Negative Accelerations - computer animation

In order to incorporate decreasing speed in an animation the time spacing between the frames must decrease, thus there exists lesser change in the position like the object moves. Generally, the trigonometric function utilized to have increased interval size the function is Sin Θ, 0<Θ<Π/2.

For n in-betweens, the time for the J^th  in-between would be computed as:

T_J = Ta + ΔT [Sin( J (Π /2)( N + 1))]

Here J = 1, 2, 3,......N

As in above Figure, the spacing among frames is reducing then the situation changes from fast motion to slow motion that is reducing acceleration or deceleration. Here we study the trigonometric function utilized to achieve this negative acceleration, that is:

Y=SinΘ in the interval of 0<Θ<Π/2

 At Θ = 0   ;

 Y = Sin(Θ = 0) = 0

 At Θ = Π /2   ;

 Y = Sin(Θ = Π/ 2) = 1

 Currently, dividing the Θ range in to N+ 1 part and plotting the graph Y Vs Θ we will find a sine curve as demonstrated below: