Re: Slur with left and/or right arrow head

[Carl Sorensen]

On 4/17/19, 9:50 PM, "Aaron Hill" <address@hidden> wrote:


    Additionally, it is important to consider velocity along the curve.  
    Based on the positioning of the control points, we may be walking at 
    times and running at others.  You see this with the variable spacing of 
    dots when you sampled a curve at regular intervals of the parameter t.  
    A value of one half for t does not mean you are halfway between the 
    initial and final points in terms of Cartesian distance.  This is why I 
    had to go through the trouble of computing arc lengths, since I needed 
    to know the slope of the curve at a specific distance from the end 
    points.
    
    My approximation for arc length and position will fail for exotic Bezier 
    curves, since I am using a fixed subdivision count; but typically ties 
    and slurs are more well-behaved in this regard.  Now when a composer 
    decides to invent notation where a slur has a cusp or loop in it, then 
    we will need to worry:

I believe that the dashed tie /slur functions have a helper function that 
eliminates the nonlinearity with t.  I started using t as a curve-length, but 
it isn't so.  So I created a subdivision algorithm that works properly.  Maybe 
in scm/Bezier-functions.scm?  I can't recall the exact name of the scm file 
right now, and I don't good access to a lilypond source tree.

Thanks,

Carl