Flash MX 2004 Games : Art to ActionScript

Figure B.1 The graph of y = x 2
Appendix B
If an ease out is required then we need a different shape to the curve. In fact we need to flip the
curve for both values. Flipping the time value will give a parameter moving by 1 − dt (if dt is a
value between 0 and 1 as described above). The quadratic of 1 − dt is simply (1 − dt)(1 − dt)
which can be multiplied out to give 1 − 2dt + dt 2 . We also want to flip the value parameter so the
result is 1 − (1 − 2dt + dt 2 ) which simplifies to 2dt − dt 2 . So the curve we want is y = 2x − x 2 ,
which is shown in Figure B.2.
Figure B.2 The graph of 2x − x 2
Such a curve is created with the code snippet:
var dt = time/duration;
_x = offset.x * dt *(2 - dt) + start.x;
_y = offset.y * dt *(2 - dt) + start.y;
In all the curves we shall study, we are using a delta time parameter dt that varies over the range 0
to 1, to create a curve whose maximum value is also 1. We use the value of the curve multiplied
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