Delaunay Implementation about pyautolens HOT 9 CLOSED

Just out of curiosity on the Step 1's pixelization_neighbors: For a given set of points, should the neighbors defined in the Voronoi term (polygons sharing edges) be the same as the neighbors defined in the Delaunay term (triangles sharing edges)?

For Delaunay, I currently compute the neighbors using this built-in function:

https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Delaunay.vertex_neighbor_vertices.html#scipy.spatial.Delaunay.vertex_neighbor_vertices

It returns a maximum number of neighbors of 9, which is the same as the maximum number of neighbors of a Voronoi tessellation.

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I would have expected the maximum neighbors of a Delaunay triangulation to be 3, corresponding to the 3 triangle edges of each pixel.

Do you know what the 9 corresponds too? And if its related to the Vornoi grid does it vary depending on the source pixelization (as I would guess Voronoi cells can have more / less than 9).

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This is an example of Delaunay tessellation. The black points are the traced pixelization grids and the white points are the circumcentres of the triangles. In Delaunay tessellation, a black point (traced pixel grid) is not associated with only one triangle, instead, it can be a vertice of many triangles. In that sense, it should have more than three neighbors. For example, the black point in the center has 7 neighbors since it connects to 7 other black points.

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(from https://gwlucastrig.github.io/TinfourDocs/NaturalNeighborTinfourAlgorithm/index.html)

Or this image shows it better. Seems Voronoi neighbors are the same things as the Delaunay neighbors.

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Does a image-pixel source-pixel pairing every have more than 3 interpolations?

Clearly, I had no idea how a Delaunay tesslation actually works lol.

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No. An image-pixel source-pixel pairing only has 3 interpolations.

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Okay, great. That plays a signifcant role in the run times of the linear algebra (especially for w-tilde) so is a relief.

It sounds like your pixel neighbors array is correct, and can be used for regularization using the standard function we have.

It may be worth checking whether Vegetti regularize in this way.

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I will check it

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