The solution I initially imagined while reading Werner's post was the "constant width" option as well, and I agree with Ron that it certainly does look nice. However, how do we then reflect it back into the rasterized domain? By aliasing it and knocking a pixel out of the tail like my attached .png?
I don't really love that option because when the process used to generate it is, in turn, reflected back into the machining/vector domain you don't get that pretty curved tail back. Doing so would mean that our description of how to make the logo has to include a conditional at the end that the design must be aliased to fit on a rasterized display. Strikes me as insufficient simplicity. So I suggest it would be better to adopt the "simple paths" approach. Then we can write a single description, essentially pseudocode, that works whether the logo is being drawn with pixels milled with an endmill, or executed through other means. [a] On Tue, Aug 23, 2011 at 6:13 PM, Ron K. Jeffries <[email protected]> wrote: > 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 > > > _______________________________________________ > Qi Hardware Discussion List > Mail to list (members only): [email protected] > Subscribe or Unsubscribe: > http://lists.en.qi-hardware.com/mailman/listinfo/discussion >
<<attachment: qi_corner.png>>
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