I just finished adding some of the standard Ease equations to my code base for use in Of Stranger Flames.
In discussion about the equations, it was requested for me to share the code here. This is not a tutorial, I don't have enough familiarity with the subject (or with math in general) to explain how every equation works. I'm just posting what I added to my own code, so others can use it if they want to.

The equations are mostly from Robert Penner's eases, which are under the BSD license. His code seems to be the ones that are used by most software, such as the jQuery, Flash, and other libraries.

Most Ease equations have the function signature:void equation(currentTime, start, distance, totalTime);
I personally like having my eases in start at 0.0, end at 1.0, and have a 'duration' of 1.0, and then I scale the input and output as desired, instead of having the equation scale it. It just makes it easier for me to understand.

That said, all my functions have the format:void equation(position);
...with 'position' being from 0.0 to 1.0.

Because Eases come in various forms (You can ease IN, OUT, IN and OUT, or OUT and IN), I made sure all the ease equations were in EaseIn form, and I created a few functions to convert the input and output to the other forms as desired.

Here's the conversion code:
http://ideone.com/6rc0Zk ([size=2]Posted as links, because all my code kept getting unformatted when hitting 'publish')

EaseFunction is: "typedef std::function EaseFunction;", which nicely permits the use of things like lambdas and functors as well as the regular ease functions. If you don't have C++11, you can just typedef it as: "typedef float(*EaseFunction)(float);" or whatever the correct C-style function-pointer syntax is.

Some of the ease equations have a few extra parameters, like ElasticEase and BackEase, so I provided some C++11 templates to convert the functions to std::functions that meet the function signature shared by the other functions. It's just a wrapper around std::bind for convenience. (I'm big on convenience! )
http://ideone.com/LPEvC6

You don't have to use C++11 to use the equations! Just the helper functions above.

I also use this function for scaling the output:
http://ideone.com/fhYHJT

Actually, mine looks like this:
http://ideone.com/hucHWu
...but that depends on a 'FloatRange' helper class I made, whereas the previous one has no dependencies.

I actually made two ScaledEase overloads, one for my Point class, and one for my Color class. I haven't tested those out yet.

I also made a Easer class, that handles most of everything inside of it. This is more for when you want persistent ease data wrapped nicely, and this class would be a member-variable of another class.

Easer.h
Easer.cpp

That also uses FloatRange, but can be easily adjusted to just use 'float begin' and 'float end' instead.

The Ease Equations

And here are a few additional ones I keep inline

The next page has graphs generated to test/demonstrate the output.

[page]

Cubic Ease In



Cubic Ease InOut



Cubic Ease Out



Cubic Ease OutIn



Elastic Ease In



Elastic Ease InOut



Elastic Ease Out



Elastic Ease OutIn



Exponential Ease In



Exponential Ease InOut



Exponential Ease Out



Exponential Ease OutIn



Linear Ease In / InOut / Out / OutIn



Power Ease In


Power Ease InOut



Power Ease Out



Power Ease OutIn



Quadratic Ease In



Quadratic Ease InOut



Quadratic Ease Out



Quadratic Ease OutIn



Quartic Ease In



Quartic Ease InOut



Quartic Ease Out



Quartic Ease OutIn



Quintic Ease In



Quintic Ease InOut



Quintic Ease Out



Quintic Ease OutIn



Sine Ease In



Sine Ease InOut



Sine Ease Out



Sine Ease OutIn



SmoothStep In



SmoothStep InOut



SmoothStep Out



SmoothStep OutIn



WeightedAverage In



WeightedAverage InOut



WeightedAverage Out



WeightedAverage OutIn



BackEase In



BackEase InOut



BackEase Out



BackEase OutIn



BounceEase In



BounceEase InOut



BounceEase Out



BounceEase OutIn



CircleEase In



CircleEase InOut



CircleEase Out



CircleEase OutIn



[page]

BounceEase was annoying me alot. I was trying to figure out how it worked, but I'm not very good with math and algorithm-thinking.

The original code looked like this:
http://ideone.com/14kyLm

And trying to figure out all the magic numbers, I eventually broke it down to this:
http://ideone.com/wGCTU9

I never figured out how the '7.5625f' value was calculated, but the others are resolved.

Unfortunately, changing the value of 'bounciness' or 'bounces' produces poor results (probably from the constant!), so I didn't bother including the code with the rest of the equations.



Links that were useful in understanding and converting the equations:
http://www.robertpenner.com/easing/ (The guy who made most of these now-common equations)

http://sol.gfxile.net/interpolation/index.html (also has good descriptions and explanations)
http://hosted.zeh.com.br/tweener/docs/en-us/misc/transitions.html
http://msdn.microsoft.com/en-us/library/ee308751.aspx

Some nice graphs:
http://easings.net/