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### How can one prove the duality of Voronoi and Delaunay?

The duality between Voronoi cells and vertices of the triangulation is pretty clear: each vertex of the Delaunay triangulation is a site in the Voronoi diagram which gets associated with its Voronoi ...
• 241

### Polynomial reconstruction on unstructured grids

You could use a Least Square fit approach to fit some polynomial via neighboring nodes. You could even make the Least Square fit weighted based on distances (potentially passed through something ...
• 4,248
Accepted

### Computing the Voronoi diagram of a region inside a box

To compute the Voronoi diagram of huge (>100 millions) sets of points, you can use the following algorithm: ...
• 2,315

### Computing the Voronoi diagram of a region inside a box

Seems like the experts are not answering your question so I will try to provide an idea. But before I do that I strongly suggest that you look up in the literature for some sophisticated methods that ...
• 621
1 vote

### Elliptic PDE finite volume method with Dirichlet boundary condition

In a cell centered finite volume setting your are discretising the fluxes over your cell boundary as you indicated. Lets say we look at one face between the cubes A and B, the calculated flux would be:...
• 2,935
1 vote

### Polynomial reconstruction on unstructured grids

It is not polynomial, but you may be interested in the Natural Neighbors interpolation (it fits well with Voronoi diagram). To evaluate the interpolant at a given point, insert the point into the ...
• 2,315
1 vote

### Computing the Voronoi diagram of a region inside a box

The simplest way of doing this is to surround your iner box with a bigger box that contains at least all the nearest neighbours of the points within your inner box. Note that there will be an issue ...
1 vote

### Computing the Voronoi diagram of a region inside a box

I understand your question as: I want to draw Voronoi diagram for a subset of points such that it is same as the one which is obtained when considering the complete set of points. Voronoi diagrams ...

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