1. Definition of concave polygon
- Defined in terms of:
凹多边形至少存在一个内角大于180度. - Definition from the boundary: The boundary of a concave polygon has at least one convex side, that is, the side has at least one interior angle greater than 180 degrees.
- From the definition of the convex hull: the convex hull of the concave polygon does not coincide with itself, that is, the convex hull vertex with at least one convex hull vertex inside the concave polygon is not on the concave polygon.
- Definition from point set: For any point inside the concave polygon, the circle centered on the point is not completely contained in the concave polygon.
In my perspective, the core definition is the angle definition, and then other definitions are derived.
2. Concave polygon judgment: side vector cross product
2.1 Principle
The cross product is based on the right-hand rule, the thumb pointing down is the negative direction, and the upward direction is positive
[Principle Analysis] How to distinguish concave polygons