Distribute spheres on ellipse pattern with python

[joão chaves]

Hey all.

I have a simple script that distributes spheres in a circular pattern (fixed by Justin Israel), and was looking for a solution that would distribute them in an ellipse/oval pattern. I am also trying to do this in bifrost, but as I have done for the circular pattern I need to understand the math first in python.

I also found this formula “(x2/a2) + (y2/b2) = 1” but not sure how to apply it.

Thank you!

import maya.cmds as cmds

degrees = 180
max_iterations = 21
t_x = 6
radius=0.15


for i in range(max_iterations):
    
    print(i)
    

    if degrees % 360 == 0:
        rotation = float(degrees) / max_iterations * i
    else:
        rotation = float(degrees) * i / (max_iterations-1)
    
    my_sphere = cmds.polySphere(r=radius)
    cmds.move(t_x,my_sphere, x=1 , absolute=1)  
    cmds.move( 0,0,0, [ my_sphere[0]+'.scalePivot', my_sphere[0]+'.rotatePivot' ], xyz=1, absolute=1 )

    cmds.rotate(rotation, my_sphere, y=1)

[Justin Israel]

Full disclosure, I am not a math guy and I didn't know the solution straight away. But I wanted to look it up and see if I could apply it, given a known max and min radius, and an angle.

I found this to be the most useful of all the links I had found: https://stackoverflow.com/a/17762156/496445

What do you think of this solution I came up with based on that? 

https://gist.github.com/justinfx/b257dc162680978786ed4fd45409c997

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[johancc]

Hey Justin. That's awesome! Thanks a lot for looking into it. The only issue I have is that it doesn't evenly distribute the spheres along the ellipse, maybe that's not easy to accomplish?
But this helps me a lot anyways. :)

[Marcus Ottosson]

> The only issue I have is that it doesn't evenly distribute the spheres along the ellipse, maybe that's not easy to accomplish?

Got an interesting thought-experiment for you. :) What would it look like to only distribute 3 or 4 spheres in an ellipse, with even spacing? Pen and paper is allowed.

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[joão chaves]

Hey. I believe it would like a diamond in case of 4.

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[Justin Israel]

On Tue, Oct 11, 2022 at 4:30 AM joão chaves <joao.c...@gmail.com> wrote:

Hey. I believe it would like a diamond in case of 4.

In the current implementation, you would have a diamond. But if the 4 points were evenly spaced, you would have a square.

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