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gistfile1.txt

//
//     |--- h ---|      h = horizon
//     /____ /____      x = current face (other face is prev face)
//     \    |\   /|     c = conflict
//      \ x |<--/---\
//   h2c \  |  /    |---- c2h (twin of prev h2c)
//       _\\| /
//          C
//


//
// Fix topological problems caused by merge.
// Namely, ensure every vertex in the face has >= 3 neighboring faces
// Omitting this step would lead to issues when the merge looks as follows:
//
// Case 1:
//   /|\             / \            / \
//  / | \   merge   /   \   fix    /   \
// (--x  )   =>   a(--x  )   =>  a(     )
//  \ | /           \ | /          \   /
//   \|/             \|/            \ /
//                    b              b
// Strategy 1: merge the faces and remove the "interior" edges (ax, xb, bx, xa). Replace them by the single "exterior" edge (ab)
// Note: We use this strategy when the "other" face is a triangle, since it only has 1 exterior edge that is simple to drop in w/o iteration
//
//         OR
//
// Case 2:           a              a
//   /|\            /|\            /|\
//  / | \   merge  / | \   fix    / | \
// (--x  )   =>   (  x  )c  =>   (  |  )c
//  \ | /          \ | /          \ | /
//   \|/            \|/            \|/
//                   b              b
// Strategy 2: combine edges ax and xb into ab and combine bx and xa into ba
// Note: We use this strategy when the "other" face has >3 edges, since replacing the 2 edges w/ 1 won't lead to a degenerate triangle like it would in the triangle case
//
// Note: We could always use a more complex version of Strategy 1 where we replace them by a chain of exterior edges (in Case 2, these would be bc and ca), but this would require yet another iteration of edges.