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