Am Montag, dem 26.01.2026 um 14:24 +0000 schrieb andy pugh: > 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. >
It is not a question of dimensions but of order of bezier polynomial. You can easily use a 5th order bezier (which has 6 control points) to interpolate from one state to another and fix the value, first and second derivative at beginning and end to whatever value you want. It is very useful in animation software to move smoothly move control points between keyframes or control (virtual) camera movement (without inducing nausea) and stuff like that. IIRC, the problem with beziers in our application is missing closed form of path length (at least for higher order beziers), you can't exactly represent conic sections like circles / arcs and it is hard to get a measure of how accurately a curve interpolates a given path and vice versa it is not easy to find a good approximation to a given curve. the approach of the opencn linuxcnc-fork seems work somewhat along that line, they use 5th order polynomials in "optimal G² Hermite interpolation", papers: https://mecatronyx.gitlab.io/opencnc/opencn/CNC_Path_Planning_Algorithms/Geometric_Operations/Geometric_Operations.html https://www.sciencedirect.com/science/article/pii/S0010448518304305 > 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. no they cant, you would need nurbs or something like that, or "just" increase resolution enough. -- Robert Schöftner <[email protected]> _______________________________________________ Emc-developers mailing list [email protected] https://lists.sourceforge.net/lists/listinfo/emc-developers
