Appears in collection : School on Low-Dimensional Geometry and Topology: Discrete and Algorithmic Aspects

This series of lectures will describe recent and not-so-recent works in computational topology of curves in the plane and on surfaces. Combinatorial and algorithmic aspects will be discussed.

Lecture 1. Historical roots of computational topology - topological invariants, combinatorial encodings, and algorithms - angle sums, rotation numbers, regular homotopy - winding numbers, signed area, point-in-polygon - graphs and Euler tours - Gauss/Dowker code planarity