On 4/17/19, 9:50 PM, "Aaron Hill" <lilyp...@hillvisions.com> 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
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