Combination of Positive and Negative Accelerations

Actually, it is not that a body once decelerated or accelerated will remain so, although the motion may include both speed-ups and slow-downs. We can model a combination of accelerating and decelerating motion through first increasing the in-between spacing and after that reducing the same. The trigonometric function utilized to accomplish these time changes is:

Y = (1 - CosΘ )/ 2 ;

0 < Θ < Π /2

 The time for the J^th in-between is computed as:

T_J  = Ta + ?T{[1 - (Cos( J Π ( N + 1))] / 2}

 Here J = 1, 2, 3,........N

 ? T=time variation between two key frames =Tb-Ta

In the demonstrated figure above, the time interval for the moving object initially increases and then the time interval reduces, leading to the simulation of motion which first accelerates and then decelerates.

Note: Processing the in-betweens is simplified via initially modeling "skeleton" or wire frame objects. This permits interactive adjustment of motion sequences. After the animation sequence is totally explained, the objects can be completely rendered.