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I trying to understand these two functions rigorously in mathematical way so I can use them for Procedural Modelling. Blender's manual page doesn't help and it leads me to this Wikipedia page which contains very advanced math (for me).

Can you please help me by telling me what are the math topics I need to learn before deriving the functions?

Looking at the Wiki page, I don't know what ''∇'' is, but I know Δ is Delta used for Derivative, what ''Gradient'' is, why are there many functions for Smooth Max Min (LogSumExp, p-Norm...) and what function out of those do Blender use?... If you can mathematically explain how Smooth Max Min in Blender work, that would be amazing! I'm so disoriented by the math in the Wiki page that I don't know where to start.

Thank you! Any help is greatly appreciated.

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    $\begingroup$ Not enough of an expert in Blender-building to make this an answer, but this might clue you in? $\endgroup$
    – Robin Betts ♦
    Commented Jan 21, 2022 at 19:06
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    $\begingroup$ Thank you! @RobinBetts . Studying the function from the Inigo Quilez page definitely is better than from the Wiki page. I saw the the function in code form too but I don't really understand how it's made (I'm not familiar with coding), hopefully some mathematicians on here can derive it. Thanks again! $\endgroup$
    – Orange Cat
    Commented Jan 21, 2022 at 21:17

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