Legal move

• Split – Always legal

• Collapse : if and only if…
  • For all vertices {k} adjacent to both {i} and {j}, {i,j,k} is a face
  • If {i} and {j} are both boundary vertices, {i,j} is a boundary edge
  • K has more than 4 vertices if {i} and {j} both are not boundary vertices, or K has more than 3 vertices if either {i} or {j} are boundary vertices

• Swap – if and only if {k,l} ? K

• Proof in Hoppe et al, TR 93-01-01 University of Washington

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