Curvature Smooth Splines

We're building SW surfaces from the ID firm's Alias surfaces. I notice that
many of the splines from Alias are not just curvature continuous, but that
the curvature changes smoothly. I'm having a heck of a time trying to match
that characteristic with SW04.

Checking the curvature combs, several of the splines look exactly like
straight lines and radius sections joined by short splines. If I simplify
the original spline I get smooth curvature, but it has reverse curvature
areas where the straight and arced sections join the short splines and areas
where the curvature is quite different from the original.

If I try to build my own curve with straight lines, radii and splines, I
can't seem to get the splines to smoothly transition to no curvature
straight lines and small curvature radii. Two point splines don't match the
original spline and the curvature is discontinous at the ends. Three points
splines can match the spline fairly well but also have discontinuous
curvature. With four point splines I can get close enough to continuous
curvature, but the transition isn't smooth. Adding more points, I don't seem
to be able to make the transition any smoother.

I seem to get the closest by making my own single spline by placing a pair
of points very close to the ends of the "straight" and "radii" sections and
two or three points in the short spline sections, but I always seem to get
wobbles in my curvature comb that I can't get rid of. Any rules of thumb on
how to place my spline points?

Should I worry about making the splines curvature smooth? Is this a
characteristic that the eye even notices?

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

 

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?.. http://www.zxys.com/swparts/curvetest.zip

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:

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

 

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"

 

Jerry,

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"

 

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.

 

Thanks for the good tips, Ed. I've been doing it the way you suggest, except
that I'm not very good about saving copies of my sketches. (Hey, it's more
exciting without a net!)

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).

 

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"