Using semi-implicit representation of algebraic surfaces

We introduced a general representation of algebraic surfaces, that we called semiimplicit, which encapsulates both usual and less known surfaces. Here we specialize this notion in order to apply it in solid modeling: we view a surface in R³ as a one-parameter (algebraic) family of algebraic low-degree curves. The paper mainly addresses the topic of performing the usual CAD operations with semiimplicit representation of surfaces. We derive formulae for computing the normal and the curvatures at a regular point. We provide exact algorithms for computing self-intersections of a surface and more generally its singular locus. We also present some surface/surface intersection algorithms relying on generalized resultant calculations.