Constant Radius Curves. A Mainstay in Good Design

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Here’s an interesting question sent in this morning by a student:

Hi Graham,
I have started on the mesh and immediately have a question, kind of a fundamental one. On the Audi design the bumper has positional breaks as it transitions up and down.

Knowing this, does the curve I just drew still want to exhibit this kind of acceleration towards the ends (like on a hood) or not?

(Pictured below)

[G

(pictured above)

This is better for the bumper, I think.

Regards,
K]

Answer:

Hi K,

The first crv. you showed has acceleration at the top and bottom, but a lot of crvs. on a model are simpy Railway crvs. and originate from the Clay Modeller using a plastic crv. template to drag a curved. sec. along say the bumper. Similarly the windscreen is usually formed by dragging 2 or 3 different crvd. alloy splines accross the clay slab and then sometimes, the edges of the windscreen or roof would be accelerated by dragging railway crvs. with a tighter rad.

Summary:

Beauty is often best created with the use of geometry. The Designer knows this and will only fiddle with pure geom. in certain areas of the ext. So Yes! the second crv. which is a constant Railway Curve is what you should stick to, but remember in complex areas, this rule may go out the window. Generally this surface would be a simple constant rad, but if the highlights are not what the designer requires he/she may well want the edges accelerated.

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Tangent Continuity, beyond the highlight

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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.

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Here are just 2 examples of the courses I run,
which will take you up to Industry enrty level. I only have time to mentor a handful of students, so please if you are interseted in applying send me your CV and your latest .wire if you have previous Alias experience. If you have no Alias experience, but are experienced on other 3D platforms, I will still consider your application seriously. The main thing I am looking for is real passion and committment to make it in the Alias Automotive Industry

“Course #1”. 6 Months website access to all video tutorials
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(Your work will be reviewed every 15 days and you will receive : feedback, instruction, tips and advice from me personally, modeling demonstrations from me on your .wire and I will supply Meshes to help you with difficult areas of your model. )
167 Euros (228 USD equivalent) per month. You will learn how to build 2 complete vehicle exteriors: Audi A5 Sportback and the Virrage Concept Car (Overbuild modeling method) . You will also get access to my “Expert Private Student” videos, which are released to your personal email from YouTube,

Kind regards and enjoy your Alias

Graham bullock B.Ed. CNAA. Des. Tech.