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The Degree Elevation of UE-spline Curves
Duan Xiaojuan,Wang Guozhao (사)한국CDE학회 2013 한국CAD/CAM학회 국제학술발표 논문집 Vol.2010 No.8
Unified and extended splines(UE-splines), which can unify and extend polynomial, trigonom etric and hyperbolic B-splines, inherit most properties of B-splines and have advantages over B -splines for modeling. This paper mainly studies the degree elevation of UE-splines. First, we construct a new class of basis functions, called bi-order UE-spline basis. The bi-order UE-splines are defined by the integral definition of splines. Then some important properties of bi-order UEsplines are given especially for the transformation formulas of the basis functions before and after inserting a interior knot into the knot vector. We finally proved that the degree elevation of UE-spline curves can be interpreted to be corner cutting on the control polygons.