# Slides — Combinatorial Surfaces

This lecture describes some of the basic building blocks for digitally encoding geometry using meshes and mesh data structures, namely simplicial complexes, adjacency matrices, and the halfedge data structure:

## 2 thoughts on “Slides — Combinatorial Surfaces”

1. Yiyuan Chen says:

What’s the boundary of a line? (Not including endpoints) I’m having a hard time figuring out from the definition

1. Mark says:

The boundary is only defined on pure simplicial complexes. The line without its endpoints is not a pure simplicial complex (because it’s not a simplicial complex), so its boundary is not defined according to our definition. If we add in the endpoints to make our line into a pure 1-complex, then its boundary is just the two endpoints, since they’re both proper faces of exactly one simplex (the edge between them)