## Have You Ever Wondered About Surface Continuity? G0, G1, and G2 Explained

In this blog post, we will look into the basics of surface development and gain an understanding of what continuity is. Years ago when I used to teach full time I would tell my students that I called it “continue-ity,” the reason being that you are essentially describing how one surface continues or flows into another surface. Technically, you could describe curves and how they flow with one another as well. So let’s get started.

G0 or Point Continuity is simply when one surface or curve touches another and they share the same boundary.  In the examples below, you can see what this could look like on both curves and surfaces.

G0 Continuity

G0 Curve Continuity

As we progress up the numbers on continuity, keep in mind that the previous number(s) before must exist in order for it to be true. In other words, you cant have G1 continuity unless you at least have G0 continuity. In a sense, it’s a prerequisite.  G1 or Tangent continuity or Angular continuity implies that two faces/surfaces meet along a common edge and that the tangent plane, at each point along the edge, is equal for both faces/surfaces. They share a common angle; the best example of this is a fillet, or a blend with Tangent Continuity or in some cases a Conic.  In the examples below, you can see what this could look like on both curves and surfaces.

G1 Continuity – Conic

G1 Curve Continuity – Fillet

G2 Continuity or Curvature continuity or Radial continuity implies two faces/surfaces meet along a common edge, are tangent, and the rate of curvature change at each point along the edge is equal for both faces/surfaces. The transition across the edge is therefore curvature continuous. This is the minimum math requirement for Class A Surface. Another way to describe this is in a situation where a reflection is cast upon the surfaces and you would not be able to tell where one patch ends and the other begins.  The examples of this in CATIA V5 would be a connect curve (with curvature continuity, or in the surface terminology in the GSD Workbench, a blend surface with curvature continuity or a fill surface that meets another). In the examples below, you can see what this could look like on both curves and surfaces.

G2 Surface Continuity

G2 Curve Continuity

There is also a G3 continuity, which follows the same process as its predecessors but controls the rate of the curvature along the curve as it transitions from one curve or surface to the other.  G3 is looking for balance on the rate of curvature – in other words, that the max value of the curvature hits its peak about the middle of the transition area. It is a bit outside of the scope of this blog post, but look for something in a future post on it, as well as how to check for these conditions in CATIA V5.

Bottom line: understanding continuity is a big deal when doing advanced surface work. At Tata Technologies we have the experts and have helped many companies with their other CATIA V5 Surfacing and Design needs as well. How can we help you?