Real implicitization of curves and geometric extraneous components

Real implicitization of parametric curves has important applications in computer aided geometric design. Implicitization of parametric curves by resultant computations may lead to super uous isolated points. Hence, an exact implicit description should consist of equations and further conditions excluding these geometric extraneous components. Although a real implicit description of this kind can be obtained by real quantifier elimination, we give a direct way to find the conditions to add for an exact description. This results in a more effective algorithm and nicer formulas.