Important Notes for Negative Accelerations
Note: Having projections of points on curve, above Y axis we will obtain a pattern similar to figure 8 that is needed to produce negative acceleration.
Having projections on y-axis we get, when we move from y = 0 to y = 1 the distance or spacing between frames continuously reduces leading to negative acceleration or slow motion.
The range 0<Θ<Π/2 is separated in N+1 parts so length of each fragment will be:
(?Θ) = (Π /2 - 0)/( N + 1) = Π/ 2(N + 1)
All Θ change produces change of
?Y = Sin((Π/ 2)(N + 1))
For J^{th} segment ?Y = Sin (J * (Π/ 2)(N + 1))
Thus, out of N in-between frames the time for the J^{th} in-between frame is:
T_{J} = Ta + ?T[Sin(J (Π /2)(N + 1))]
Here T=Gap among two key frames=Tb-Ta