Algebraic Curve Fitting Technique Based On Implicitization

Curve and surface fitting is a basic research in computer-aidedgeometric design (Computer Aided Geometric Design). Traditional curvefitting construct an approximate continuous curve to pass through thediscrete points over the plane or space. With the emerging needs of thenew reality, researchers began to explore the curve fitting problems forcertain segments of parametric curves in theory, and develop a numberof new techniques and methods.In the classic geometric modeling, parametric curve is widely usedbecause of its simple structure, easy computing, graphics and convenient;Meanwhile, the implicit curve has its unique advantages, such as theshape containing more information, the shape closed about thegeometric flip operation, more suitable for certain fields. Research thechanging between implicit representation and parameterrepresentations has been a hot and difficult problems. This study is tolearn the thought of the approximate implicitization of parametric curves,we propose a new method of curve fitting.In the overall framework of the approximate implicitization method,the paper uses the traditional approximate implicitization based on∞ norm and the weak approximation implicitization based on2-norm todeal with curve fitting problem, and then we give algorithm flowseparately. Later in this article we use examples to illustrate the validityand effectiveness of the approximate fitting methods, and discusses theimpact of the choice of the number and times of function of the base tothe curve fitting, and the fitting results when the curvature of parametriccurves is larger and intersect points between intersect curves.