814 views

### Sierpinski carpet with GraphData

Is this graph in the list among the so-called "standard" structures used in GraphData? However, I have not found yet anything like "Carpet" or "Sponge" in the list ...
1k views

### How to perform Loop subdivision on a triangle mesh with Mathematica?

(Cross posted on Wolfram Community) Every now and then, the question pops up how a given geometric mesh (e.g. a MeshRegion) can be refined to produce a (i) finer ...
2k views

### Dual graph of an arbitrary (planar) graph

Every planar graph has a dual. How can I obtain it with Mathematica? I know that GraphData provides the DualGraph property for ...
892 views

### What are some useful (or hidden) properties of MeshRegion?

There is quite a bit of powerful functionality built in to MeshRegion, but it seems to be lacking in some areas. For example: extracting a list of edges that live ...
1k views

### How to find adjacent polygons of a specific polygon in a VoronoiMesh?

I have developed some code for VoronoiMesh objects, and I am able to find the polygon with the highest number of adjacent polygons. How do I then find the indices ...
160 views

### Cell-adjacency Graph of a Square Mesh

Consider the list of points pts = {{1, 1}, {1, 2}, {2, 1}, {2, 2}} I want to use them to define a 2x2 square mesh using ...
522 views

### Calculate dual graph of planar Graphics map

This diagram from a Wikipedia article illustrates what I hope to accomplish in Mathematica: I have a planar map in Graphics format. Here are two very simple ...
144 views

### Adjacent faces in a discrete mesh

I have a MeshRegion R and I want to extract all pairs of adjacent faces efficiently. The way that I've been computing this is demonstrated below: ...
188 views

### Improve “Game of Life” on a mosaic

I had the idea of generalizing Conways Game of Life from a regular lattice to act on a Poisson Voronoi mosaic (tessellation). The code below works but is maybe not the best idea in terms of speed. I'...
320 views

### How to create a neighboring list for a given triangulation and find the triangle and construct the tile?

I am new to Mathematica and I am currently in need of some help with creating a neighboring list of triangles for a given triangulation and finding the path to the triangle containing the random point ...
141 views

### Performing queries on mesh structure in a clean way

I have the following problem, which can be stated geometrically as follows: List all pairs of vertex coordinates in a mesh region of measure 2 (a surface consisting of triangles) where these points ...