I ended up using a modified cos curve
https://www.screencast.com/t/SQokVZO0PpKH
f(x)=cos(x/(1+(x/7)^1)) +1
g(y) = e^(-y^2)
z=f(x)^s*g(y)^t: s=0.5, t=1
Btw this graphing calculator is great!: https://www.runiter.com/graphing-calculator/?app=win-681109358
@mfb - Oh that is excellent! I am not sure how to generalize it to a 3D shape; if we simply rotate around the maximum then our shape again becomes symmetrical. As in my reply to @mathman, the shape should look "like you took a regular Gaussian bell and smudged it in one direction."
FYI the way...
@mathman - actually I am specifically *not* looking for a z-ward cross-section that looks like an ellipse - the shape I am looking for is distorted so that the cross-section looks like an exaggerated egg: one end narrow, the other wide. More like you took a regular Gaussian bell and smudged it...
That is super-cool, and will allow me to squish and rotate the bell; however, all the resultant shapes are still bilaterally symmetric. Not so much egg-shaped as oval. I would very much like to find a way of producing a 3D shape with a 2D cross-section similar to this...
I am new to these forums - if I have posted in the wrong place please let me know.
Standard 3D Gaussian bell: z = e^-(x^2) * e^-(y^2)
From along the z-axis this looks "round".
I would like a generalized f(x, y) which would look egg-shaped from above - possibly quite distorted..
I thought at...
Hello All - I work in Unity and sometimes bite off a bit more math than I can resolve :). I am hoping to find some occasional guidance on these forums.
Thanks!
Broos