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1991•International Journal of Computational Geometry & ApplicationsRequires access

ON THE NORMAL PARAMETERIZATION OF CURVES AND SURFACES

Xiao-Shan Gao, Shang-Ching Chou

Open publisher page 24 citations

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.

About this research paper

What this paper is about

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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OpenAlex reports 24 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available 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.

Key concepts: Parametric statistics, Parametric equation, Mathematics, Conic section, Parametric surface, Algebraic equation, Set (abstract data type), Simple (philosophy)

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