This paper proposes a new representation method of plane curves and develops a novel model in parameterization. Implicitly parametric curve is defined on the implicit curve and has a parametric form, which combines the advantages of parametric form an...
This paper proposes a new representation method of plane curves and develops a novel model in parameterization. Implicitly parametric curve is defined on the implicit curve and has a parametric form, which combines the advantages of parametric form and implicit form. For a given curve, the conversion among the implicit representation, parametric representation and implicitly parametric representation are provided. As the application of implicitly parametric curve, a parameterization method of closed implicit curves is addressed. We provide a model to construct an implicitly parametric curve for implicit curve, which is a smooth mapping from the standard shape to the implicit curve without overlap and satisfies some constraints. The implicitly parametric curve is obtained by solving the constrained minimization problem. An approach is provided to get the parameterization based on the implicitly parametric curve. Several examples are given to illustrate the effectiveness of the parameterization method.