Good local behavior of offsets to rational regular algebraic surfaces

Local information on the shape of a regular surface is provided by the well-known notions in Differential Geometry of elliptic, parabolic and hyperbolic points. Here, we provide algorithms to check that, for a given distance, the offsetting process does not introduce relevant local changes in the shape of a surface, under the hypothesis that the surface is described by means of a rational, regular, real parametrization. Also, we provide algorithms for computing intervals of distances with this nice property.