Non Rational Bezier curves (Also NURBS) can represent circular curves... or any curve for that matter.
One could also decompose an arc into enough bezier segments beyond the needed precision at which point they are close enough. -Curtis On Mon, Jan 26, 2026, at 9:24 AM, andy pugh wrote: > On Mon, 26 Jan 2026 at 00:17, Luca Toniolo <[email protected]> wrote: > > > > plan link did not come through properly, not sure why > > > > https://forum.linuxcnc.org/38-general-linuxcnc-questions/33459-linuxcnc-s-curve-accelerations?start=640#341856 > > I still don't think that's the right link? > > I was unclear if Bezier curves could be extended out of 2 dimensions, > and found that they can be defined in an arbitrary number of > dimensions. > Apparently it is quite common to use 4D curves for smooth motion in > both space and time. > > So, would a 10D Bezier be inherently jerk-limited? (9 CNC axes + time). > > It does seem that there are (at least) two considerations. It doesn't > matter how G2-smooth the path is, there can still be jerk _along_ the > path if the velocity is not constant. > But a G2-smooth path would help with curve-to-arc transitions. > > A little web searching suggests that a Bezier can't 100% accurately > match a circular arc, though they can get close for smaller > subdivisions of a circle. > > It's probably important to remain aware of the fact that circular > interpolation is important in manufacturing, and whilst some > corner-cutting on sharp corners is probably accepted by machinists, > circles that ar not circular would cause raised eyebrows. (though this > might be a distinction that disappears in the context of real machine > physical accuracy) > > > -- > atp > "A motorcycle is a bicycle with a pandemonium attachment and is > designed for the especial use of mechanical geniuses, daredevils and > lunatics." > — George Fitch, Atlanta Constitution Newspaper, 1912 > > > _______________________________________________ > Emc-developers mailing list > [email protected] > https://lists.sourceforge.net/lists/listinfo/emc-developers > _______________________________________________ Emc-developers mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/emc-developers
