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Conformal Circle Packing. After a couple of days with studying the mysterious Doyle spiral, I’ve decided to test an approach of circle packing from conformal geometry.

Conformal Circle Packing

Poincare disk (studied earlier at here, here and here and here) is used as the hyperbolic representation of space. First, I linked a regular hexagonal grid data structure and rebuilt it after the hyperbolic distortion finding this result: Pretty much like a voronoi subdivision, but a very different thing in fact. My second attempt was to create a circle packing out of this: However I couldn’t manage to tell Grasshopper about it, but at last, the definition managed to create some circle compositions close to (but not exactly) a perfect packing: You can download the Grasshopper3D definition of my study here; [GHX: 0.9.0006] (right-click and save target as…) Here is a small phrase, briefly explaining the history of circle packing, P.L.

Kangaroo discussions and examples from GH forum. Sg2011 cluster: use the force Through Kangaroo, the live physics plug-in, this cluster will explore ways of using the simulated interaction of physical forces and real-time spatial inputs to develop novel form-finding processes. cluster champions members view all image albums.

Kangaroo discussions and examples from GH forum

Packing circles on surfaces. Circle packing in grasshopper (of fixed radius) A couple of months ago, I saw this video on youtube and found it really interesting.

Circle packing in grasshopper (of fixed radius)

The video shows exactly what I am trying to achieve in one of my projects, but I have not been able to work out how to do this. I will try and show the different solutions I have tried, and hopefully someone will be able to explain to me how I should resolve it. (controlled circle packing, fixed radii) My first attempt (see 1st image) shows a random grid of points, of which the ones that fall inside the main circle are deleted. circles are then drawn around each point, of which the radius is matched to the distance of the next closest point. This leads to a serious of floating pairs of circles, which are not of a regular size and do not all touch. I then found these articles on the designcoding website, which were interesting with relation to my project.

The prcedent video appears to show an iterative solver, as there are many iterations that move towards the final stage. Searching for a Full Circle Packing. Since last week, I’m very curious about circle packing.

Searching for a Full Circle Packing

There are a couple of complete solutions on the internet. I’m still at early steps of such a solution yet. A full circle packing means that it does not include any gaps and each circle is tangent to all possible neighbors. Sounds easy in Grasshopper but I couldn’t see any solution yet. There a some circle packing attempts but they have gaps. It might be much easier in a recursive scripting environment, but I believe there is a method to model a solution in dataflow, particularly in Grasshopper3D. We used to take a “Circle tan tan” function and use it to create the circle that is tangent to two others easily and quickly. Which can be defined in Grasshopper like this: This way, we can create three tangent circles just by entering their radii. Here is my Grasshopper3D document: [GHX: 0.9.0006] But it’s true!

I’m sorry, I couldn’t show you spectacular circle packings here. Searching for a Full Circle Packing. Circle Paking Kangaroo.