I am working through Computational Geometry in C 2nd Ed. and there is a brief talk about non-simple polygons before getting into simple polygons (which are the core of the field).
The book defines a polygon as:
- Adjacent segments share a common point
- Non-adjacent segments do not intersect
My first confusion came from definition (1) which seems redundant. Doesn't the term adjacent in geometry imply the existence of a common point? If so, wouldn't (1) be unnecessary?
My second confusion came from this shape:
(Credit to this post)
There are two "intersection points" in the center. I have labeled the way I saw the segments below:
Is the reason this violates (2) because
s9 (for example) all share a common point and thus "intersect" there? I am sort of confused because these would all be adjacent because they share a common vertex and so it would be okay (per the definition) for them to intersect like they are.
I wanted to make sure before pressing forward. After getting out of geometry a long time ago before I started my CS degree my knowledge has since degraded on the subject.
Any help would be great - thank you!