Qi-Hardware logo: cutting corners

Ron K. Jeffries rjeffries at gmail.com
Tue Aug 23 20:13:15 EDT 2011


To my eye, "constant width" looks simple and elegant.
---
Ron K. Jeffries




On Tue, Aug 23, 2011 at 17:05, Werner Almesberger <werner at almesberger.net>wrote:

> Last but not least, here's a technical issue: the logo has several
> right angles. Right angles are something that doesn't really exist
> in nature and some machining/production processes only allow a
> rough approximation.
>
> For example, a CNC mill can make very pointy convex corners but
> concave corners are always round. This is because the rotating
> mill bit can only cut a circular area, and we can't reach the
> inside of the corner without cutting into the adjacent walls. (*)
>
> (*) Which is sometimes done, but it's probably something we don't
>    want to use in the case of the logo.
>
> The drawing on the right side of
> http://downloads.qi-hardware.com/people/werner/logo/corners.pdf
> illustrates this.
>
> Source:
>
> http://projects.qi-hardware.com/index.php/p/wernermisc/source/tree/master/logo/corners.fig
>
> The circular bit (black circles and half-circles) moves along the
> dark blue edge. By doing so, it removes material in the area
> shown in pink. The resulting edge, shown in light blue, is curved
> at the second corner.
>
> Furthermore, which corners are convex or concave changes with the
> side from which we approach them. If we want to engrave the logo,
> we'd remove material from the inside of it. This is shown on the
> left side of the second row. The thin read line is the path along
> which a tool with radius 1 unit would move.
>
> This leaves various rounded corners. I've marked some of them with
> small red arrows.
>
> If we want to make a relief ("embossed") of the logo, we remove
> material surrounding it. This is shown in the right side, with the
> tool path shown in green. Most of the corners are convex and thus
> nice and pointy, but there are still two rounded ones left.
>
> I called these "simple paths", because they're just a set of
> straight lines. They minimize the difference from the original
> shape but have the perhaps undesirable property that engraving and
> embossing produce different results.
>
> We can change the shape such that is can be produced both ways.
>
> On the left side, all sharp corners have been rounded to arcs with
> the same radius. It's basically a combination of the weaknesses of
> both of the simple paths.
>
> On the right side, a constant stroke width is maintained by
> varying the radii of the arcs along which the tool moves.
>
> These drawings show the worst case in which the overall spacing
> can still be maintained. With a tool radius smaller than one unit,
> the rounded corners could be made sharper than shown.
>
> Thi leaves us with two questions:
>
> - first of all, do we want to make rounding an integral part of
>  the design ? This could be in the form of having two variants of
>  the logo. (We we mandated rounding in general, this would then
>  raise issues with techniques that prefer right angles over
>  curves, such as low-resolution raster images.)
>
> - if we consider rounding an implementation issue and not part of
>  the underlying concept, what would be the advice to people who
>  mill the logo ? Use the simple paths ? Or pick one of the
>  "universal" shapes ?
>
> - Werner
>
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