I'm seeking an easing function that is the twin of the popular Ease-In-Out easing function-- enter image description here

Desired Behaviour

Begins quickly, slows down in middle, ends quickly.


Keep your eye on the black portion of the screen in this Sonic Heroes Stage Intro animation. Notice how the black screen gives way quickly at first, slows down when the screen is half-revealed, then quickly disappears. https://youtu.be/pnLvwfvHCV4?t=71

Here's a quick reference of what the graph should look like

enter image description here

My attempts at curve fitting and experimentation haven't given me the equation / function I need, unfortunately. Any help would be appreciated!

  • 1
    $\begingroup$ Have you tried the inverse of the Ease-In-Out function? $\endgroup$
    – robjohn
    Sep 7, 2016 at 4:17
  • $\begingroup$ The curve shown in the video appears to be simply a concatenation of two regular ease-in-out curves. $\endgroup$
    – Anon
    Sep 9, 2016 at 1:08

1 Answer 1


How about this:

$y(x) = (x^3-2x^2+x)m_0+(-2x^3+3x^2)+(x^3-x^2)m_1$

where $m_0$ and $m_1$ are two positive constants.

Bigger $m_0$ and $m_1$ will result in more wavy curve. Here are two examples:

Example 1: $m_0=m_1=3$
enter image description here

Example 2: $m_0=m_1=4$
enter image description here


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