Matrix-based implicit representations of rational algebraic curves and applications Original Research Article

Given a parameterization of an algebraic rational curve in a projective space of arbitrary dimension, we introduce and study a new implicit representation of this curve which consists in the locus where the rank of a single matrix drops. Then, we illustrate the advantages of this representation by addressing several important problems of Computer Aided Geometric Design: the point-on-curve and inversion problems, the computation of singularities and the calculation of the intersection between two rational curves.