Degree Elevation of Algebraic Hyperbolic B-spline Curves and Corner Cutting Based on Bi-order Spline

Abstract

The authors consider the degree elevation of algebraic hyperbolic(AH) B-spline curves and prove that the degree elevation of AH B-spline curves can be interpreted as corner cutting process in theory.A new class of basis functions,to be called bi-order algebraic hyperbolic B-spline basis functions,is constructed and discussed by the integral definition of spline.This class of basis functions has bi-order property and the transforming formulae between AH B-spline and bi-order AH B-spline lead to the corner cutting for degree elevation of AH B-spline curves.