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What is the algorithm which transforms the octree/quadtree into a grid? i.e, getting the adjacency or connectivity between the cells in order to be able to perform interpolation, gradient,...etc. I am trying to do it on the fly. I ended up using the following procedure:

  1. Check if a voxel is to be divided.
  2. If true, create new 4 quads or 8 voxels.
  3. For each face (or edge in case of 2D), update the connectivity by checking neighbors of the parent cells.

However, it is not clear to me how to control the maximum refinement ratio.

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The one paper you need to know is the one by Burstedde and collaborators on the implementation of the p4est library: p4est: SCALABLE ALGORITHMS FOR PARALLEL ADAPTIVE MESH REFINEMENT ON FORESTS OF OCTREES. It is detailed to the point where you don't want to read it, but if you need to read it because you need a specific algorithm, then that is the place.

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    $\begingroup$ Thanks for the answer. I needed to read all the points actually $\endgroup$
    – Al-Farouq
    Commented Nov 16, 2021 at 13:45

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