{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/polyhedron-kernel-computation-using-a","title":"Polyhedron Kernel Computation Using a Geometric Approach","arxiv_id":"2202.06625","date":"2022-02-14","proceeding":null,"authors":["Tommaso Sorgente","Silvia Biasotti","Michela Spagnuolo"],"abstract":"The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have been proposed for polyhedra. The most acknowledged solution for the kernel estimation is to solve a linear programming problem. On the contrary, we present a geometric approach that extends our previous method, optimizes it anticipating all calculations in a pre-processing step and introduces the use of geometric exact predicates. Experimental results show that our method is more efficient than the algebraic approach on generic tessellations and in detecting if a polyhedron is not star-shaped. Details on the technical implementation and discussions on pros and cons of the method are also provided.","url_abs":"https://arxiv.org/abs/2202.06625v1","url_pdf":"https://arxiv.org/pdf/2202.06625v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"polyhedron-kernel-computation-using-a","repo_url":"https://github.com/tommasosorgente/polyhedron_kernel","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}