Thomas Morley <thomasmorle...@gmail.com> writes: > ' > > Am Do., 25. Apr. 2019 um 17:21 Uhr schrieb Benkő Pál <benko....@gmail.com>: >> >> David Kastrup <d...@gnu.org> ezt írta (időpont: 2019. ápr. 25., Cs, 16:46): >> > >> > Thomas Morley <thomasmorle...@gmail.com> writes: >> > >> > > Background: I'm exploring whether it would be feasible to draw higher >> > > order bezier-curves, splitting them in cubic ones. >> >> you can't split a Bezier curve into lower order ones, only approximate. > > Bad wording of mine, sorry. > I meant 'approximate'. > >> > So usually your goals would be better served by >> > allowing _multiple_ cubic beziers in a row with suitable continuity of >> > derivatives (and thus some aspects of the control points) provided >> > automagically. >> >> which is called B-splines. is it possible to use (cubic) B-splines directly? > > B-splines are also mentioned in one of the linked sources, but > currently can't deal with them. I'll continue exploring ;)
It just means that you draw a number of Bezier curves through a number of curve points maintaining as many continuous derivatives as your Bezier degree can deliver per point and then filling the remaining degrees of freedom at the end points with suitable boundary conditions. Typical choices are "periodic", namely keeping all derivatives at the end the same as at the start, or "natural", making the final derivatives zero. I may have some Bezier curve booklet as well but it's likely with examples in BASIC and not necessarily all the math is correct. -- David Kastrup _______________________________________________ lilypond-devel mailing list lilypond-devel@gnu.org https://lists.gnu.org/mailman/listinfo/lilypond-devel
