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For your first question, constructing the adjacency graph of the "partitions" (what you call "cell groups"): Let's say you have an array $p_K$ in which you store for each cell $K$ which partition $p$ it belongs to. Also assume that you have a (sparse) array $a_{KL}$ whose entries are true if cells $K$ and $L$ are neighbors ("adjacent&...


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I would leave out a few things to make it more simple. This is how we do it for our code which is capable of using polyhedral meshes: https://github.com/nikola-m/freeCappuccino-dev/blob/master/src/mesh/geometry.f90 It is so called face based data structure. We use divergence theorem to compute geometrical data like volumes and cell center coordinates. This ...


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If $(x_i,y_i)$ is the centroid of the triangle, then $$ \frac{1}{\Delta_i}\int_{\Delta_i}{p(x,y)}\,dx\,dy = p(x_i,y_i) = \bar{\psi}_i $$ This is mid-point quadrature, which is exact for an affine function. The centroid of a triangle is the arithmetic average of its three vertices. Note that $$ x_i = \frac{1}{\Delta_i} \int_{\Delta_i} x dx dy = \frac{1}{3}\...


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Why don't you take a look a HEALpix which provides a nice equal area hierarchical triangulation of the surface of the sphere with no distorted triangles: https://healpix.jpl.nasa.gov/ https://en.wikipedia.org/wiki/HEALPix https://healpix.sourceforge.io/ Here's the NASA illustration of the hierarchy: The package has been instrumental in producing maps and ...


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Maybe this is not a full answer to your question. However, I am currently developing my own unstructured mesh generator and found this toolbox quite helpful. Perhaps there are some algorithms which will help you. Matlab or Github Short (not complete) overview of the genetic algorithms for the TPS problem: Solves the classic Traveling Salesman Problem (TSP)...


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