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Abstract: The manuscript presents a theoretical proof in conglomeration with newdefinitions on Inaccessibility and Inside for a point S related to a simple orself intersecting polygon P. The proposed analytical solution depicts a novelway of solving the point in polygon problem by employing the properties ofepigraphs and hypographs, explicitly. Contrary to the ambiguous solutions givenby the cross over for the simple and self intersecting polygons and thesolution of a point being multiply inside a self intersecting polygon given bythe winding number rule, the current solution gives unambiguous and singularresult for both kinds of polygons. Finally, the current theoretical solutionproves to be mathematically correct for simple and self intersecting polygons.



Autor: Shriprakash Sinha, Luca Nanetti

Fuente: https://arxiv.org/







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