Orientation, Convexity-Concavity and Inclusion Query Algorithms for Polygons Using the Edge-Azimuth-Length Concept

A metric square with each side of 2 units long is constructed inside the given polygon, and the azimuth of a radial vector, taking y-axis as north direction, is represented in terms of edge-azimuth-length (EAL), i. e. the overall length of the square edges included between their crossing points with y-axis and the given radial vector, resulting in a monotonically continuous function value ranging from 0 to 8, as the azimuth increasing from 0° to 360°. Orientation of a polygon and convexity-concavity of a vertex can be detected by verifying whether the EAL values of consecutive edges are increasing monotonically or not, while point inclusion query can be clarified by taking the given point as origin and summing-up the incremental EAL value of each edge: ±8 means included and 0 means not.