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.