Siska Ádám - 2008-08-25

Logged In: YES
user_id=1349179
Originator: YES

Base of the problem: there's no way to know the exact trajectory of the Bezier-curves, unless exactly calculated.
Possible solutions:
1) Replace Bezier with circle arc. (Might look awful and cross to other staves when applied to long slurs, but fast.)
2) Replace cubic Bezier with cuadratic (one control point). In this case a 2nd order equations must be fulfilled by least squares method. Not so slow and not so bad quality.
3) Calculate the points with fitting the 3rd order equations applying least squares. Might be slow, and it's quite complicated mathematically, but looks pretty nice. Some resources might be found in the Internet (f.example Lilypond source code and/or Matlab routines.)