Abstract
A set of parametric equations of an algebraic curve or surface is called normal, if all the points of the curve or the surface can be given by the parametric equations. In this paper, we present a method to decide whether a set of parametric equations is normal. In addition, we give some simple criteria for a set of parametric equations to be normal. As an application, we present a method to find normal parametric equations for conics. We also present a new method to find parametric equations for conicoids, and if the parametric equations found are not normal, the missing points can also be given.
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