5/30/2023 0 Comments Unit disk graph wolframI included it as an illustration of how to extract the dual lattice, which may be useful for some other tilings. In this last graph, not all non-boundary vertices have the same number of neighbours. the dual) using IGMeshCellAdjacencyGraph. These can be converted to graphs using IGMeshGraph, or to face-face adjacency graphs (i.e. There is IGLatticeMesh which uses (a post-processed version of) Mathematica's built-in periodic tiling data to generate various meshes. Here's a demo through a few examples: IGTriangularLattice IGraph/M now has some new lattice graph generation features that might be useful (though not every graph of the type you describe can be generated through these functions). SelectAdmissableArcs[g_Graph, candidates_List, nvertices_Integer, Regular planar tilings are trivially present, but this code also generates Platonic graphs corresponding to regular Platonic polyhedra (these close on themselves, and don't have a "boundary"), and graphs corresponding to tilings in hyperbolic geometry. Some of the visualizations are a bit messy, but I think it works correctly.īasically it tracks the planar graph boundary and tries to add new edges in regularity-admitting locations. Compute answers using Wolframs breakthrough technology & knowledgebase, relied on by millions of students & professionals. The (open) unit disk can also be considered to be the region in the complex plane defined by, where denotes the complex modulus. There is a solution for hex grid, that could be used together with a unit disk graph method described above.Īdmittedly the implementation below is not as simple or efficient as I wished. Unit Disk - from Wolfram MathWorld Geometry Plane Geometry Circles Unit Disk A disk with radius 1. Obviously, I've got crazy graphs that were not even close to a regular lattice. Randomly connecting vertices in a graph with no edges while their power is less than n. This was an interesting experiment by itself, however, I wasn't able to provide an algo for putting points in the right places. Generating coordinates for a vertices in $R^2$, and then building a Unit Disk Graph. I've realized that it this approach is dependent in a way I am selecting vertices from the periphery and extremely sensitive to a starting graph. NestList, where on each step I am taking one of the boundary vertices bv and adding a few vertices, so that bv is not in the periphery anymore, and new vertices are taking its place. One can think of boundary vertices as a periphery of the graph.Īs you can see from my explanation, I have some difficulties with strict mathematical description of my problem, and I think this is why I am struggling so much trying to solve it. Vertices from B can will have less than n adjacent edges. Cubature schemes, in this case for uniformly weighted integration over the unit disk, enable exact evaluation of numerical integrals of polynomials but have. To put it in more strict form, I need a subgraph of a finite lattice where each vertex have exactly n neighbors, except a set of "boudary vertices" B. with hexagons, or triangles instead of squares)? Is there a way to make a generalized solution (e.g. There is a function GridGraph that generates a finite square lattice graph.
0 Comments
Leave a Reply. |