| _version_ | 1866901745477615616 |
|---|---|
| author | sinha, shriprakash |
| author_facet | sinha, shriprakash |
| contents | <div> <div> <div> <p>The current work revisits the point-in-polygon problem by providing a novel solution that explicitly employs the properties of epigraphs and hypographs. Using concepts of epigraphs and hypographs, this manuscript provides a new definition of inaccessibility and inside, to accurately specify the meaning of inclusion of a point within or without a polygon. Via Poincar ́e’s ideas on homotopy and Hopf’s Degree Theorem from topology, a relationship between inaccessibility and inside is established and it is shown that consistent results are obtained for peculiar cases of both non-intersecting and self-intersecting polygons while investigating the point inclusion test w.r.t. a polygon. Through illustrative examples, the novel method addresses the issues of • ambiguous solutions given by the Cross Over for both non-intersecting and self-intersecting polygons and • a point being labeled as multiply inside a self-intersecting polygon by the Winding Number Rule, by providing an unambiguous and singular result for both kinds of polygons. The proposed solution bridges the gap between Cross Over and Winding Number Rule for complex cases. I provide here the MATLAB code for executing the Point in Polygon algorithm. It also contains data for running the code.</p> <p> A short description of the files and how to run the code - </p> <ul> <li>The link in the section "identifiers" below, shows the sequence in which the files need to be executed in MATLAB.</li> </ul> </div> </div> </div> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15265568 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | MATLAB code for Point in Polygon Problem via Homotopy and Hopf's Degree Theorem sinha, shriprakash <div> <div> <div> <p>The current work revisits the point-in-polygon problem by providing a novel solution that explicitly employs the properties of epigraphs and hypographs. Using concepts of epigraphs and hypographs, this manuscript provides a new definition of inaccessibility and inside, to accurately specify the meaning of inclusion of a point within or without a polygon. Via Poincar ́e’s ideas on homotopy and Hopf’s Degree Theorem from topology, a relationship between inaccessibility and inside is established and it is shown that consistent results are obtained for peculiar cases of both non-intersecting and self-intersecting polygons while investigating the point inclusion test w.r.t. a polygon. Through illustrative examples, the novel method addresses the issues of • ambiguous solutions given by the Cross Over for both non-intersecting and self-intersecting polygons and • a point being labeled as multiply inside a self-intersecting polygon by the Winding Number Rule, by providing an unambiguous and singular result for both kinds of polygons. The proposed solution bridges the gap between Cross Over and Winding Number Rule for complex cases. I provide here the MATLAB code for executing the Point in Polygon algorithm. It also contains data for running the code.</p> <p> A short description of the files and how to run the code - </p> <ul> <li>The link in the section "identifiers" below, shows the sequence in which the files need to be executed in MATLAB.</li> </ul> </div> </div> </div> |
| title | MATLAB code for Point in Polygon Problem via Homotopy and Hopf's Degree Theorem |
| url | https://doi.org/10.5281/zenodo.15265568 |