Log In  42    Cart #easingcheatsheet-2 | 2020-11-28 | Code ▽ | License: CC4-BY-NC-SA 42 `load #easingcheatsheet`

in the Pico-8 command line to load it straight into your Pico-8 application! Easing functions are ways of modifying the rate of change for a linear interpolation function. You may have used these in animation programs (unity, blender, etc.) by manually editing animation curves. This editing isn't all that possible without a large engine backend, but you can easily create short math equations to imitate some of the commonly used curves. This is what I've done here, implementing a set of functions for these curves, and creating a little demo so you can see how each of them changes your interpolation!

## Code

All of these functions are completely self sufficient (don't rely on anything outside the function), so you can easily pick and choose which ones you want! (476 tokens for all of them)
(also, none of the functions have any safety regulations, so passing values outside of 0-1 will result in unintended behavior. Be careful! you could also add t=mid(0,t,1) to the start of the functions to clamp the values)

 ```function easeinquad(t) return t*t end function easeoutquad(t) t-=1 return 1-t*t end function easeinoutquad(t) if(t<.5) then return t*t*2 else t-=1 return 1-t*t*2 end end function easeoutinquad(t) if t<.5 then t-=.5 return .5-t*t*2 else t-=.5 return .5+t*t*2 end end```

### Quartic functions

(these are very similar to quadratics, but flatter at the start and steeper towards the end)

 ```function easeinquart(t) return t*t*t*t end function easeoutquart(t) t-=1 return 1-t*t*t*t end function easeinoutquart(t) if t<.5 then return 8*t*t*t*t else t-=1 return (1-8*t*t*t*t) end end function easeoutinquart(t) if t<.5 then t-=.5 return .5-8*t*t*t*t else t-=.5 return .5+8*t*t*t*t end end```

### Overshooting functions

 ```function easeinovershoot(t) return 2.7*t*t*t-1.7*t*t end function easeoutovershoot(t) t-=1 return 1+2.7*t*t*t+1.7*t*t end function easeinoutovershoot(t) if(t<.5) then return (2.7*8*t*t*t-1.7*4*t*t)/2 else t-=1 return 1+(2.7*8*t*t*t+1.7*4*t*t)/2 end end function easeoutinovershoot(t) if t<.5 then t-=.5 return (2.7*8*t*t*t+1.7*4*t*t)/2+.5 else t-=.5 return (2.7*8*t*t*t-1.7*4*t*t)/2+.5 end end```

### Elastic functions

(these functions overshoot slightly and then oscillate near the edges of the range, like an elastic band)

 ```function easeinelastic(t) if(t==0) return 0 return 2^(10*t-10)*cos(2*t-2) end function easeoutelastic(t) if(t==1) return 1 return 1-2^(-10*t)*cos(2*t) end function easeinoutelastic(t) if t<.5 then return 2^(10*2*t-10)*cos(2*2*t-2)/2 else t-=.5 return 1-2^(-10*2*t)*cos(2*2*t)/2 end end function easeoutinelastic(t) if t<.5 then return .5-2^(-10*2*t)*cos(2*2*t)/2 else t-=.5 return 2^(10*2*t-10)*cos(2*2*t-2)/2+.5 end end```

### Bouncing functions

(these functions hit the edge values early, then bounce back a few times)

 ```function easeinbounce(t) t=1-t local n1=7.5625 local d1=2.75 if (t<1/d1) then return 1-n1*t*t; elseif(t<2/d1) then t-=1.5/d1 return 1-n1*t*t-.75; elseif(t<2.5/d1) then t-=2.25/d1 return 1-n1*t*t-.9375; else t-=2.625/d1 return 1-n1*t*t-.984375; end end function easeoutbounce(t) local n1=7.5625 local d1=2.75 if (t<1/d1) then return n1*t*t; elseif(t<2/d1) then t-=1.5/d1 return n1*t*t+.75; elseif(t<2.5/d1) then t-=2.25/d1 return n1*t*t+.9375; else t-=2.625/d1 return n1*t*t+.984375; end end --(ease in+out function omitted, it doesn't really make sense for any uses IMO)```

### Other useful functions:

 ```--(linear interpolation between a/b) function lerp(a,b,t) return a+(b-a)*t end --(finds the t value that would --return v in a lerp between a/b) function invlerp(a,b,v) return (v-a)/(b-a) end```

## Crediting:

If you use these in your own code, please just put a link to this BBS post in a comment near the function! I want to allow anyone reading your code to be able to find this and use it as well, for learning purposes.
All of the easing functions in this cart are based/translated from this site: https://easings.net/

Also, feel free to suggest any functions I'm missing! I omitted some of the functions that I thought were redundant/not commonly used, but correct me if I was wrong with that assumption!

P#84765 2020-11-27 21:13 ( Edited 2020-12-02 14:20) 1 This is such a nice resource, thanks for sharing! For those of us who haven't done "real" math in more than 30 years, this is a huge help.

P#84778 2020-11-27 22:53  This is beautiful! Thank you!

P#84787 2020-11-28 08:14  This is a super resource.
Thanks for creating it! 🤓👍

P#84954 2020-12-02 19:45  In your snippets below the cart, what is the difference between easeinout and easeoutin? The cart doesn't seem to have the latter.

P#91171 2021-04-27 04:41  @TBMcQueen those are at the bottom of the menu, after all of the other curves! I added them after I originally posted so they weren't mixed in with the others.

P#91188 2021-04-27 14:23