In Inventor you can create curves and surfaces with different degrees of smoothness. This feature has been present for a reasonable amount of time in the most recent versions, and we can find it both in the sketch environment ("smoothed" constraint) and in the modelling environment.

For example, if we open the fillet creation/edit form in order to create a fillet, a panel with options will come out. Among the options you can choose between tangent and smooth, the latter option says " smooth fillet (G2)", as you can see in the image below.

The purpose of this article is to help you to understand what smooth connection means and to make a few considerations as well.

When we talk about CAD, and you hear about how smooth a surface is, what it is really meant is how good the transition zone between two patches is, these patches put together build a larger surface. In a few simple words, we are talking about how the continuity of curvature is.

In some areas of mechanics, you have to deal with curved and round surfaces, just imagine some design objects, or the cars’ hood, or simply a computer’s mouse. These, like many other objects, have curved and complex surfaces, which are impracticable to model with a single patch. The technique used for modeling them is to create more surfaces and then combine them together, possibly making sure that the conjunction between them is not visible, otherwise the result is not aesthetically pleasant.

This applies for both bidimensional and tridimensional surfaces. Let’s see the cases that may occur:

**No connection** and therefore no way to talk about continuity.

**G0 level**: the two curves simply touch each other at the ends (so no mathematical continuity, just end points coincident). The only condition here is: end points in the same position.

Going up with the continuity level we are required to put conditions on the derivatives: the first, the second and the third.

**G1 level**: it requires that the two curves have, at the point where they touch with each other, the same first derivative, it means they must be tangent to the end. A typical example of this type of continuity is the mechanical fillet.

**G2 level**: not only it requires the two curves have the same first derivative, but also the same second derivative at the exact point where they touch each other. This means that in addition to being tangent they must also have the same curvature.

This is a fundamental condition for all surfaces that have an aesthetic value. With these conditions you will make sure that the surface shows no discontinuity, even if it is being illuminated from different angles. Simply, watching the object you will not be able to understand where a patch begins and where the other ends.

**G3 level**:

In addition to the continuity G1 and G2’s requirements, it requires that also the third derivative is the same, which means that it has the same rate of variation of the curvature radius.

In Inventor there is no G3 constraint for lines and surfaces. This is a fairly specialized requirement, usually needed by those who model, for example class A surfaces in the automotive environment. In these kind of areas other tools are usually used, such as Alias, Catia or other tools.

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