.
If the reference curve isn't an arc or line it will be necessary to create a
Datum Evaluate feature and use a radius of curvature dimension (assuming a
parametric relationship is desired).
Click to expand...

I've not used that before, but it sounds handy. Why is it bad?
 
jeff4136 said:
(3) What programs might roll it all up in a neat 'contraint' function?
I don't know any of the answers.
Click to expand...


It sounds like these high end style programs utilize advanced analysis and diagnostics for their higher order surface creation. It seems like the next step would be to use the mathematical model to constrain the cv's at the start.
 
picture the control verticy (alias) ... when you turn control points (proe). If the curve is converted to a five degree you simply gain more control over the curve geometry for the subtle tweaks alias users enjoy. Pro/E user can get close to that kind of control.Key word close.

Back when I first started surfacing 1993 at Motorola I heard Alias users there (Leon Soren an alias spokesperson from the early days) exclaim more control over curve geometry.I would then add points to the curve tweak data not realizing I was adding more spans to the curve.That defeats the A-Class laws making the curve geometry more complex for no good reason other than software limitations.

Forcing G2 in the curve does not work well and it brakes. I ask PTC to give me real g2 continuity contrasts and they give me a room number. That's a different department.I get around that with the ford interior on my surfacing presentation to the international community PTCUSER event http://www.proetools.com/talk/ <notice the ford. It is a work around but that what I am good at. Workaounds!

I cover much of this type of stuff thru serious comparisons in the last day of a one week class to the more advanced users.

I invited some industrial designers over from core77 just now.
Edited by: design-engine
 
I think I need a refresher. I remember you running thruthe Alias comparisonbut sometimes I need to see something 2 or 5 times before it sinks in. Its going to take me weeks just parsing thru all the linkson this post.


So the fifth degree curve has 6 cv's and G3 manipulates 3 of them closest to the connection? From one of the previous links each cv has some weight of basis function Ni,k(t). Does degree of continuity affect the weight?I guess this would mean that when you up the connection a G and the cv's move differently, ("slower"?). Maybe this was explained but I missed it.
 
Jacek,
> I do not know what particular benefits one can have ...
> ... apart of feeding its own curiosity(that is my reason).


Sometimes curiosity is all that drives me as well and I do tend to
limit my scope to whatever 'practical' application might be of interest
at the moment. But, there's always the next unknown application waiting
around the bend. ;^)


We've probably all seen, when importing models, a message saying something
to the effect of "Surface was split due to G2 discontinuities.". Anyone
know what that means and why it occurs? The answer is buried in this
discussion. (Hint: knot multiplicity)
_ _ _ _


Bart,
> Forcing G2 in the curve does not work well and it brakes.
> I ask PTC to give me real g2 continuity contrasts and
> they give me a room number. That's a different department.


Your explanations would be well served by graphic demonstrations of what
you're trying to describe.


Are we talking about 'forcing' continuity where bounding conditions will
doom us to failure (quite common for G2 constraints) or, and I think this
is it, the limitations of system generated solutions and qualities inherent
to degree 3 b-splines vs. degree 4 or 5 beziers? In that vein the pics
(which are contrived and actually represent all assumptions because they
are all interacting) show two conditions commonly encountered:
(1) A 'nervous' blend; if it is even possible (I don't think it is) to
contort a degree 4 or 5 bezier in a similar manner you'd, at least,
have to work a lot harder to do so.
(2) An equal, but reversed, curvature. It's a little tricky to understand
without knowledge system algorithms. But it is obvious that the logic
involved to solve for a degree 5 curve (6 CVs, 3 for each end allowing
independent curvature solutions for each end) is simpler than adding
knot spans to a degree 3 curve.

(I do wonder about the algorithms involved. I've mentioned, re
defining curvature by explicit CV positioning that the solutions
are ambiguous. I've often wondered how the real guys (programmers)
actually deal with the situations. Talk about over my head ... makes
me dizzy.)




_ _ _ _


mgnt8,
> Does degree of continuity affect the weight?


I'm not following the specifics of your question but just thought I'd
mention; "weight" has multiple meanings, could be (1) bulge / stretch /
influence factor or it could be (2) the fourth 'coordinate' value of a
rational curve CV. Either meaning ~could~ be applied to a continuity
discussion but, as far as I know (? so this is, in part, a question) the
only rational curves Pro/E will create are elliptical or hyperbolic conic
arcs.
Edited by: jeff4136
 
The way I see understand the weight of a surface generated from a curve stems from simply 'spans' or knots. The surface has an isoparm or a not in it then it is considered heavy and probably not an a-class surface.

I have posted images of that stuff on the forum before.
Edited by: design-engine
 
... Just thought I'd add: Similar to deg 5 curves and G2 solutions, a degree 7 curve will allow independent G3 solutions.


I would also like to pose the question: Does Alias have an explicit G3 Constraint?
 
yes.... depending upon exactly what explicit means. In Alias v13 you have a blend curve tool that explicitly lets a designer define up to g4. Let me finish playing with RSD and Ill post some images.



g4.jpg

Notice in the pull out for the blend curve tool that we have options all the way to G4
Edited by: design-engine
 
> The way I see understand the weight of a surface generated
> from a curve stems from simply 'spans' or knots.


Ok, there's a third definition.


> The surface has an isoparm or a not in it then it ...


Isoparametric curve or a knot? The definition of an Isoparametric Curve
is a curve on a surface at U(t) or V(t). Correct? If so there are an
infinite number of isoparametric curves on a surface.


I think it's important to understand the definitions, in whatever context
they are intended, of terms if we're going to use them. The subject matter
is confusing enough as is.


> depending upon exactly what explicit means.


Can you 'contrain' or 'set' G3 or can you 'achieve' it by manipulating CVs
(or whatever means)?


> Let me finish playing with RSD and Ill post some images.


Super deal. Routed systems are no fun anyway. ;^)
 
When I forced the blend curve to G4 I automaticly got 3 spans to the curve.

Should i define spans
Knots
Degree of the curve
Isoparms

g401.jpg

In this image we have two surfaces with blend curve joining them (middle).The close curve has g4 constraint (which is why the surface has the knots (isoparms) on only one side. The other Blend curve is only g1 on each side.
Edited by: design-engine
 
our Alias Instructor is trying to get the administrator of Design Engine (the school) to fly in an Automobile designer consultant for a Saturday Auto styling class for just us. I just became friends with him on Linkedin.comGuess if the economy tanks we will not be able to do it.
Edited by: design-engine
 
Span is ambiguous but generally accepted as a "piece" of a spline where a specific basis function is used. The span between knots. Are we in agreement?


Knot and degree have established (ISO?) definitions.


Isoparm, as you intend, means an isoparametric curve coincident with knot position?



Edited by: jeff4136
 
yes.

Ispoparms come from the extra span in a curve but only show up on surfaces. PTC and wikipedia refer to those as knots.A curve in Pro/E sketch mode that has an extra pick point to define the curve (three digged points to define it) would be two spans.

spans01.jpg

proe sketch showing two splines both with two spans. The top one has control points turned on and the bottom with out control points.Both would three degree two span curves.Build a surface off that then you get a span in the surface (proe does not display ispoparms or knots) I am trying to get PTC to let us have a display setting in the Model Display settings for Knots/ispoparms.

Currently we have to export the model to Alias to see. In a class I say.... "if you want to sit at the cool table at GM then you have no ispoarms in your geometry"
Edited by: design-engine
 
killer PDF! We can now model with those similar techniques in pro/ENGINEER with the SE tool. i have already designed the class (with our Alias instructor).

Its a lot to throw into a one week surfacing class and should be a complete separate week. I saved that one off Jeff! You still can not create a curve on surface in Alias Studio 2009 where you force tangency on one end or the other like in ISDX.Notice in your PDF they create the curve, force tangency then project.I teach that technique in Pro/ENGINEER surfacing too.
Edited by: design-engine
 
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