Research On The Convexity-preserving Of NURBS Interpolation Curve Based On Weight Factor

NURBS curves are widely used.How to modify the existing curves to meet the requirements of the designers is particularly critical after the construction of the NURBS curve.In practice,a set of discrete points are often given,then the designer is required to construct a NURBS curve to pass those points.It has a wide range of applications,such as image reconstruction,given the value of the aircraft type point to draw the aircraft lines,etc.Although,the curve obtained by the interpolation method can achieve the desired results,it is still difficult to meet the actual requirements.Because the NURBS interpolation curve is not easy to control and can't guarantee the convexity-preserving of the curve,it has a great uncertainty of the shape of the curve.Therefore,we need to make further shape adjustment of the NURBS interpolation curve.The NURBS curve has a partial modification,the weight factor and its corresponding control vertices only affect the shape of the curve in the u?[u_i,u_i+p+1],it makes the NURBS method more flexible.The influence of weight factor on the shape of the NURBS curve is clear and intuitive.However,at present,people can't flexibly use the weight factor.Because an improper value of the power factor will lead to very bad parameters,so that the curve does not have convexity-preserving,or even destroy the structure of the curve,which will not be able to control or predict the shape of the curve.Explore the scope of the convexity-preserving of the weight factor of the NURBS interpolation curve wills enable the modeling personnel to control the weight factor conveniently and correctly,to the weight factor more freely,to bring out NURBS's potential.Therefore,study the convexity-preserving of NURBS interpolation curve based on weight factor is very indispensable.This study mainly consists of five parts:?1?We explore the interpolation theory and algorithm of the NURBS curve with the constraint of the end vector,and discuss the arithmetic of the node vector group and the inverse control vertex of the interpolation curve with the vector restriction at the endpoints.?2?The dissertation proposes the specific steps of convexity-preserving through amending the value of the weight factor to regulate and control the local shape of the interpolation curve,and proves the influence of weight factor on the shape of interpolation curve through example analysis.?3?We discuss the influence of different values of the weight factor on the curve shape.In order to ensure the accuracy of the convexity of the weight factor,this study clearly demonstrates the influence of the end guidance vector on the convexity by numerical examples.?4?This paper gives an optimization algorithm of the convexity-preserving of the weight factor of NURBS interpolation curve based on the curve interpolation and the weight factor.This study implements computer simulation through numerical examples,controls the weights with purpose and procedure,and then defines the scope of the convexity-preserving by observing the changes of the interpolation curve with this operation.Then we discuss the influence of the relationship between the weight factors on the convexity-preserving of NURBS interpolation curve,which further improves the accuracy of the scope of the convexity-preserving.?5?We give the application in the design of ship modeling.