a Chainring

Before the year 2000 began, the folks at Counterbalance Bicycles were waiting to open their doors to the public, and Mr. Adam Smith painstakingly traced his well-worn 52-tooth front ring to circumscribe his shop's logo. Xerox-enlarged typewriter letters were carefully placed and glued around the edge, and a pan-balance and calipers were added.

ABCdzyne began work on the website's logo in quite the same order, first with measuring and "machining" shiny chrome pixels, then finding an old typewriter font, and finally choosing a nice brass for the instruments.

Enter Constructive Solid Geometry, better known as CSG. A bunch of boxes and cylinders, differences, unions, and intersections are all you'll need.


one big disk, a
very thin cylinder

-


fifty-two tooth holes,
and the center

=


most of a chainring


two sexy ovals
(scaled cylinders)

+


a tab (box) for the spider (above),
and some sexy curvy tabs (boxes
minus an oval to join to the ring)

=


to create most
of a hanger


now, take our hanger

and perfom an
intersection
(the areas
common to both

the shapes)


with a simple box

and voila!


we're getting
somewhere!


and now take
our keyhole...

-


and poke some
appropriate holes

=


and there you
have it!


remember our chainring?

+


reproduce our hanger
fivefold...

=


Tada!

Of course you can't just stop there, try differencing out 104 tiny boxes tipped in at 15 (and -15 on the back, naturally) to make the teeth sharp and more realistic.

This is, however, kind of punishing to the renderer, taking a lot longer to draw. Oooh, that's shiny chrome.

But lo, that one's on a dead hard drive of years past. At least I've got it explained all nice how to do it, shouldn't take too long with that precise explanation. There's a fancy many-toother in the sprock() macro, with star-holes cut out that ought to last you.

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01.19.10 ABCdzyne