Faces with holes

[edemaine]

@amandaghassaei points out that the current spec does not deal with holes in faces (without subdividing them somehow), e.g.

+-----+
|     |
| +-+ |
| | | |
| +-+ |
|     |
+-----+

We should extend the spec to handle this. The tricky part is doing so in a backwards-compatible way.

---

Proposal 1:

• faces_boundaries: for each face, list of boundaries, first of which is outside and rest are interior holes
• boundaries_vertices/edges: counterclockwise (?) order of vertices/edges for the boundary, similar to current faces_vertices/edges
• faces_vertices/edges: can still list all vertices/edges on boundary of face (union of face's boundaries), but order is no longer particularly useful.
• When no boundaries listed, assume each face is a single boundary and already in ccw order. So this makes everything backward-compatible: when not using holes, can use FOLD as is, but when dealing with holes, work with boundaries structures instead of faces_vertices/edges.
• frame_attributes of holey (?) and nonHoley (?) to specify whether boundaries are in use

The downside of this approach is unneeded complexity: boundaries don't really need to be first-class, because will generally be used by exactly one face.

---

Proposal 2:

• faces_vertices becomes an array of array of vertex indices, one array per boundary, where first boundary is exterior and ccw, and other boundaries are holes and cw
• faces_edges (optional) similarly becomes an array of array of edge indices

Key question for this approach: do we want v2 to allow both forms (each element of faces_vertices is an array of indices, or an array of array of indices), or just the hole-supporting form (each element of faces_vertices is an array of array of indices)?

[edemaine]

Update on this topic: FOLD 1.2 supports "J" assignment for join edges, which is one way to represent holes (subdividing holey faces into simply connected faces).