To my eye, "constant width" looks simple and elegant. --- Ron K. Jeffries
On Tue, Aug 23, 2011 at 17:05, Werner Almesberger <[email protected]>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 > > _______________________________________________ > Qi Hardware Discussion List > Mail to list (members only): [email protected] > Subscribe or Unsubscribe: > http://lists.en.qi-hardware.com/mailman/listinfo/discussion >
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