On the matter of beziers I found that the fastest way to calculate them in OpenSCAD is using the matrix representation, which isn't commonly discussed. If you can do something with matrices it will almost always be the fastest method in OpenSCAD. I changed the BOSL2 general order N bezier from the recursive de Casteljau method (that you have below) to the matrix method and got a 10-20 times speed improvement, which can make a difference when doing bezier surfaces with lots of points. The continuous curvature rounding stuff I did required 4th order beziers. acwest wrote > On the subject of bezier's, I implemented them in my own libraries with: > > function linearBezier(p0, p1, t) = p0 + (p1 - p0) * t; >> >> function quadraticBezier(p0, p1, p2, t) = linearBezier(linearBezier(p0, >> p1, t), linearBezier(p1, p2, t), t); >> >> function cubicBezier(p0, p1, p2, p3, t) = >> linearBezier(quadraticBezier(p0, >> p1, p2, t), quadraticBezier(p1, p2, p3, t), t); >> > > where all 3 functions take an argument t which is between 0 and 1, the > fraction of the path along the curve. > linearBezier (only named that for consistency, and I thought it was funny) > finds a linear interpretation between two points, quadraticBezier finds > the point along the parabolic segment defined by the 3 points, and > cubicBezier (the one normally used in most graphical applications) finds > the point along the cubic curve defined by the 4 points. > > On Thu, Jan 28, 2021 at 6:49 PM Lou_Papet < > loupapetjpr@ > > wrote: > >> I agree with you. I will perhaps surprise you but I do not appreciate >> what >> is done today, especially in the automobile sector without taking the >> electric ones which are, for me of course, an hoax against the planet! >> ... >> My 2CV is 42 yeaers old !... >> "Pourquoi faire simple quand on peut faire encore plus simple !..." >> *"Why keep it simple when you can make it even simpler ! ..."* >> "Le plus simple est de ne pas faire.....seulement si c'est possible !..." >> *"The easiest way is not to do ..... only if it is possible ! ..."* >> >> ------------------------------ >> Sent from the OpenSCAD mailing list archive >> <http://forum.openscad.org/> >> at Nabble.com. >> _______________________________________________ >> OpenSCAD mailing list >> > Discuss@.openscad >> http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org >> > > _______________________________________________ > OpenSCAD mailing list > Discuss@.openscad > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org -- Sent from: http://forum.openscad.org/

Yes, it is a mathematical game allowed by the formulation of Bézier curves but I believe that the most used are cubic Bézier curves to concatenate, easier to handle especially for Bézier surfaces and used in a large part of 3D softwares with the B-splines. Le ven. 29 janv. 2021 à 03:12, A. Craig West <acraigwest@gmail.com> a écrit : > On the subject of bezier's, I implemented them in my own libraries with: > > function linearBezier(p0, p1, t) = p0 + (p1 - p0) * t; >> >> function quadraticBezier(p0, p1, p2, t) = linearBezier(linearBezier(p0, >> p1, t), linearBezier(p1, p2, t), t); >> >> function cubicBezier(p0, p1, p2, p3, t) >> = linearBezier(quadraticBezier(p0, p1, p2, t), quadraticBezier(p1, p2, p3, >> t), t); >> > > where all 3 functions take an argument t which is between 0 and 1, the > fraction of the path along the curve. > linearBezier (only named that for consistency, and I thought it was funny) > finds a linear interpretation between two points, quadraticBezier finds > the point along the parabolic segment defined by the 3 points, and > cubicBezier (the one normally used in most graphical applications) finds > the point along the cubic curve defined by the 4 points. > _______________________________________________ > OpenSCAD mailing list > Discuss@lists.openscad.org > http://lists.openscad.org/mailman/listinfo/discuss_lists.openscad.org > -- *"Pourquoi faire simple quand on peut faire encore plus simple..." "Le plus simple est de ne pas faire.....seulement si c'est possible !..."*