An original goal of algebraic geometry was to understand curves and
surfaces in three dimensions. From these roots, algebraic geometry has
grown into a theoretically deep and technically sophisticated field. Recently,
questions from robotics, computer vision, computer-aided geometric
design and molecular biology, together with the development of computational
methods, have brought these original questions back to the forefront
of research. The implicitization of parametric surfaces, the geometry of
molecules, mechanical design and computer vision all lead to problems that
are challenging from the perspective of computational algebraic geometry