Study On Some Problems In Geometric Design And Calculation

In resent years,international scholars begin to emphasize "geometric calculation". They think that "geometric design" is not able to describe such a branch of learning such as CAGD,which has a rigorous mathematical foundation as well as important applied background. And yet,"geometric design and calculation " not only widens the studying range in the field,but also gives it new vigor.In this paper,the first chapter is introduction,in which we briefly review some know-how of geometric design and calculation. In the second chapter some problems for degree reduction of Bezier curves and surfacesare studied. In this chapter,degree reduction of Bezier curves with points constraints is proposed and the new approach of constrained optimization is brought in light. The stepwise method for degree reduction of rectangular Bezier surfaces is further discussed. The advantage of this method is that the method of curves can be directly used on rectangular surfaces for degree reduction. In the third chapter,modifying the shape of NURBS surfaces and rational Bezier curves with geometric constraints is studied. The problems based on weights are discussed. In the chapter four,extension algorithms for B-spline curves are investigated. The new step-iterative method of parameterization by accumulative arc length is proposed. Finally,extension algorithms for NURBS curves are discussed by means of homogeneous coordinates.