Electromagnetic field theory as a basis for the odd parity rule incomputational geometry

• Autores: Sumit Ghosh
• Localización: The International journal of engineering education, ISSN-e 0949-149X, Vol. 16, no. 1, 2000, págs. 68-72
• Idioma: inglés
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• Resumen

  • The issue of point location is an important problem in computer graphics and the study of efficientdata structures and fast algorithms is an important research area for both computer graphics andcomputational geometry disciplines. When filling the interior region of a planar polygon incomputer graphics, it is necessary to identify all points that lie within the interior region andthose that are outside. Sutherland and Hodgman are credited for designing the first algorithm tosolve the problem. Their approach utilizes vector construction and vector cross products, and formsthe basis of the `odd parity' rule. To verify whether a test point is within or outside a given planarpolygon, a ray from the test point is drawn extending to infinity in any direction withoutintersecting a vertex. If the ray intersects the polygon outline an odd number of times, theregion is considered interior. Otherwise, the point is outside the region. In three-dimensional space,Lee and Preparata propose an algorithm but their approach is limited to point location relative toconvex polyhedrons with vertices in 3-space. Although it is rich on optimal data structures to reducethe storage requirement and efficient algorithms for fast execution, a proof of correctness ofthe algorithm, applied to the general problem of point location relative to any arbitrary surfacein 3-space, is absent in the literature. This paper argues that the electromagnetic field theory andGauss's Law constitute a fundamental basis for the odd parity rule and shows that the odd parityrule may be correctly extended to point location relative to any arbitrary closed surface in3-space