#linuxcnc-devel Logs

Dec 23 2022

04:13 PM andypugh: Did anyone look at that Splines video that I linked to on the mailing list?
04:20 PM andypugh: It made me wonder if there is a simple matrix polynomial for a G2 cutter path in 9 dimensions that would be inherently finite jerk.
05:14 PM rmu: andypugh: didn't look yet, but i suppose bezier splines of sufficient dimension should fit
05:15 PM andypugh: The video really is excellent. At the end I read a comment and only then realised it was an hour long. It was that interesting.
05:16 PM rmu: *watching*
05:17 PM rmu: what do you mean with "simple matrix"?
05:18 PM rmu: the thing that kind of sucks with bezier splines is there is no closed parameter form where parameter is curve length
05:30 PM rmu: andypugh: https://pomax.github.io/bezierinfo/
05:32 PM andypugh: The matrix developed at timestamp 51:46 for example. What if P0, P1, P2 etc are ppints defined in 9D space by your G-code?
05:35 PM rmu: 35min to go ;)
05:35 PM andypugh: Does continuity of acceleration guarantee finite jerk?
05:36 PM andypugh: Think of the P(n)s as trajectory points in 9D LinuxCNC space as you watch.
05:36 PM rmu: 9d means 2 sets of the usual cartesian coordinates and a set of angles? what angles are used in linuxcnc and if you can treat them as a vector
05:39 PM andypugh: My feeling is that we should stop trying to imagine what it means to blend between angles and linear coordinates, and let the maths handle it
05:39 PM andypugh: Just accept that P is a vector ov XYZABCUVW
05:45 PM rmu: so if you use 5th order bezier curves to represent (tangential) velocity, you can achieve a "tangential" jerk limit. if the tool is to make a tangential transition from line to circle, there will be a step in acceleration of axis perpendicular to the line and that step is not jerk limited. there is a forum thread from me about that and a very experimental branch
05:51 PM andypugh: I have played around in 2D with a no-lookahead finite jerk rasterer, bt it was such a digression from the problem I was meant to be working on that I moved on.
05:52 PM andypugh: The current LinuxCNC TP uses circular blends, and I am not sure that they map well to more than 3D.
05:53 PM andypugh: The B-spline is probably finite-jerk bit does not touch the control points _or_ the segments.
05:53 PM andypugh: We basically aim to touch the segments and get within a tolerance of the control points. It’s a very similar, but different puzzle, I think,
05:54 PM rmu: it becomes an optimization problem. stay within constraints of jerk/acceleration/tolerance and keep speed as close to feedrate as possible.
05:56 PM andypugh: Indeed, but achieving that as a set of constraints on a set of simultaneous equations seems more manageable than trying to understand what it means in the world we live in.
05:57 PM rmu: according to twitter, real world jerk is unlimited, yes.
05:59 PM rmu: I think clothoids have some nice properties for toolpaths, and somebody posted the paper on the forum, but I didn't bookmark it.
06:09 PM Tom_L: https://www.researchgate.net/publication/331894176_Toolpath_Smoothing_using_Clothoids_for_High_Speed_CNC_Machines/link/5d2e8bc592851cf4408a7c0c/download
06:09 PM Tom_L: that?
06:13 PM andypugh: Maybe I need to find the bit of my brain that used to do maths.
06:14 PM rmu: Tom_L: looks somewhat familiar, but not sure due to covid brain ;)
06:15 PM Tom_L: i can relate to that for sure
06:17 PM andypugh: During my PhD I was familair with the “Reciprocal effective mass Tensor”. I doubt that I can get back to there, but hopefully wou;dn’t need to.
06:20 PM rmu: what was your phd in? solid state physics?
06:26 PM andypugh: Optical fibres.
06:30 PM andypugh: So, sort-of. The _actual_ project was really micro-machining, ie making 10nm thick slices of 100um optical fibres for EDAX analysis, but I got into the reaosns that they needed that elemental distribution.
06:32 PM rmu: i remember dealing with christoffel symbols in some weird general relativity context, but wouldn't know how to visit that topic again either ;)
06:33 PM rmu: no phd
06:45 PM rmu: the video really is excellent.
07:35 PM andypugh: I think it’s one of the best I have ever watched. It must have been a ton of work.