Useful functions
The following mathematical functions are useful for smooth movements of two-dimensional objects.
Smooth transition from origin to point
Function
f(x) = \frac{-2k}{n^3} * x^3 + \frac{3k}{n^2} * x^2
Preview
Example with k=3 and n=2:
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
f(x) = \frac{2k}{n^3} * x^3 - \frac{3k}{n^2} * x^2 + k
Preview
Example with k=2 and n=3:
Description
Graph starts at (0,k) and ends at (n,0) with a smooth transition between these points.