A new approach (extra vertex) and generalization of Shoelace Algorithm usage in convex polygon (Point-in-Polygon)

TL;DR

This paper introduces a novel extension of the Shoelace Algorithm for efficiently determining point inclusion in convex polygons, generalizing its application to line segments and polygons, with promising test results.

Contribution

It presents a new approach and generalization of the Shoelace Algorithm for point-in-polygon problems, enhancing efficiency and applicability.

Findings

The new method is more effective than existing approaches.

Testing confirms improved performance in Python implementations.

Generalization to line segments and polygons broadens the algorithm's usability.

Abstract

In this paper we aim to bring new approach into usage of Shoelace Algorithm for area calculation in convex polygons on Cartesian coordinate system, with concentration on point in polygon concept. Generalization of usage of the concept will be proposed for line segment and polygons. Testing of new method will be done using Python language. Results of tests show that the new approach is more effective than the current one.