A Jordan curve is a planar, simple, closed curve: a continuous loop that does not intersect itself. A rectangle, or any polygon’s perimeter, is a Jordan curve. section 15.1.1
In graph embeddings, an edge can be represented by a section of a Jordan curve joining two vertices. The edge must avoid self-intersection and must not meet another edge or a non-endpoint vertex. section 15.1.1 section 15.1.2
Valid and invalid boundaries
Treat a rectangle’s perimeter as valid: it closes and has no crossing points. Reject a twisted or self-crossing loop because its border intersects itself. section 15.1.1
Figure 15.4 Examples of Jordan and non-Jordan curves. A Jordan curve is a closed curve whose border doesn’t have intersection points (it’s not “twisted” like the last two examples). Notice how a rectangle (or any polygon’s perimeter) is a valid Jordan curve. For graphs’ edges we’ll use sections of Jordan curves, so the only restriction will be that it must not self-intersect in any point.
Compare ordinary closed loops, rectangles, and twisted curves to identify closure and self-intersection constraints. section 15.1.1
