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Original mesh:
Incremental Decimation applies a series of decimation operators:

By reversing these operators, we can reconstruct from the decimated mesh


In order to make a Halfedge Collapse operator reversible, we need to store:

• Position of the source vertex which was collapsed:
• A pointer to the target vertex towards which was collapsed:
• Pointers to the two boundary vertices which were adjacent to both and before the collapse:

Thus, each operator is stored as


Selective Refinement
If we want to undo an operator

the problem might be that one of the opposite vertices or does not exist:

• / might not exist yet if it is still not expanded
• / might not exist anymore if it has previously been split

In order to solve this problem, we store the refined mesh as a binary forest where the leaf nodes are the unrefined vertices and each inner node corresponds to a decimation operator.

During decimation, we remember from which original vertices our mesh started out. Initially, we store at every triangle corner a pointer to the incident vertex. As we decimate the mesh, these triangle corner labels remain intact. When we store an operator, instead of storing , as the vertices in the decimated mesh, we store the values stored in the respective triangle corners.

If we want to refine at a vertex , we find the two opposite vertices , in the currently refined mesh by walking up the binary forest of operators until we find vertices that have already been instantiated.