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A topological question: Why is it that these two corners, despite having the "same" topology, subdivide so differently?enter image description here enter image description here

I know its something to do with concave vs convex corners, but does anyone have a technical explanation or link that I can refer to?

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  • $\begingroup$ Despite having the same topology, they are completely different form so the difference in form after subdivision should not be surprising. The only logical expectation here would be that because they have the same topology, they will have the same topology after subdivision as well. $\endgroup$ Apr 27, 2023 at 7:42

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To illustrate the situation, this is due to this vertex that is on top of the two triangles, not directly because of the triangles, but because it is not supported, on its sides (as opposite to the one below it).

If we activate the subdivision surface modifier, then show where the point is when the subdivision is applied:

enter image description here

If we just keep the two concerned lines, from above, with on top below the resulting curvature, and on the bottom part the vertices added when the modifier is applied:

enter image description here

When convex, the exact same thing occurs, but that apparently has no visible consequence because the vertex is pushed inside its above surface.

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