Hi Jean-Paul,

RE: two curves

> The bottom one is the shape I want (based on a blueprint, etc.).
> I built it by blending two straight lines with a G2 blend,
> thus getting a 3-segment curve. If revolved, lofted etc.,
> it will show identical segments in the surface, a less
> than desirable outcome if it can be avoided

I have to disagree with your statement, the curve you created with the G2 blend will give you a technically smoother surface than the top 'single segment' curve.
The joins between those curves have no bearing on the smoothness, they are part of the NURBS world, if you were to create a surface, either by revolving, lofted etc. from the G2 curve and rendered it, there would be no signs of those joins, it would show a continuous smooth surface, and the 'single segment' curve would look good also, but it's not perfect.

I try to model with the simplest geometry possible, lines, circles and arcs where possible, in that way I know I have sound geometry, when I use the modeling tools on these curves things tend to work more smoothly, like Booleans and blends.

I reproduced your curves and took them into a CAD program that has analysis tools, (I think Rhino has the same tools) to show you what I mean.

Here are the curves in MoI, I added an additional one which is made up of 5 segments, 3 straight lines and 2 arcs.



Here are the three curves analysed showing there curvature combs, the smoother the comb the better.



As you can see the top curve is the most undesirable, technically, If you were asked to model something by a company who required A-class surfaces for that shape, sorry to say but the top 'single segment' curve would be rejected, if they analysed it that is.

If Rhino has the comb tool you can manipulate the 'single segment' curve until you get smooth looking combs.

Cheers

@ DannyT

I agree with what you say. It is a pity I discarded the curves I drew this morning, but I did evaluate the curvature with the combs tool that Rhino has too. I concur with your analysis, although I think that my “single” curve did not display such a poor continuity.

My point was rather that it would be better to have surfaces that are made with continuous curves (but proper, smooth ones) rather than segments because they lend themselves much better to further transformation like cutting, booleans and blends etc. than if there is a segment line in the middle of a cut-out opening for which you want a blend with another piece.

In this recreated example, the bottom curve is the 3-parts with G2 blend one, and the top is the single smooth one. The combs show similar fairness, although the G2 curve is somewhat cleaner. The surfaces generated with both curves look very similar, and indeed the various toolds in Rhino (zebra, environment map etc.) are nearly identical. The G2 curve is possibly a bit better, but not by much.



But I would anticipate less trouble with the surface generated from the single curve when working with the cut-out circles, as the edges running across a segment line are segmented.

I think the segmented seam curves will become less of a factor as MoI matures.

Hi Danny, just a quick note on continuity - when you have a curve that is a "single segment" (formed with only one single spline instead of multiple splines touching end to end), if it is the most common cubic curve than that does give you an internal G2 continuity throughout the whole spline unless there are special things like fully multiple knots or stacked control points.

That's for NURBS curves though - a "bezier curve" as often made by 2D illustration software is not as good for G2 continuity because it basically has fully multiple knots for every curve span.

It's pretty frequent for curvature combs to be somewhat misused and over obsessed with though - when the comb itself has cusp points in it, that is actually G2 continuity, that's when the curvature is equal at a juncture point.

When the comb is completely smooth throughout, that actually means G3 continuity, where the rate of change of the curvature is continuous, not just the curvature itself being continuous.

There is not really as much of a physically noticeable difference between G2 and G3 continuity like there is between G1 and G2 with reflection lines.

The other thing is that it can often be better to be more concerned with "fairness" rather than the actual technical continuity. Pieces can be technically continuous but still have poor curvature distribution. Continuity is about how things match up at a certain point but not really about how they are distributed which tends to be actually more important in shaping.

- Michael

Hi Jean-Paul,

If you like no seam lines in your models, then yes, I agree in what your doing, but there would be some situations where you can't avoid them, I think the extra work has minimal effect for the final outcome, like the model with the seams is quite acceptable, you can still apply a fillet around the hole the only difference is you have to pick 3 edge segments, but it still fillets.

All I'm trying to say is one method is as good as the other, I don't think in saying that the model with seams, is less than desirable is a correct statement.

Cheers
~Danny~

Hi Michael,

> It's pretty frequent for curvature combs
> to be somewhat misused and over obsessed
> with though - when the comb itself has cusp
> points in it, that is actually G2 continuity,
> that's when the curvature is equal at a juncture point.

I agree with this, I don't really use comb analysis much myself.
I was just trying to point out to Jean-Paul that there was nothing wrong with the curve with the G2 blend that produced seams in the model.

I was trained with all these rules in producing 'technically correct' curves and felt then that it took the gloss off 3d modeling a bit.
There's a definition I like for A-Class surfaces that I came across.

"An A-Class surface is a surface that is smooth and appealing to the eye"

So I figured no matter how the surface was built, as long as it looked smooth and flowing and the reflections were good, it didn't really matter what degree or how many segments and what the comb looked like for the underlying spline.

Cheers