Quadratic B-spline Curves With Adjustable Shape Parameters

Adjusting the shape and position of curves and curve surfaces by the method-Com-position Curves by parameters, is the major topic in recent function approximation domainreaching works. Low order B-Spline Curve with simple structure, agility, and smooth con-nectivity is one of the most frequently used curves in CAGD. In this paper, we focuseson spline curve shape changes through control vertexes changes and the control vertexeschanges are fulfilled by transforming matrix with shape parameters. This article illus-trates the processes of curve shape adjustment by adding more control vertexes throughtransforming matrix with shape parameters and by using parameter changes to adjust theposition of control vertexes.Major conducted works are as follows:Firstly, the paper explains and analyzes the theory and its application status quo ofB-Spline Curve shape adjustment.Secondly, the paper gives out the method to adjust B-Spline Curve shape by usingcontrol vertex transforming matrix with shape parameters. The method consists of twoparts. One is to adjust the curve shape near the endpoints of B-Spline Curve. The otheris to adjust the curve shape excluding the endpoints of B-Spline Curve. Furthermore,the paper discusses the classification and the important relationship between curve shapeadjustment and parameter value range.Last, the paper provides some geometric modeling examples which derived by usingcontrol vertex transforming matrix with shape parameters.More specifically, the paper gives out construction method of B-Spline Curve withshape adjustment parameters and analyzes the geometric meaning of the parameters andthe curve shape change caused by shape parameter adjustment. On one hand, B-SplineCurve has complete properties and the basis function hasn’t been changed during theprocess of changing curve shape by parameter range adjustment, therefore, the propertiesof this B-Spline Curve generated by this method are obvious. On the other hand, based onthe facts that Spline Curve has outstanding locality characteristics and mainly depends on control vertexes and basis functions, the transforming matrix can reach the goal of localityadjustment. Using this method can construct multiple curve segments which satisfy localityrequirements and to satisfy whole requirements and locality requirements of curve design.