Hi Mike, ok but what I have been trying to describe is that all you need to do is run Rebuild on that bendy curve and then after you have done that the rebuilt version of it has "arc length parameterization" - meaning that it will be a match to a simple single line as far as traveling along each in a uniform manner.

So if you want your revolve or extrude to have a "uniform traveling speed" matching property to a straight line, it's not necessary to construct such a complex multi-point straight line version of your curve like you are doing there, instead do a rebuild of your bendy curve before you construct your surface out of it and just have a simple regular line segment for the line.

Also note that none of this applies to curve-to-curve flow at all, it only deals with distance as traveled along the curve and so parameterization and control point spacing does not have any effect there.

Anyway, the key thing that I'm trying to explain is that yes - your bendy curve there that was drawn from Draw curve > Freeform > Control points has uneven parameterization as you currently show it. But if that uneven parameterization is going to cause a problem for you later on with surface-to-surface Flow then just run Rebuild on it (with "Refit to tolerance mode, not # of points mode), and the resulting rebuilt curve does not have uneven parameterization on it anymore. An even arc length parameterization is one of the properties of rebuild.

- Michael

> Hi Mike, ok but what I have been trying to describe is that all you need to do is run Rebuild on that bendy curve and then after you have done that the rebuilt version of it has "arc length parameterization" - meaning that it will be a match to a simple single line as far as traveling along each in a uniform manner.

Thanks Michael, that has awesome potential!

Let's take a look at how to implement this:

PREPARATION FOR FLOW BY USING REBUILD+UNWRAPCURVE



(looking at the pic)
The first curve at the top is the original spline representing the profile of our TARGET Flow surface.
The second curve in the middle was derived from the same profile curve using the Rebuild command. I chose 100# points, which as Michael pointed is used to build arcs or (near) even displacement along the curve's path.
The third line was derived from the profile curve using the new UnwrapCurve script.
It has also been rebuild (Rebuild) using 100# points, though it is still straight.

The advantage of using UnwrapCurve is to derive a line that is a close approximation of the true length of the profile curve when it is stretched out.
Therefore, when used as a Flow target, there shouldn't be too much overall length or dimensional distortion in the final result.
The goal is to make the original objects appear to flow along a surface naturally.

Now I'll use the profiles:
Note - You can also rebuild and unwrap curves (up to all four sides) to make a more complex Network.
In this case, I Extrude the profiles and the line in order to create Target and Reference surface to try Flow with.



As you can see in this pic, the underlying points (isocurve) structures of these surfaces are constructed from the points within the profile curves.
These underlying arrangements will determine the the final placement of the flowed objects regardless of the appearance of the surfaces.


Here, I'll create a nice pattern to be flowed onto a surface created from my original profile:



I chose these pentagon/circle shapes to make a test pattern. Their shapes make it easy to see any relative distortion on the spatial arrangements when flowed.


And here is the result!:



The Flow result on the top surface derived from the original profile curve has an awful displacement. (awful for what I needed in this instance) The distortions follow the "parameterization" of the control point arrangement in the original spline. This effect has advantages too and allows you to do neat things where this type of distortion is needed.

Ah! And you can see the Flow result in the middle. It has a very consistent-looking displacement.
For the Flow placement of shallow object arrangements, you can get very natural results this way.
Of course, the displacement of a flow is most accurate at the base surface level. As you move through the W (above and below) of the surface, distortion will occur due to the variances in the angular re-arrangements of the flowed objects. In other words, pinching and expanding will naturally occur.

I'm curious to try both a U and V arrangement.

Cool. I sense a new round of creativity is about to begin :)

Ed

yeah,... lol...

Peace,
Rich_Art. ;-)

Oh the shear power and glory!
Michael throwing new scripts and features into the mix is like throwing fresh meat into a shark pool. ;-)




Oh yes... there is much potential here.
Though there is a little distortion along the middle, these Flowed objects placed quite well.

With this model I first made a ring shape by Sweeping a single arc around two bent circles.
I didn't use the surface created by the sweep, but I was able to project some lines to give me some accurate arcs.

All four boundary arcs were Rebuilt to 50# points. I made an extra one in the middle to help with making the Network.
So I made a 50x50 isocurve surface with Network for the side of this ring shape.

I used UnwrapCurve to make the four lengths needed for the planar reference surface.
I had to approximate the arc curve for the sides. Flattening one of the original arcs in an "ortho" direction helped make that.

I made sure to Rebuild the flat curves to the same number so that the two surface would jibe when Flowed.

A method like this means I have more control when Flowing art, type or patterns on something like a ring.
I didn't have to contend with squeezing or anything strange... I know some of you are itching to try this out!
Not that this could not be more easily achieved by guessing and going for a straight flow, but this works so well. ;-)

Hi Mike, those are great looking results!

You may want to use the "Refit to tolerance" mode for the rebuild though (try with a tolerance of 0.001), since that mode is able to add more detail to the rebuilt curve only in areas where it is more bendy, while at the same time giving a result that has an evenly distributed parametrization.

Also you should get the same results that you show with just leaving the line totally alone, you should not need to rebuild the line.

There is not any need to actually get the exact same number of control points in both the base and target curves - what you instead need is for each curve to have an evenly distributed parameterization which a line will already have without rebuilding it.

- Michael

Thanks for the pointers!

> You may want to use the "Refit to tolerance" mode for the rebuild though (try with a tolerance of 0.001)



Ehh... :-/ For some reason, that way ends up with unevenly distributed points.

Hi Mike,

> Ehh... :-/ For some reason, that way ends up with unevenly distributed points.

Yes it does, and it's supposed to - it adds more refinement in areas that are bendy.

But it also at the same time uses a knot vector spacing for the generated curve so that the parameterization matches that point spacing.

So the actual curve that is generated there has an even parameterization and will generate the same kind of "no stretching or squishing" result even though it has a non-uniform distribution of control points.

The key quality of the curve that you want to have is not actually "evenly distributed control points" - the thing you are looking for is actually "evenly distributed parameterization". The result of Rebuild with "refit to tolerance" mode will deliver that despite having non-uniform control point distribution.

- Michael

"evenly distributed parameterization".

Something we dont/cant see.... Part of the underlying definition of the geometry.....

Like how sausage is made.... ;-)

Oh, thats just wrong.... (or is it right?)

Hi Burr,

> Something we dont/cant see.... Part of the underlying definition of the geometry.....

Yup, the parametrization comes from one of the pieces of data that makes up a NURBS curve - the "knot vector".

The data for the knot vector is just a list of increasing numbers like this for instance: 5, 6, 10, 20, 52

That knot vector there for example makes a curve that has a domain of 5 to 52 - that means that for every value between 5 and 52 the curve can be evaluated at that parameter value to produce a point location. That numeric range from 5 to 52 is the "parameter space" of the curve - a one-dimensional space that's part of the curve definition. Surfaces have 2 knot vectors, one for the U direction and one for the V direction and so they have a two dimensional parameter space.

The knot vector is not something you usually see directly because it would involve some huge spew of super techno-geek information that you would not particularly be able to do anything with.

But the knot vector comes into play in the overall mechanics of how the NURBS curve works - the relative spacing between different knots is one thing that affects how much influence the control points in that region of the curve have on the shape of the curve. Just to complicate matters there is also another totally separate type of data called "weights" that can also affect a control point's influence but the weights exist primarily because the particular type of influence they have is able to be leveraged to produce exact conic sections.

Being able to have different spacing between knot values is what gives the "NU" to NURBS, the NU stands for "Non-Uniform".

One of the main reasons why it is good to have this ability to do different knot spacings is to be able to more naturally set up interpolation through data points that deals better with the data points having some different spacing between them. When you try to interpolate an uneven distribution of points with a uniform spline (uniform means a knot vector with all equal spacing between all the knot values), it basically tries to produce the same length curve spans between each point and that makes for a sort of excess amount of curve being left over in areas where the points come closer together and that excess curve area makes for curly-cue type shapes in those areas.

The Rebuild command with the "fit to tolerance" method produces a curve that has a non-uniform knot spacing, but the spacing is based on the distances between the interpolated data points, so it matches the point spacing and makes the parameter space relate evenly to 3D space.

I've tried to make MoI set up in general so that you don't have to worry so much about these kinds of things, but it so happens that parametrization does come into play with surface-to-surface flow. I was able to make it not an issue in curve-to-curve flow since it is possible there to map distance traveled along each curve rather than just mapping parameter values from the base curve to the target curve. With a surface it's not so easy to do that since a surface can be warped and bulgy in multiple directions and have different distances across it in different areas.

And then to make things even more confusing, I guess it's even misleading when I wrote "evenly distributed parameterization" - to be more correct I guess it's more like "consistent distribution of parameter space as to 3D space".

- Michael

Michael, that was absolutely intriguing information. I had no clue it took so much to make a nice surface. (years of being stuck with four-point 2-D Brazier curves).

My PC at home is absolutely a giant lump of mud and it took two hours to do this version... man what a sad difference.




It worked!!! And it's even cleaner and more well groomed than the version using the arc-spacing points # method.

...interesting.... ;-) Chalk one up for Parameteorologicalivation!

Hi Mike, yup the "refit to tolerance" mode can tend to help resemble the original curve more accurately since it's adaptive and can add more detail just in bendy areas.

After you have done a rebuild like that, the result is all ready to go as far as eliminating parameter-space compression or stretching and it doesn't particularly matter how many control points are in the result.

So anyway, after all this I hope this explains why you it's not really needed to have an "unwrap to line with same control point structure" - instead of worrying about replicating the uneven spacing in your line it's far easier to just rebuild your bendy curve and then it's all ready at that point and will then match to a simple 2 point line segment just fine.

- Michael

Hi Michael,
Thanks for that explanation... I somewhat understood the original statement, but this explanation actually helps me in understanding some other stuff. In partucular, handeling data I read in with the opennurbs.dll. I would love to have big, long threads about it, though, I know that doesnt really fit into MoI's purpose or need.

Thanks again for taking the time with that response! Much appreciated.
Burr

Hi Burr, no problem!

Are you doing some kind of special project using OpenNURBS directly for your own program?

If you're stuck with dealing with 3DM data or understanding how some of the data is structured, you can open up a new thread with some questions in it if you like and I can try to at least point you in the right direction...

- Michael

Wow, thanks Michael,
At some point, I may take you up on that. Right now, I am just working on basics, that are just fundamentals I need to understand to undertake the task. I had an intent in doing some work with stuff to "add-on" to MoI.

""""""Are you doing some kind of special project using OpenNURBS directly for your own program?""""""""""

Yes. I'm working on reading 3dm data to my own viewport to interact with MoI, with minimal user managment...Like, at the moment, I can proceed with IGES, because I can read IGES, but that extra step kindof defeats the whole mission of MoI. So, I have a bit of work to do with just the simple 3dm studies, before I know what my questions are. (Also, alot of my goals became your goals, so I'm still on the fence)

I may find my goals to be a bit above my head, but if I get my head above ground, then some of the questions may be very helpful...

The offer is very valuable to me.... Thank you for that.

Burr

Hi Burr, do you mean one of your goals with your own 3DM reader was to do a curve length unwrapper like this one here? Do you have some other specific stuff that you are trying to get done?

- Michael

Hi Michael,
"""""""""do you mean one of your goals with your own 3DM reader was to do a curve length unwrapper like this one here?""""""""
No, totally unrelated... It was just a better understanding of what the underlying definition is.. Kindof like learning to read what I'm looking at when looking at the raw NURBS data. An analogy could be understanding how to write html with notepad instead of a wysiwyg editor. If I could write a 3dm file with notepad and then just compile it, I would be better at working with it!

This new function is also very cool for know the the length of curves ;)