Juan Gerardo Alcázar

TL;DR: An algorithm for computing the topology of a real algebraic space curve C, implicitly defined as the intersection of two surfaces, is presented and it is shown that any curve can always be linearly transformed to be in general position.

TL;DR: A novel and deterministic algorithm is presented to detect whether two given rational plane curves are related by means of a similarity, which is a central question in Pattern Recognition, and as a by-product it finds all such similarities.

TL;DR: A good number of theoretical results on symmetries of polynomial curves, algorithms for detecting rotation and mirror symmetry, and closed formulas to determine the symmetry center and the symmetry axis, when they exist are provided.

TL;DR: The paper presents a novel, deterministic, and efficient method to detect whether a given rational space curve is symmetric, using well-known differential invariants of space curves, namely the curvature and torsion.

TL;DR: The problem of determining a real finite set of z-values where the topology type of the level curves of a (maybe singular) algebraic surface may change is addressed by analyzing the real roots of a univariate polynomial; namely, the double discriminant of the implicit equation of the surface.