Lower bounds of distances between algebraic surfaces and space curves

• Autores: Juan Gerardo Alcázar Arribas , Carlos Hermoso Ortíz
• Localización: Monografías de la Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza, ISSN 1132-6360, Nº. 43, 2018 (Ejemplar dedicado a: Proceedings of the XVI EACA Zaragoza Encuentros de Algebra Computacional y Aplicaciones), págs. 31-34
• Idioma: inglés
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• Resumen

  • We present on-going work to compute lower bounds of distances between an implicit algebraic surface, and a space algebraic curve. The main idea is to use the level surfaces of the polynomial defining the surface: one computes the level surface of the polynomial which first intersects the curve, and then the lower bound is computed as the distance between such level surface, and the original surface. The idea is useful to find lower bounds of distances in situations involving some simple surfaces which are, however, widely used in Computer Aided Geometric Design, like ellipsoids, surfaces of revolution, or cylindrical surfaces.