TWO BASIC APPROACHES TO SIMPLIFICATION

• BOXING PRINCIPLE:
  - Subdivide space into cells, and identify vertices in a cell.
  - Bound on perturbation error of vertices.
  - No guaranteed reduction of complexity.
  - Missed opportunity for simplification (chain straightening)
  - topological change somewhat mild
  - RELATED IDEAS: snap-rounding, numerical rounding, clustering
• DECIMATING PRINCIPLE:
  - Delete some vertices and re-triangulate
  - E.G. delete an independent set (Kirkpatrick/Dobkin)
  - Guarantees reduction of complexity.
  - No bound on perturbation error.
  - severe topological change likely
• HYBRID APPROACH:
  - combine the two