Game Engine Architecture

528 11. Animation Systems

time-synchronized, as they must be when performing a smooth transi-

tion. This approach is depicted in Figure 11.28.

We can also control how the blend factor β varies during the transition.

In Figure 11.27 and Figure 11.28, the blend factor varied linearly with time.

To achieve an even smoother transition, we could vary β according to a cubic

function of time, such as a one-dimensional Bézier. When such a curve is ap-

plied to a currently-running clip that is being blended out, it is known as an

ease-out curve; when it is applied to a new clip that is being blended in, it is

known as an ease-in curve. This is shown in Figure 11.29.

The equation for a Bézier ease-in/ease-out curve is given below. It returns

the value of β at any time t within the blend interval. βstart is the blend factor

at the start of the blend interval, tstart , and βend is the fi nal blend factor at time

tend. The parameter u is the normalized time between tstart and tend , and for con-

venience we’ll also defi ne v = 1 – u (the inverse normalized time). Note that

the Bézier tangents Tstart and Tend are taken to be equal to the corresponding

Clip A

t

β Clip B

1

0

A’s local timeline

freezes here

tsta rt ten d

Figure 11.28. A frozen transition, in which clip A’s local clock is stopped during the transi-

tion.

Clip A

t

β Clip B

1

0

tsta rt ten d

Figure 11.29. A smooth transition, with a cubic ease-in/ease-out curve applied to the blend

factor.