An improved judgement algorithm of point in-out convex polygons

TL;DR

This paper introduces an efficient algorithm for determining whether a point lies inside or outside a convex polygon by transforming the problem into a quadrilateral point-inclusion test, significantly reducing intersection checks.

Contribution

It presents a novel method that simplifies convex polygon point-inclusion testing into a quadrilateral problem, improving efficiency over existing algorithms.

Findings

Fewer intersections compared to traditional methods

Algorithm complexity is O(1) to O(n)

Significant improvement in judgment efficiency

Abstract

This paper proposed a method to judge whether the point is inside or outside of the simple convex polygon by the intersection of the vertical line. It determined the point to an area enclosed by two straight lines, then convert the problem of determining whether a point is inside or outside of a convex polygon into the problem of determining whether a point is inside or outside of a quadrilateral. After that, use the ray method to judge it. The complexity of this algorithm is O(1) to O(n). As the experimental results show, the algorithm has fewer intersections and greatly improves the efficiency of the judgment.