Hi Brian, I didn't really tackle that in the help file because it is pretty difficult to describe without going into technical details.

Basically it has to do with smoothness.

When 2 curves or surfaces are tangent to one another, that is one level of smoothness.

But there are additional levels beyond that - for example if you have a line and then and arc meeting such that they are tangent, there is still a change in "curvature" between them.

Curvature is basically what radius of a circle a curve resembles at any given point, kind of like how much it is bending at any one point along it. If the curvature between 2 different curves is the same when they meet, that is called G2 or curvature continuity. Tangent is G1 continuity. G3 is a shared rate of change of curvature between the 2 pieces.

The options that say "Blend" mean that instead of a circular arc, there will be a somewhat more organic and arbitrary shaped curve between them, with the given amount of continuity (G1 = tangent continuous, G2 = Curvature continuous, G3 = rate of change of curvature continuous).

One other thing is that the higher types of continuity also require more complex surfaces to be built - tangent requires 4 points for each cross-section, G2 requires 6 points for each cross-section, and G3 requires 8 points for each cross section. So the geometry gets heavier as you use higher continuity.

Things that are curvature continuous have some interesting properties when it comes to reflections - just tangent continuous things will cause a break in the reflection where it crosses the line between the 2 surfaces, while G2 continuous surfaces will have a smoother looking reflection line. So these things tend to come into play a lot more for objects that are highly reflective like car bodies.

- Michael