3- Construct height filtrations for a set of vectors in S^2.

[KiyoshiAndres]

• [ ] Function takes [x,y,z] in R^3 with x^2+y^2+z^2+1, and a mesh.
• [x] Make a function that returns the height of a point.
• [x] Make a data structure that collects:
  • [x] vertex location in original array
  • [x] vertex height
  • [x] vertex coordinates
• [ ] Make a function that checks if the height of a point is less than a threshold.
  • [ ] For each vertex, if it's less than a threshold, add the vertex to a vertex list, and record its array position.
• [x] #7
• [ ] #10

Optimization for function that produces the actual filtration:

• [ ] Remove the vertex from the list if it passes the height check.
• [ ] At the start of each iteration, make a copy of the previous lists, and adjoin to them the new vertices/faces.
• [ ] Function outputs a sequence of meshes (the sublevel set filtrations)