Sorry... meant rational curves....
On Fri, May 29, 2026, at 8:37 AM, Curtis Dutton wrote: > 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
