Optimal Parameterization Of Rational Parameter Curve

Curve is the computer aided design (CAGD) and computer graphics (CG) one of the keyresearch object.Its rational parameter is commonly used in the geometric modeling and designof a kind of representation,for example,the commonly used to rational parameters of theBézier curve and B-spline curve.At the same time,rational parameter curve is widely used inthe mathematical model in the modern geometric design system.In recent years,it has been animportant research hot spot and trend,there are many scholars all around it to do a lot ofrelated research[1-7].Therefore,the main research object of this paper will be selected forrational parametric curves.At present,the parametric technology of curve has wide application in many fields, suchas geometric modelling and mechanical engineering drawings fields.For example,in theprocess of garment bulk production automation,technical personnel hope that when machinesewing clothes according to the model design of the curve,it can make each needle pointsmove on the curve moving at a constant linear speed,namely the arc length parametric.But,itsform is extremely complex,large amount of calculation,and its not directly to be effectivelyapplied to all kinds of design.At the same time,in terms of the commonly used form ofrational parametric in CAGD,it also can’t take its arc length as a parameter.Thus,most scholarsbegan to convert ideas to look for all kinds of representation of optimal parametric curvealgorithm towarding to close to the direction of the arc length parametric[8-16].Based on theabove issues involved,The main research content of this article is to discuss the rationalparameters of optimal parametric curve.In order to solve the above questions,this paper puts forward a kind of any number oftimes can be determined rapidly and accurately rational parameter curve algorithm of optimalparametric equations according to the given standard of literature [15].First of all,a sufficientcondition of the optimal parametric equation of rational parametric curves is given,namelytwo endpoint parameters rate is equal and is the most value.Then,for the general situation ofrational parametric curves,the optimal parametric equation of a kind of new algorithm isproposed.In the end,with the algorithm in this paper compared with the parameterization results of other algorithms,the results show that the algorithm is simple,reliable and smallamount of calculation,good effect,wide scope of application in this paper.On a great extent,the proposed method makes the computer in the geometric shape andmechanical drawing was improved work efficiency.It also for subsequent about rationalparameter curve laid the foundation for the further theoretical research and practicalapplications.