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[Adam Getchell <>]

Hello all,

I’m working on a bistellar flip for 3D triangulations, briefly as follows:

Step 1: Find a candidate edge for which a circulator around that edge obtains 4 incident cells.

Step 2: Get the 2 vertices comprising the candidate edge.

Step 3: Get the remaining 4 vertices in the 4-cell complex (there are 6 vertices in the cell complex).

Step 4: Obtain a new pivot edge between 2 different vertices for which a circulator around that pivot edge would obtain 4 new incident cells comprised of the 6 vertices.

Step 5: Find the 8 neighboring cells of the original 4-cell complex.

Step 6: Delete the old cells.

Step 7: Create the new cells using the same 6 vertices.

Step 8: Assign the 8 neighboring cells to the cells in the new 4-cell complex.

Details here: https://github.com/acgetchell/bistellar-flip

The issue is at the conclusion of Step 8, all cells have been verified as valid, cell orientations have been verified/reoriented, but the triangulation itself is not valid.

The error is: “neighbor of c has not c as neighbor”

My question is, do I also need to track the 32 neighboring cells of the 8 neighbors of the 4-cell complex being flipped? (And in my test case, the 8 neighbors are all infinite.)

Is there some other mistake?

Thanks for your advice,

Adam

P.S. I have looked at the Tetrahedral Remeshing package at Sebastien Loriot’s suggestion. I’m presently unsure if any of those functions (e.g. construct_opposite_vector_3_object()) are relevant.

-- 
Adam Getchell
https://adamgetchell.org