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What is the math behind such animated trajectories?

What kind of math is something like this? C ++.

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Additional examples on this MSDN page are here .

UPDATE . A more specific question was asked. What is the math / animation theory for Penner tweens ^ ? How did you come up with these formulas? What are the mathematical principles based on?

Me and math, we are not BFF! I am working on a multi- FLOATanimator of values ​​for the user interface that I am writing, and I was wondering what mathematics was from the point of view of a C ++ programmer to create such a trajectory.

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