Ease functions are important for interpolation of just about anything. Popular functions are "smoothstep" or "ease in" and "ease out". This images shows what they look like for x[0,1] and y[0,1]:

There are other popular functions for ease in and ease out, e.g.

The nice picture was plotted with http://fooplot.com

linear: y=x, ease out: y=(x-1)^3+1, ease in: y=x^3, smoothstep: y=3x^2-2x^3,y=sin(x*PI/2), y=1-cos(x*PI/2) |

*y=sin(x**resp.***PI/2*)*y=1-cos(x*PI/2)*. What is important about those functions is if they're C1- and/or C2-continuous when you want to combine functions. C1-continuity means that the first derivative or the tangent of the function is the same for*x=0*and*x=1*, meaning you can piece together two of the curves and there are no sudden changes or jumps for*y*. C2-continuity means that the second derivative or how the tangent changes is the same.*y=**sin(x**and***PI/2*)*y=**1-cos(x*PI/2)*are not C1-continuous, but you can use them to start/end a linear interpolation for example.The nice picture was plotted with http://fooplot.com

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