The Research On Relationship Between Degree Elevation Of NUAT B-spline Curves And Corner Cutting

In the fields such as Computer Aided Geometric Design(CAGD) and geometricmodeling, free-form curves and surfaces play an important role, degree elevation isone of the most important technique in the modeling method of free-form curves andsurfaces.This paper presents the degree elevation of non-uniform algebraic-trigonometricB-spline(NUAT B-spline) curve, proves that the geometric meaning of the algorithmis comer cutting, and also proves the convergence of the control polygons series ofNUAT B-spline curves. Our main idea is elevating the degree of NUAT B-splinecurves one knot interval by one knot interval. In the end, a new class of basisfunctions, to be called bi-order NUAT B-spline basis funtions, is constructed.This thesis focuses on the problems as follows:Firstly, the research background is introduced in the chapter one.Secondly, the problem of degree elevation of NUAT B-spline curves and the mainidea are described in the chapter two.Thirdly, a new class of basis functions, to be called bi-order NUAT B-spline basisfuntions, is constructed in the chaper three, and the comer cutting algorithm of thedegree elevation is proved.Fourthly, the convergence of the control polygons series of NUAT B-spline curvesis proved in the chapter four.Finally, in the chaper five this thesis draws the conclusions and talks about someprospects.