Offset Approximation Curve Based On Interval Bézier Curve And Its Application

The Offset curve is also called a parallel curve,which is a collection of points equal to the normal distance of points on a given curve.In recent years,isometric curves have been widely used in computer-aided design,such as robot navigation,tool trajectory calculation,NC machining and so on.The Offset curve,because of its complicated structure,cannot be effectively processed by the industrial application,it has the interval Bézier curve with strip region,its boundary structure is relatively simple,but the interval Bézier curve with rectangular control vertex is not high enough in fitting effect,enveloping and equidistant.In this paper,the arrangement of the control vertex of the interval Bézier curve is replaced by a rectangular polygon,and the circle is gradually approximated,which will make the whole envelope region boundary more approximate to the Offset curve.The results show that the algorithm is simple and can realize the overall error estimation.The full text content is divided into the following chapters.The first chapter is the introduction,mainly expounds the research background and significance of the subject,as well as the current research situation at home and abroad,introduces the main research methods in recent years,finally,on the basis of predecessors,puts forward the main problem of this paper,namely,the Offset approximation curve based on interval Bézier curve.The second chapter is the preliminary knowledge,mainly introduces the concept of Bézier curve,the concept of B-spline curve,the realization of three-time Bézier curve and the realization of three uniform B-spline curve,which lays a theoretical foundation for the algorithm of equidistant approximation curve based on interval Bézier curve..The third chapter mainly introduces the boundary composition and realization of the interval Bézier curve,and the relation between the interval Bézier curve and the equidistant line.In the fourth chapter,the concept of Offset curve is introduced emphatically,and a new algorithm of Offset approximation curve is proposed based on the boundary composition principle of the interval Bézier curve,and compared with other relative Offset curve approximation algorithms.The fifth chapter introduces the application field analysis of this kind of equidistant curve approximation algorithm,and points out the direction that can be further studied in the future.The sixth chapter is the summary and prospect of the full text.