At 2023-06-07T09:54:29-0400, Douglas McIlroy wrote: > 3. It isn't said that arcs run counterclockwise. > > 4. It could be said that the center of an arc is adjusted to the > nearest point on the perpendicular bisector of the arc's chord. This > would allay sticklers' anxiety about overconstraint and sometimes > allow one to make a reasonable guess rather than calculating it.
I'm still figuring out a way to demonstrate this (for my own edification and comprehension, not to encumber our manuals with an example of it, since it seems pretty deep into the weeds). But today I _did_ learn that the arc's end point (h, v) is relative to the (adjusted) center, _not_ to the initial drawing position, which I had assumed, and once I started playing, I got a surprise. If I squint, I can see the reasoning. As the successive vertices of a polygon \D'p' are drawn from their predecessors, the center of an arc can be thought of as a vertex with no line plotted to (or from) it. Nevertheless I mean to make this explicit. A little play also reveals the significance of counterclockwise circumscription. Here's a small exhibit if others would like to experiment. .sp 2i \h'1i'\Z'.C'\v'0.5i'\D'a 0 -0.5i 0 -0.5i'\v'0.5i'\ \h'2i'\Z'.C'\v'-0.5i'\D'a 0 0.5i 0 0.5i'X .sp 2i \h'1i'\Z'.C'\h'-0.5i'\D'c 1i' Regards, Branden
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