In this paper we consider rational Bézier curves with control points having rational coordinates and rational weights, and we give necessary and sufficient conditions for such a curve to have infinitely many points with integer coefficients. Furthermore, we give algorithms for the construction of these curves and the computation of theirs points with integer coefficients.
We study some geometric configurations related to projections of an irreducible algebraic curve embedded in onto embedded projective planes. These configurations are motivated by applications to static and dynamic computational vision. More precisely, we study how an irreducible closed algebraic curve embedded in , of degree and genus , can be recovered using its projections from points onto embedded projective planes. The embeddings are unknown. The only input is the defining equation of...