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G2 by constraining poles?

Genius
Genius
During creating splines in sketch, G2 continuity can be set up. But once the creation process is finished, any further editing operation would destroy some constraints of the spline, often leading to failure of the whole model.
 
Therefore I'm thinking about avoiding set continuity constraints during spline creation, but applying certain constraints on the poles to achive desired continuity later.
 
If a spline is to be G2 contiuous with a straight line, I can simply constrain two poles on the line as shown below.
 
Image.png
 
If a spline is to be G2 contiuous with another spline, I'm lost. Is there any trick to get it done?
 
Image.png
 
Thanks!
6 REPLIES

Re: G2 by constraining poles?

Siemens Phenom Siemens Phenom
Siemens Phenom

I would not recommend that working method.

Much better to work with splines outside of the sketcher. Use the Studio Spline constraint functions.

Steve V

Re: G2 by constraining poles?

Genius
Genius

Hi @StevenVickers

 

Yes, splines outside of the sketcher are very robust choice. But I must say that, the temptation of the flexibility, of constraining poles to control the spline shape in sketcher, is really difficult to resist.

 

Thanks!

Re: G2 by constraining poles?

Siemens Phenom Siemens Phenom
Siemens Phenom

Hi,

 

One thing that might help is this:

The spline can create a G2 constraint, but there is an additional part in the dialog to this that constraints the spline even further. You can set the tangent magnitude and lock it. This constraints two DOF's (degree of freedom) on the first pole completely and one DOF on the second pole.

 

See movie below.

(view in My Videos)

This might not solve your problem, but maybe this tip gives you new ideas on how to constrain the splines in sketcher.

 

The other value overwrites the radius size that was inferred from the arc with a fixed value. You probably do not want to toggle that on.

 

Regards, **bleep**

Re: G2 by constraining poles?

Siemens Phenom Siemens Phenom
Siemens Phenom

There is a fairly simple formula for the curvature of a Bezier curve at an end-point. For example, see formula (2.13) in http://cagd.cs.byu.edu/~557/text/ch2.pdf.

 

Geometrically, this formula is a statement about certain lengths and distances, so conceivably you could use it to concoct suitable constraints on the curve poles.

 

However, this doesn't seem like a very good approach, to me.

山田
yamada

Re: G2 by constraining poles?

Genius
Genius

Hi @DickBaardse Thanks a lot for your tips and information!

 

Hi @Yamada

 

The formula (2.13) for calculating the curvature at a point on a spline is exactly what I'm looking for.

 

As you said, it is not a very good approach. However, when you have a big model and need to add a G2 constraint to a spline in sketch, to constrain the poles seems to be the only choice. In my experience, to click open and edit an exising spline would destroy some consraints and lead to disaster for the whole model.

 

Following the reference you cited, the curvature radius at a spline point can be calculated as shown below. Very good!

 

As @StevenVickers said in a previous thread, "NX in general will create a non-rational spline, that is the weight of each control point (pole) is the same." So I set w0/w1/w2 all to be 1.

 

Image.png

Image.png

Image.png

Re: G2 by constraining poles?

Siemens Phenom Siemens Phenom
Siemens Phenom

NX will almost always create polynomial splines, so setting all the weights equal to 1 is the right thing to do. Glad it worked.

山田
yamada