Your next reading will take a dive into purely combinatorial descriptions of surfaces, i.e., those that capture connectivity, but not geometry. These descriptions and data structures will provide the foundation for all the geometry and algorithms we’ll build up in this class. (The reading also provides the essential background for your first written and coding assignments!)
The reading is Chapter 2, pages 7–20 of our course notes, which can always be accessed from the link above.
Your short 2-3 sentence summary is due by 10am Eastern on February 19, 2020. Handin instructions can be found on the assignment page.
If anyone is looking for a more precise discussion of “combinatorial surfaces” beyond [oriented] simplicial complexes, you may want to check out this great set of notes from Jeff Erickson:
Computational Topology — Cell Complexes
The halfedge mesh we introduced in lecture will in general encode complexes beyond oriented simplicial complexes—in particular, it will describe a 2-dimensional CW complex. If we limit each face to having three sides, then a halfedge mesh will encode a \(\Delta\)-complex. (See the notes above for definitions!)