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