Convex polygon :
A polygon is said convex if the line that joins any two points of the polygon is entirely inside the polygon.
Convex polygon Non-convex polygon
A function D, usually called distance, that respects the following properties when applied to x, y and z :
1. D(x, y) >= 0 (positiveness) 2. D(x, y) = 0 iff x = y (identity) 3. D(x, y) = D(y, x) (symmetry) 4. D(x, y) + D(y, z) >= D(x, z) (triangle inequality)
Monotone chain :
A chain C (i.e. a sequence of edges) is said to be monotone in a direction D if any line L orthogonal to D intersects C in exactly one point.
Monotone chain Non-monotone chain
A polygon P is monotone in some direction if an orthogonal line intersects P in no more than two points ; a convex polygon is monotone in any direction.
Simple polygon :
A polygon with no self-intersecting edges. Since a polygon is defined by a sequence of vertices, a priori nothing prevents any self-intersection of its edges.
Supporting line :
Straight line L passing through a vertex of a polygon P, such that the interior of P lies entirely on one side of L. The supporting line is a generalization of the tangent.