That's a good question. My initial thought was to limit the arc to blending only 1/3rd of a line segment. In the case you describe, the circle-approximating polygon would have the corners rounded off. It would be a very similar shape to the parabolic blends, and you'd probably only notice the difference with a microscope.
Another way to get closer would be to allow 1/2 of the new segment (and all of the remaining previous segment) to be replaced with the blend arc. If your circle was made of many identical-length short lines, you'd have instead a chain of short arcs. The radius of the arcs would depend on the original polygon. If the lines were circumscribed, the radius should match exactly. If the lines are inscribed (or somewhere in between), then the effective circle radius will be a little smaller. Unfortunately, I think this is a case of "garbage in, garbage out"; in that it's not clear from the toolpath what the exact radius is. -Rob On Mon, Oct 14, 2013 at 8:31 PM, andy pugh <[email protected]> wrote: > On 15 October 2013 01:02, Robert Ellenberg <[email protected]> wrote: > > > > https://www.dropbox.com/s/o5he7ijpplkvc8r/Trajectory%20Lookahead%20with%20Arcs.pdf > > > > I'm curious what everyone thinks of this strategy, and if there are any > > pitfalls or risks I didn't think of. > > I am curious about what you get when a circle is defined as many short > lines. It seems like the arc-blend should recreate a perfect circle, > but probably a smaller one than intended. > I suspect that the parabolic blend makes a less perfect circle, also > smaller than intended. > > -- > atp > If you can't fix it, you don't own it. > http://www.ifixit.com/Manifesto > > > ------------------------------------------------------------------------------ > October Webinars: Code for Performance > Free Intel webinars can help you accelerate application performance. > Explore tips for MPI, OpenMP, advanced profiling, and more. Get the most > from > the latest Intel processors and coprocessors. See abstracts and register > > http://pubads.g.doubleclick.net/gampad/clk?id=60135031&iu=/4140/ostg.clktrk > _______________________________________________ > Emc-developers mailing list > [email protected] > https://lists.sourceforge.net/lists/listinfo/emc-developers > ------------------------------------------------------------------------------ October Webinars: Code for Performance Free Intel webinars can help you accelerate application performance. Explore tips for MPI, OpenMP, advanced profiling, and more. Get the most from the latest Intel processors and coprocessors. See abstracts and register > http://pubads.g.doubleclick.net/gampad/clk?id=60135031&iu=/4140/ostg.clktrk _______________________________________________ Emc-developers mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/emc-developers
