-This question is technically more math related, but it has to do with a simulation so I am here first. I can post this in the math SE instead if needed.
I am in the process of trying out some mesh deformation simulating the effect of sand/dirt being poured in a pile (Think hourglass sand) and I am trying to determine the best way to calculate the spread instead of becoming increasingly taller. I don't intend on actually matching sand/dirt physics, I just want to get my mesh to be somewhat close to the shape that pile would make as it grows.
I'm pretty sure that Normal Distribution is what I want, so in my desmos graph below, think of f(x) -green line- as the current dirt/sand piling up (where I am at in my code) and f1(x) -purple line- as the spread version (what I want to happen instead).
f1(x) is not correct but I think it is pretty close. Essentially i need the area of f1(x) to always equal the area of f(x) but as f(x) gets taller, f1(x) gets wider and taller, but not as tall as f(x).
<a title="View with the Desmos Graphing Calculator" href="https://www.desmos.com/calculator/ir8if2u8qq"> <img src="https://s3.amazonaws.com/calc_thumbs/production/ir8if2u8qq.png" width="200px" height="200px" style="border:1px solid #ccc; border-radius:5px" /></a>
I hope this makes sense to you gurus. If not, I can try to clarify more.
Edit: Also, if you open that graph, the slider for variable 'h' is the one im essentially trying to work with.