Surface G0, G1, G2 Values 3

[baggieboy]

Hi there.
I was wondering if anyone could outline a few things for me. I'm currently trying to teach myself 'freeform' surfacing from CAST. However, when producing a surface it asks to set G values. What are they and when should i use G0, G1 or G2?
Thanks in advance!

 

[JohnRBaker]

OK, in it's simplest sense, the Gx designations describe the relationship between the adjoining faces of two surface that share a common edge.

In the case where two surface share a common edge but the adjoining faces are NOT smooth or continuous, it's said that these surfaces are G0 continuous.

In the case where two surface share a common edge and the adjoining faces are tangent, it's said that these surfaces are G1 continuous.

In the case where two surface share a common edge and the adjoining faces are curvature continuous, it's said that these surfaces are G2 continuous.

And there's even a case where if two surface share a common edge and the adjoining faces have the same rate of change of curvature, or acceleration, it's said that these surfaces are G3 continuous.

Anyway, I hope that helps explain what these designations mean.


John R. Baker, P.E.
Product 'Evangelist'
NX Design
Siemens PLM Software Inc.
Cypress, CA

http://www.siemens.com/plm

http://www.plmworld.org/museum/

 

[hudson888]

John is right in what he said perhaps I can expand to address the later part of you question. I believe you also wanted to know where to use the various kinds of curvature continuity. In the same vein as what John has described I'll give you some information about that for each type.

We can refer to these conditions as continuity constraints although the term continuity strictly speaking only applies to G2 and above. Unless you're into styling or industrial design you probably won't use G2 or G3. That is the short answer that can save you some reading below.

G0 means the ends or edges of curves or surfaces will meet the curve or surface that they are G0 with. Anyone who knows what tangency means will have deduced as much from John's post, because G0 it less than G1 which implies tangency. They can meet at any angle and have a G0 condition just so long as the two surfaces or curves touch either at the endpoints or edges respectively. This condition allows surfaces to be sewn or curves to form closed loop which will allow you to create solids for example.

G1 means tangency again just as John said. As with all of these conditions as the numbers increase one exceeds the other. Within the dialogs it is generally the case the G1 also implies or imparts a G0 condition and so on. In NX and several though I believe not all CAD systems as the G number increases the number of control points aligned with the base geometry will also increase. For tangency the first control point will align with the slope of the base geometry at the point where they meet. You need to get into control polygons a little to understand how curves and surfaces are built in CAD. Tangency is necessary to building good models in order to have blends and other swept geometry be constructed successfully. In fact the most common tangent features are corner radii or radius blends on surfaces or solids. In general engineering models require this basic level of smoothness it describes formed processes, provides for mold flow and promotes good structural integrity, (lack of stress raisers or fault lines). In most senses though it is simply what we have come to expect in the idealizes world of CAD modeling.

G2 is the first real continuity condition it is described in terms of knot points by the two nearest the end aligning with two on the opposite base curve or surface. It means that they have the same curvature locally where the ends meet. The difference between a radius that is tangent and circular in section and an edge blend that is curvature continuous is largely aesthetic. Light strikes a radius the point of tangency departure near the edges of the radius often showing as two highlights on either side of the center of the radius. A curvature continuous blend can be controlled so that the light strikes the surface as a single highlight at or near the apex of the blend, depending on how it is built. For styling purposes this is far superior and throughout the whole model edge conditions need to be continuous if light is to fall on highly reflective surfaces so that the product has pleasing highlights. This is in fact called highlighting and is used extensively in automotive and industrial design applications. In those circles the surfaces are usually referred to as A-class.

G3 is one better than G2 for surface continuity. It allows more control to reach further into the surfaces from the edges. Not only is the curvature continuous but the rate of curvature continuity is also said to be continuous. In practical purposes three control points re aligned and the degree of shape control is extended by that much. When used for A-class surfacing it allows surfaces including blends at the edges to be lead in a long way with a high degree of control over the results. Leading in means setting back the edges a lot further from the corners (these edges would be tangent lines of radius blends and are still widely referred to as such). In most cases the increased control provides better smoothness which hopefully translates to better highlights and improved styling.

These conditions apply to the ends of curves being created. In terms of the geometry that they're being applied to that condition may be applied anywhere along another curve or surface not just at the ands. The assumption being that you may want to create geometry first and trim it back later or use it elsewhere. In the majority of cases however it is also applied at a corresponding edge or endpoint of a line.

If you are keen on styling or A-class surfacing then my advice would be to study industrial design over reading about the maths of curves. While the maths of curves is quite interesting in its own right, it won't help you that much with using CAD packages unless you intend to write your own software. You need to know about control polygons and surface design basics starting with the kind of explanations I have offered above in order to real ramp up you surfacing skills.

Freeform surfacing is the basic surface package the comes with most Advanced Designer and above bundles, and which will suffice for most engineering needs. It can also double as a good industrial design tool, but the real A-class functions belong to the Studio surface module.

Best Regards

Hudson

 

[NXMold]

Check out

http://en.wikipedia.org/wiki/Nurbs

, it explains a lot of this as well.