【摘要】 样条曲线的升阶是CAD系统相互沟通必不可少的手段之一.由于双阶样条的升阶算法具有割角性质,因此具有鲜明的几何意义.以代数双曲B-样条为例,证明了样条曲线经过不断升阶之后,其控制多边形序列会像Bézier曲线一样收敛到初始的代数双曲B-样条曲线.利用文中得到的结果,就可以像Bézier曲线一样,通过几何割角法生成B-样条曲线?双曲线?悬链线等常用曲线.更多还原

【Abstract】 Degree elevation of spline curves is an essential technique for communication between CAD systems.Since degree elevation algorithm by bi-order Spline can be interpreted as corner cutting process,degree elevation of Spline curve has obvious geometric meaning.Taking algebraic hyperbolic B-spline curve as an example,it is proved that Spline curve’s control polygon sequence will converge to the initial algebraic hyperbolic B-spline curve after degree elevation continually.By this conclusion,common curves including B-spline,hyperbola and catenary curves can be obtained by geometric corner cutting as Bézier curves.更多还原