Overview table with the different approaches to solve the Dynamic Foam with Currents in the edges: Dynamic Foam and VoroX with a Dual Voronoi-Delaunay mesh, and also the suggestions for a new version with Weighted Voronoi, and a marching method to search along the edges.
The top layer has 3 methods to search the pressure distribution in the edges of the Voronoi Mesh, but it doesn’t change the Voronoi Mesh physically.
I. Particles move ‘live’ along the Edges, this is used in the Dynamic Foam program made by Nick McDo: https://github.com/weigert/DynamicFoam/wiki/System-Dynamics
II. Use a search in the Geomatric matrix using Markov Chains like how Googles Page Rank works, this used in VoroX made by Benoît L.t: https://github.com/blegat/VoroX.jl
III. This is a new suggestion to use short local search by marching the edges and being blocked when running into a sharp angle.
This layer is about finding out the weight of each edge.
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B. This next layers are how we apply the results from A to the mesh(es) and physically change the Voronoi (and Delaunay) Mesh and get a new Voronoi lay-out. With two columns:
Green: Dual Voronoi-Delaunay mesh: particles or weights on the Voronoi Mesh makes it’s dual-Delaunay edges contract, and shifting the centroids of the Voronoi Cells.
Orange: Weighted Voronoi: the total weights of a the Edges of a Voronoi cell change it’s Sphere size (pressure) and the Spere-packing changes due to each Spere new size.
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Some diagrams regarding a Marching model.
A couple of short walks done in the direction of each connected edge to measure the weight of each edge.
