As Alias modelers, we know all too well the added value of making our surfaces curvature continuous to each other.

As it is clearly and distinctly noticeable in the highlights of polished surfaces, and even to some extent matte plastics.

However, did you know it is not just an aesthetic thing?

Of course, we can plot a curvature comb on a set of tangent continuous surfaces and notice an abrupt jump and this tells us it is even from a geometrical standpoint not smooth.

Now put yourself in the shoes of the downstream process, when your Alias models go into a solid modeling package

to start fleshing out the model into manufacturing ready and fully detailed parts. Here topology is king, and even in the world of a mechanical solid modeler, curvature can be king, too.

Take this first example of tangency degradation when performing the additional fillet (shown in red) to round off the area where the cylinder meets the base surfaces:

Here in an excerpt regarding the above image:

“As picture shows, the contact curves (where the rolling sphere touches the underlying surfaces) often have puzzling corners. In fact, if the underlying surfaces are not G2, then the contact curves will not be G1. The corners are often surprising for users, and they then waste time trying to figure out what they did wrong. The algorithm is producing an answer that is “correct” (assuming we use the rolling sphere approach) but is often undesirable.”

Or perhaps take this excerpt from the Spatial (solid modeling kernel component) website:
“ACIS prefers that curves and surfaces generally be G2 continuous, but will allow G1 continuity at the knots of curves and surfaces. The C++ class discontinuity_info records discontinuity information. It is used internally by ACIS in the curve and surface extension and intersection algorithms. Certain iterative processes may converge slowly, or not at all, if there are significant discontinuities.”

Now to put that into a little bit of perspective,

the above excerpt is talking about a single surface or curve being G2 with-in, not multiple surfaces joined together like in the Alias image shown at the start of this article. In that case… to be honest, geometrically speaking a solid modeler won’t really care if they are merely tangent continuous across the edge.

Nevertheless, I hope this has given you at least a little bit of additional insight, and why (at least to some extent) curvature continuity is not just aesthetic!

Happy surfacing,
Kevin de Smet (advanced student at Learning Alias)

Kevin De Smet is currently modelling Electrical Harnesses for Bombardier
and continues to study Surfacing at an Advanced level with LA. We would also like to  thank him for his contribution to the LearninAlias Body of Learning Material.

www.learningalias.co.uk

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