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README.md

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+# Useful functions
+
+The following mathematical functions are useful for smooth movements of two-dimensional objects.
+
+## Smooth transition from origin to point
+
+### Function
+
+```math
+f(x) = \frac{-2k}{n^3} * x^3 + \frac{3k}{n^2} * x^2
+```
+
+### Preview
+
+*  [Preview](https://www.desmos.com/calculator/kxsbfgjnnz)
+
+Example with $`k=3`$ and $`n=2`$:
+
+<img src="https://gitlab.paulaumann.com/paul/functions/-/raw/master/imgs/func01.png"  width="300" height="300">
+
+### Description
+
+Graph starts at origin `(0,0)` and ends at `(n,k)` with a smooth transition between these points.
+
+## Slight variation of the first function
+
+### Function
+
+```math
+f(x) = \frac{2k}{n^3} * x^3 - \frac{3k}{n^2} * x^2 + k
+```
+
+### Preview
+
+* [Preview](https://www.desmos.com/calculator/lsaoejeuwt)
+
+Example with $`k=2`$ and $`n=3`$:
+
+<img src="https://gitlab.paulaumann.com/paul/functions/-/raw/master/imgs/func02.png"  width="300" height="300">
+
+### Description
+
+Graph starts at `(0,k)` and ends at `(n,0)` with a smooth transition between these points.