difference between arc and freeform curve

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 From:  wimverbe
6581.1 
why is it impossible to create an arc with the freeform tool?

I create a 90 degree arc, radius = 3 units, then I create a freeform curve with exactly the same control points, and I get 2 different curves. even moving the points of the arc, then placing them back to the original spot, generates a perfect quarter circle, but it is impossible to mimick that with only 3 points of a freeform curve. see below, the selected one is the freeform curve. both curves have show points on.

it seems that there is different formula behind the 2 types of curve, but when integrating the arc in a larger path, and disassembling it again, the properties stay the same.

it's not a big deal, but it puzzles me...
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 From:  anto matkovic (AMM)
6581.2 In reply to 6581.1 
yeah that's possibility of Nurbs, set of same points does not means the same curve. Arc or circle, if I'm correct (I could be totally wrong), this is the case when nurbs curve is 'rational', parts of NURBS curve are affected by multiple points.
In some DCC apps, like Maya or Softimage, it's possible to change the way how curve is drawn, relative to control points- but not to make the perfect circle or arc ( again if I'm correct). In MoI, formula is chosen by method you used for drawing.
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 From:  Michael Gibson
6581.3 In reply to 6581.1 
Hi wim,

> it seems that there is different formula behind the 2 types of curve

Yup, there is... NURBS curves have an additional value that is stored with each control point, the additional value is called a "weight".

The control point curve doesn't use weights, well it technically uses them but has them all set to the same value which means they don't have any effect.

The arc curve has the weights set to particular values to make the shape of the curve come out to an exact conic section (arc, ellipse, parabola, hyperbola type shapes). Like Anto writes above when a curve uses weights the curve is called a "rational" curve, it's what the R in NURBS stands for.

You can this in action by using the Draw curve > More > conic command. That will allow you to create a variety of different conic curves where you can have the same 3 control points for each of them but have different result shapes because of different weights being applied.

So yeah the trick is that there is an additional piece of information (weights) that is being used for the arc case and that's what is different from the freeform control point case, the freeform curve has all weights set to 1.

- Michael
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 From:  BurrMan
6581.4 In reply to 6581.3 
Can we get weight editing? Like the ability to go back to the RHO setting part of the conic?
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 From:  noskule
6581.5 In reply to 6581.4 
yes, I vote for that to. Now, in cases where I need a real arce in a curve I have to use two tools to get a cure done.
~nos

EDITED: 26 Mar 2014 by NOSKULE

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 From:  DannyT (DANTAS)
6581.6 In reply to 6581.5 
Burr dude,

I just want to get an understanding of where you would use weight adjustment on a curve? it's just that do we really need to get this deep into the workings of NURBS, then what, knot adjustment, degree adjustment I've have access to all of those in NX I've looked into them probably twice in the 12 years of using the software.

Just curious
~Danny~
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 From:  wimverbe
6581.7 
Thanks all! I have learned again!

cheers
wim

EDITED: 26 Mar 2014 by WIMVERBE

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 From:  noskule
6581.8 
@danny
The idea would be that you get an exact arc when the previous and following point of a given (not-corner-)point has the same distance and is a corner point. For example used in guide rails where you have freeform curves mixed with arces and the arc has a fixed radius. The benefit would be you could draw the guide rail in one step/with one tool instead of using lines arc and freeform tool.
~nos
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 From:  noskule
6581.9 
btw, would it be possible to have a shortcut for switching on/off the cornerpoint option while drawing a freeform curfe?
~nos
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 From:  BurrMan
6581.10 In reply to 6581.6 
Hi Danny.

""I just want to get an understanding of where you would use weight adjustment on a curve?""""""""

I was envisioning it helping me in reverse engineering. I could use it in conjunction with rebuild, and then use it to get some actual numbers to crunch things together.

But it's more that I wished I had NX probably... :o

Also, I can do pretty much anything I need to do in MoI now, and just ran out of things to ask for/about!

Maybe I could get double entendre-varying-blend edit-connector package-add-on-manipulator added to the next beta? :)
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 From:  bemfarmer
6581.11 
Just wondered if rebuild uses weights?
:-)

- Brian
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 From:  Michael Gibson
6581.12 In reply to 6581.4 
Hi Burr,

> Can we get weight editing?

Yeah eventually I think that will get added in, I want to have some point properties that show up when you select just one point and I guess weight can be included there.

It's not really all that useful though.

- Michael
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 From:  Michael Gibson
6581.13 In reply to 6581.5 
Hi nos,

> yes, I vote for that to. Now, in cases where I need a real
> arce in a curve I have to use two tools to get a cure done.

That will still really be the case even if you could edit the weight, because it has to be set to a very specific particular value (like square root of 2) in order to generate an exact arc piece.

It's better to use one of the arc tools when you want to make an arc.

- Michael
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 From:  Michael Gibson
6581.14 In reply to 6581.9 
Hi nos,

> btw, would it be possible to have a shortcut for switching on/off
> the cornerpoint option while drawing a freeform curfe?

Yup, you can do that currently by holding down the Ctrl key when you click points, when you hold down Ctrl it's the same thing as if you had checked the corner point option.

- Michael
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 From:  Michael Gibson
6581.15 In reply to 6581.11 
Hi Brian,

> Just wondered if rebuild uses weights?

Nope, rebuild does not use weights itself.

Weights in NURBS curves are primarily useful for generating conic sections related stuff, not really for general purpose fitting operations. They way they work is kind of hard to deal with intuitively, they work by a projection of 4D coordinates into 3D by dividing the x,y,z coordinates by the weight value. But the math works out well doing this for generating conic sections though.

They can sometimes be used as a curve editing tool, when you manipulate the weight it will have an effect of pulling the curve more towards that point. That's not very often used though but it's the main reason why I would add it in later on at some point.

- Michael
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 From:  noskule
6581.16 In reply to 6581.13 
hi michael
but isn't the "very specific particular value" allways the same when the the distance between a curfe point and a previous and a following corner point is identical? The identical distance I can do simply with a constration line / reorient.

~nos


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 From:  Michael Gibson
6581.17 In reply to 6581.16 
Hi nos,

> but isn't the "very specific particular value" allways the same
> when the the distance between a curfe point and a previous
> and a following corner point is identical?

I guess maybe so, I don't quite remember the details off the top of my head. But you would need to type in some kind of formula for generating the weight value. That will probably be pretty weird, I don't think it will be very useful for what you are talking about.

For a segment like you show above you can use Draw curve > More > Conic for that - when each endpoint of the conic is snapped on to the end of a curve, the intersection point between those end tangents will be available as a snap point for the middle shoulder point pick, it will show as a tan/tan snap point. Then put in a rho value of 0.5 to make an ellipse conic, the ellipse will be a circle if the conditions are right for that.

- Michael
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