# Help! Ellipses seamless pattern

Hello everyone.
I am trying to make a pattern similar to the one shown in the pictures that fits inside the surface but I can’t find a precise and controlled way to fit the ellipses.
Any help would be greatly appreciated.

seamless ellipse pattern.gh (11.2 KB)

Make a circle packing then scale1d?

get the bounding rectangle of the ellipses. get it’s width and the width of the surface and then use basic algebra to uniformly scale the ellipses so their width matches the surface.

This has no surface in sight but can be adapted to fit any rectangle. Clearly a Bounding Box (Union) describes a relevant rectangle whose dimensions can be calculated without actually using one. Similarly, The R1 and R2 values can be derived, given a rectangle and the number of ‘Cols’ and ‘Rows’.

This was a hack through the weeds until a light bulb went on, identifying the tangent point of two offset ellipses (at 1/2 of R2) and their distance apart (yellow group). That distance was critical!

ellipse_grid_2021Oct27a.gh (23.8 KB)

P.S. Well, ‘R2’ is trivial to determine from the height of rectangle (YR = 3.2825) divided by number of ‘Rows’+0.5: Example: `R2 = 3.2825 / 2.5 = 1.313`

‘R1’ isn’t so straight forward, might need to sleep on that one. See gray group at bottom:

ellipse_grid_2021Oct27b.gh (28.3 KB)

Might need this?

1 Like

Wow, thank you all for the quick response!
@Joseph_Oster i will definitely try this one. thanks for your dedication.

i might give a try with this one.
Thanks @DanielPiker

Standby, I have a much improved version. And I solved the issues of deriving R1 and R2 from rectangular boundary dimensions, ‘Rows’ and ‘Cols’, which I think is very cool.

P.S. Here is the much improved version. It corrects the mislabeling of ‘R1’ and ‘R2’ sliders that were actually ‘D1’ and ‘D2’ (major and minor axis “diameters”). And It allows a single column instead of always working with pairs of ellipses.

The gray ‘Analytics’ group at the bottom shows how to derive ‘R1’ and ‘R2’ from bounding rectangle dimensions ‘XR’ and ‘YR’ using a derived “magic ratio” constant ‘D1_F’ (gold group).

ellipse_grid_2021Oct28a.gh (33.1 KB)

It’s only a few steps from here to accept rectangle dimensions ‘XR’ and ‘YR’ as slider inputs and generate the ellipse grid accordingly.

BINGO!!

ellipse_grid_rectangle_2021Oct28a.gh (26.3 KB)

3 Likes

Here’s the other approach I mentioned - scaling a circle packing:

ellipses_in_rectangle.gh (13.8 KB)

2 Likes

Amazing! Thanks a lot
Saved me

thanks @DanielPiker

Just to show you one of the intentions behind this.
This is one part of the project. Thanks for your help

A harem tower?

1 Like

Hello, i was wondering if it would be possible to make some kind of scale gradient keeping the tangency between ellipses and within the perimeter.

Gave it a shot, how’s this?

projectedEllipses.gh (88.4 KB)

1 Like

i would love to get something similar to that but instead of deforming the ellipses while they get bigger. just maybe get to make them increase in size without deforming by reducing the number of these.
scale ellipse grading pattern.gh (18.5 KB)

I’m not sure what you mean - scaling the ellipses uniformly, rather than in one direction? Then you will run into tiling issues, but that’s maybe what you are after.

Can you find an image of the sort of thing you want? Or try drawing it in Rhino, even if the tangencies aren’t perfect.

Yes, exactly. i dont mind if there are tiling issues as long as they stay tangent and all the ellipses inside the boundary.

Then I think you are looking for something like circle packing, but stretched in one axis (Like Dan suggested right at the top)

Check this out:

1 Like

As proposed by @jopsa2 use the link and use a scale NU (say scale with a factor in X dirrection= in order to work with circles and then go to ellipse with a scale NU with 1/factor in X.

4 Likes