Curvature Smooth Splines

Jerry,

You're not going to be able to mimic this because SW splines or the tangent relation control for the continuity you are seeing from the Alias or even Rhino curves does not exist in SW (or we don't have access to it currently).

example we're talking about?..

Can the average person see this... it's subjective but yes they and you can see this and the machine cutting the material sees this. Does not having C2 or G2 or better effect adjacent boundaries and create problems when trying to work with other related curves and surfaces?.. yep!! Is it important for ID work?.. yep!!

The foundation of creating smooth transitions is to have C2/G2 or better control, SW does not have this.

Are there rules for getting the points or comb to be smoother.. well, you can zoom up really close, change the wireframe quality setting or even the spin box value and use the ctrl key when dragging or adding points and control frames but it's all eyeballing from there on.. Personally, adding a point close the the merge creates more problems and the turbulence your are seeing. So, yeah, you can tweak and fudge as you are doing now... but, as it is now with SW, you will not be able to attain what Alias or Rhino have....

What are your alternatives.. 3rd party tools like, GW3D or SurfaceWorks...

SW curve continuity control really has and does suck, period.

Otherwise, put in a ER for adding D-Cubes 2D/3D continuity controls since SW Corp can't seem to do it themselves.

..

Jerry Steiger wrote:

Jerry:

Paul's basically right about the current spline tangency and continuity functions in SW. I've bombarded SW with examples of where even the limited functions that do exist don't work or don't work correctly.

There may be something else you can try, though. Have you given the "fit spline" any thought? Instead of drawing line spline arc and not getting the results you're looking for, maybe you could just draw line arc and make a fit spline.

Sometimes a fit spline will waver a bit where there are big changes in curvature, so the spline kind of overcompensates to one side and then comes back where it belongs. You may be able to control this by playing with the tolerance value or by deleting / adding / moving control points near the change similar to what you have been doing. The smaller the radius you're trying to fit, the tighter the tolerance you'll need to use.

Also, have you tried a Face Fillet with the "curvature continuous" switch turned on? It basically uses a spline based fillet instead of an arc based fillet. You still specify a radius value which turns out to be kind of an approximation, equivalent or average. If you create a fillet like this and convert entities on the edge created, and turn on the curvature comb, you may see little fluctuations in that too. I think the real problem is more likely to be that the display for the comb is fairly inaccurate, although I really can't cite any evidence.

I think the best way around this at the moment is to avoid the tangency issue altogether by making it all a single continuous spline. The curvature within the spline should change smoothly. I'd recommend not including sharp corners in the fit spline inless you want them rounded.

good luck

matt

"Jerry Steiger" wrote in news:c4pimc$2khiq2$ snipped-for-privacy@ID-200869.news.uni-berlin.de:

Is SW restricted to cubics?

Try adding two (or three well-spaced points ON the curves you wish to be tangent (C2) to and using them to define your spline. Then try trimming the spline back to the actual entity ends away from those extra points. Might work; might not. Depends on how "trim" actually works ....

Which is probably why the original designer worked in Alias. If he had the tools available in SW, he might have been working with it, and look how easy my job would be! And SW would have sold a few more seats.

Thanks for the example. The curves I am working with are even worse in a sense. Your curves are curvature continuous. Mine are even "smoother"; the transitions in the curvature are also smooth. (For the mathematically inclined, the first derivative of the curvature, or the second derivative of the spline, is also continuous.)

It's the "better" part that I was particularly concerned. Is it good enough to get my curves C2, or at least very close to C2? I've never seen any discussions about C3, which is what I am talking about, assuming that C1 is continuous curves and C2 is continuous curvature of the curves.

I was kind of afraid that was the answer.

Yeah, I've been learning that. The hardest part seems to be transitioning to a straight line.

I need to make more ERs. It's so much easier and fun to complain to this group.

Thanks for the help!

Jerry Steiger Tripod Data Systems "take the garbage out, dear" "

Whoops! Fit Spline was actually the first thing I tried. I wrote and re-wrote the note several times as I tried out various ideas. At some point I guess I dropped all of the comments about Fit Spline.

This was the problem I ran into. The curvature would go negative at the transitions between the sharp and shallow curvatures. It seemed to be more painful to try and get the Fit Spline tweaked than it was to just generate my own. Plus the "roughest" Fit Spline that came closoe enough to the original still had a lot more points than my version.

The particular curves I am working with now define the outline of a window in the part. I did use the Face Fillet with the Curvature Continuous option to generate the frame around the window. Seems to give me a pretty good match to what Alias made.

That's what seems to be working out best.

Thanks, Matt!

Jerry Steiger Tripod Data Systems "take the garbage out, dear"

Yep!

Understand. It's very good C2/G2 and better or C3/G3 and beyond.

Yeah, we don't have C3.

Good enough depends on the what the client is after or what is expected from the consumer? It may be good enough for most cases or where polishing and texturing will help hide the imperfections. Otherwise, it depends on the exposure of the transitions/blends?

So, depending on the transition/blend, I say good in the sense that SW C2 is good if the user is careful as you are trying to be with noting the curvature comb and distortions at/near the tangency. The other modeling systems generally have very good C2 and can be generally considered good enough as they are.

As for discussions on C3... well, maybe C2 should work very good first? Otherwise, yeah, it would be great to have options which force a C3!! Then, we can bitch at a different level!? 8^)

Yep, close one eye and use thumb and stick tongue out and bite really hard!

Well, the more we get the better chance it will be implemented?? More competition.... we need more competition.... and of course, fewer gear heads! 8^)

..

I don't think so. I can make a spline with an arbitrary number of inflection points. Seems like a cubic could only have one. Or does "cubic" mean something different in CAD/CAM land than it does in high school math?

I didn't come up with a way to use this method that helped in my particular case, but you can make an extended spline with points outside the region of interest and trim it off to just the part you want. When you trim it, nothing moves and the curvature comb doesn't change.

Thanks, Cliff.

Jerry Steiger Tripod Data Systems "take the garbage out, dear"

Not really BUT splines can be made up of segments (and usually are).

IF you have N control points and degree M allowed (max) you get segments if N-1 > M. Each segment is usually "smooth" with it's adjacent segments, at least for the second derivative.

Hence is you have 4 control points a cubic can be one segment (and the entire splins). If you are limited to cubics and have 5 points you get two segments.

You may be able to see what's going on if you look at an IGES export file, I don't recall.

IIRC Some systems allow NURBS of up to degree 18 or so. But as the degree goes up ALL the calculations needed to deal with the data (from making visual images to calculating intersections to NC) goes up very rapidly.

Naturally, if one system uses a higher degree polynomial then the system the data is being exported to you can have some problems in approximating things (try a cubic approximation of a 17th degree rational polynomial ). Not to mention exact accuracy.

I think that's what I suggested .

Hope it worked. How closely can you test or compare?

I tried extruding a surface from a 6 point spline that would require two cubics, then exporting to IGES. I thought it might show up as two faces when it came back in from IGES, but it showed up as a single face. Reading the IGES report, it said that there were two composite curves and two lines. This seemed to imply that the the spline was really a composite. It also said that there were 6 B-spline curves in the part, as if the spline were formed from 3 sections. But when I tried simpler two and three point splines, they all reported exactly the same.

Jerry Steiger Tripod Data Systems "take the garbage out, dear"

Any rules of thumb on

Nothing new, but here's a few that help me-

- use as few spline points as possible. Fewer points=smoother spline. Keep testing to see which ones you can delete

- use that start and end tangency on the spline (which I know you are doing anyway, but always good to remember. If the end of a spline has nothing to be tangent to, add a centerline to it)

- make very, very small tweaks to get that final smoothing. Turn your spin box to .001" and use the spin box in the property manager for the really delicate spline point maneuvers

- Before risking your spline to a potentially damaging edit, close out of the sketch, copy the sketch, and paste the copy on the same plane. Then drag the copy up the tree, above the original sketch, so you have it as a reference for the tweaks. Also, if things go south, you can refer to the copy to get the spline back to where it is supposed to be. For the new folks, remember - once you close out of a sketch, you lose any ability to undo what you just did. I like to save copies of the sketches as a revision history within the model instead of saving dozens of rev files which can be very hard to compare. Also, other things being equal, sketches on planes are preferred to sketches on faces because if you copy and paste to a face I don't know of any reliable way to repeatedly get the copy to land aligned with the original. Sketches copied from a plane and pasted on that plane line up automatically.

-Turn on your inflection points

-a couple of tightly spaced points can make radical things possible, but your requirement to be extremely precise goes up. If you can do the final tweaking with the mouse on the screen, I admire you - even holding down the CTRL key to disable inferencing and working in a split view with one showing the whole spline and the active view zoomed in really tight, I have trouble getting control on the screen that rivals spin boxes.

Single entity.

Two *lines*? Should show as two segments perhaps ... what was the degree shown?

Two & three points would only require less than a cubic (though cubics can be used .. you just get 0 for some terms.) Think of it his way: 2 points = line = degree 1, 3 points = conic section (such as a circle) - degree 2.

Does SW support splines of more than degree 3? Do you have any options to control such?

Yesterday's revelation was that two point splines somehow know that they were two point splines, even after you insert spline points in them. If you insert spline points into a three or more point spline, the points slide along the curve nicely. If you insert spline points into a two point spline, the points drag the curve along with them as they move, stretching it taut behind them and bunching it up in front of them. It doesn't matter whether you insert the new points one at a time or all at once. It doesn't matter whether the spline started life as a two point spline or was reduced to a two point spline by removing spline points.

The work arounds I've come up with are to either delete the "used-to-be-a-two-point" spline and replace it with a three or more point spline or delete the points and replace them with points closer to where you expect them to go.

So, two point splines are very nice where you can use them, but beware of their history if you really need a spline with more points!

Jerry Steiger Tripod Data Systems "take the garbage out, dear"

Whats kind of fun to know is that a 'two point spline' isn't a 'two point spline'. To get their behavior, SWx adds a hidden point near each end of the spline that we cannot access, edit or remove. You can manipulate the hidden point from the user end by making the two point spline tangent to something or, as you said, start with a three point spline which is at least one point less than a two point spline really is (unless you add tangnecy, which gives you a five point spline).

Been following the discussion in a casual way and this may already have been said....

A two point Non-Uniform Rational B-Spline (end point definitions only) is a degree 3 (minimum) curve. A NURBS curve, by definition, must have [degree +

1] control vertices (not fit points); e.g. the two point spline will have four control vertices. To achieve G1 (tangent) continuity the control vertices (the "hidden points near each end") are manipulated either directly by the user or transparently, depending on the software. To achieve G2 (curvature) continuity at both ends the curve must have a minimum of five control vertices, though it will usually have six (and can still be a two fit point curve, though it will be a degree 5 curve) and the two control vertices nearest the end point are manipulated to achieve continuity.

The smoothest, most relaxed curves (and much of the time it's all that's needed to get the curvature you want) are obtained by using a two fit point spline and defining some end condition (depending on what the particular software offers; tangent, curvature, perpendicular) and varying the condition "weight", span between control vertices (assuming the software gives the user controls to do so), to adjust the curve into the desired shape. Doing this will usually result in lighter, smoother, happier surfaces than adding fit points to the curves (a point I believe Mr. Eaton has made before).

Don't know how much of this is applicable (exposed to the user) in SW, but it may help explain what's going on behind the curtains.

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Four points total makes it a cubic. Probably for the NURBS math.

In the first place it should look like a line .... and probably act like one.

Three points should be less than a cubic. Might they not be adding one "hidden" point in this case as well?

Odd ...

Thanks, Ed, it's good to know these little details. It still doesn't explain the stretching and bunching behavior when moving points that are added to an initially two point spline.

Jerry Steiger Tripod Data Systems "take the garbage out, dear"

Deleting a simple explanation of some of the spline math

That's my problem with SW splines. In order to make the user interface simpler, SW hides almost everything behind the curtain, crippling my ability to get the job done.

Jerry Steiger Tripod Data Systems "take the garbage out, dear"