RT info:eu-repo/semantics/article T1 Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution A1 Alcázar Arribas, Juan Gerardo A1 Goldman, Ron K1 Equations of a surface K1 Conical surface K1 Surface of revolution K1 Shape recognition K1 Cylindrical surface K1 Ciencia K1 Matemáticas K1 Mathematics AB Given an implicit polynomial equation or a rational parametrization, we develop algorithms to determine whether the set of real and complex points defined by the equation, i.e. the surface defined by the equation, in the sense of Algebraic Geometry, is a cylindrical surface, a conical surface, or a surface of revolution. The algorithms are directly applicable to, and formulated in terms of, theimplicit equation or the rational parametrization. When the surface is cylindrical, we show how to compute the direction of its rulings;when the surface is conical, we show how to compute its vertex; and when the surface is a surface of revolution, we show how tocompute its axis of rotation directly from the defining equations SN 1077-2626 YR 2016 FD 2016-11-07 LK http://hdl.handle.net/10017/27210 UL http://hdl.handle.net/10017/27210 LA eng NO Ministerio de Economía y Competitividad DS MINDS@UW RD 29-mar-2024