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# 1 18-03-2011 , 02:41 PM
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Join Date: Mar 2011
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some issues with curves and surfaces


I've been working with nurbs for a while, and since I am quite new to the thing, I have encountered some problems. Though I find it hard to explain them, I will try it.
1. Create a curve (cubic: degree 3) with the cv tool. give it more than four control vertices (8 would do). Make two random curve points (don't snap them to edit points). Detach the curve. Take the middle curve and show its control vertices. And now create a new curve with the cv tool by snapping to those vertices of that curve. What happens is that you will have 2 curves now, both with the same ammount and positions of Control vertices, and still they are different curves. I didnt get that.user added image
2. when you detach a curve, it will create 2 or more curves. When u zoom in to it very (very) close with an orthographic view, and keep pressing undo,redo,undo,redo, you will see that the curves continuity or flow changes. This doesn't happen when you snap you curve points. When you do that, and you detach the curve, the 2 or more curves that are the result keep the same continuity. I didn't get that either..user added image
3. Is there a way to create a perfect circle curve? Even when I create a circle with 49 vertices and one with 50 vertices, they still are different from each other. I can prove this have those 2 circles on the same position with the same size, than create a new straight curve through them, so that it looks like a "Q", than select them all and select "cut curves". The straight curve will be divided into 3 curves, instead of 2.
Wouldn't it be more fair of the perfect circle would be achieved with 8 control vertices. And when you create one with more vertices, it just will stay the same qua curvature? This annoys me.user added image

I believe that's about it. Hope it sounds familiaruser added image.

# 2 18-03-2011 , 04:36 PM
Join Date: Dec 2005
Location: Toronto
Posts: 3,374
Hi lucris, welcome to simply maya. That all sounds very mathy... I think ctbram might have some good answers for you, since he's pretty up on NURBS and continuity and such.
For 3, just go Create > NURBS > Circle... haha. But I think I see what you're saying. Have you tried using the rebuild curve tool? That might give you more control over standardizing your curvature etc. Hope that helps.

# 3 19-03-2011 , 02:59 PM
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Join Date: Jan 2004
Location: Michigan, USA
Posts: 2,998
1) Your issue has to do with parameterization, more specifically non-uniform parameterization. Your initial curve with 8 CV's will have 5 spans (8 minus 3) and 6 edit points (0 to 5).

This is all evenly parameterized == one unit between each edit point.

Now you cut a section from the middle of the initial curve leaving you with three curves. If you now look at the curve attributes you will see the parameterization is no longer uniform.

In my case my initial curve had 5 spans and was parameterized from 0 to 5

After cutting the center section I have 3 curves with non-uniform parameterization:

curve 1 - 2 spans from 0 to 1.361
curve 2 - 4 spans from 1.361 to 4.204
curve 3 - 1 span from 4.204 to 5

and tangency between the curves is maintained (G1 continuity).

Now if I draw a new curve by snapping to the CVs of the middle curve (curve 2) I get a slightly different curve! Why? Because the parameterization has changed! The new curve 2 (in my case) has the following:

new curve 2 - 4 spans from 0 to 4

Which means the new curve has uniform parameterization. Interestingly the new curve still maintains G1 continuity with curves 1 and 3. It's just the inner rate of curvature changes and so the middle section of the curve changes.

The bad news is Maya is an "artsy fartsy" program and although much of its NURBs tools where derived from a true surfacing application (studiotools now called alias) the necessary tools to adjust parameterization to correct this problem were not ported. Thus Maya's NURBs tool set is incomplete and you have to just deal with its quirks.

What you can do is after cutting the curves rebuild each with either uniform or curves selected. Yes, this will change the curves a bit but now each of the three curves will have uniform parameterization AND G1 continuity.

Now if you create a new curve by snapping to the CV's of any the 3 newly parameterized curves you will find the curves match their parent curve exactly because they will both have the same parameterization (ie all integer values).

The remaining two questions are dealing with the exact same problem. When you cut any curve you change its parameterization so that it is no longer uniform. Although, I am not sure if Q3 is true. If you cut a circle its shape should not change so I am not sure what you doing there.

You are never going to get a "perfect circle" only one that is such a close approximation as to be indiscernible from a perfect one unless you do as you did and zoom in infinitely close and if you are looking for that level of accuracy then Maya is not the application to use.

"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675

Last edited by ctbram; 19-03-2011 at 03:13 PM.
# 4 23-03-2011 , 12:16 PM
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Thank you. I think I quite get the thing now. Do you know of any site (or perhaps a book) that goes deep into understanding nurbs? A bit on the same level (or higher) as the question i asked.

# 5 23-03-2011 , 02:05 PM
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Join Date: Jan 2004
Location: Michigan, USA
Posts: 2,998
Unfortunately, for Maya I cannot think of any unless you go back to a book written for maybe Maya 4.x or lower. NURB's were more in favor then and there were not a lot of competitors (like rhino3d).

Maya's NURBs are really not very good (for detailed surfacing work) and have been neglected for some NINE! releases of maya since 4.x! My feeling is that Maya's NURBs are not destined to be improved in the near future (if at all) because there are much better applications available and alias would have to do a ground up re-write to really compete.

Sorry for the bad news. It saddens me as well as I started as a NURBs modeler and really appreciate there power. But such is life.

"If I have seen further it is by standing on the shoulders of giants." Sir Isaac Newton, 1675
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