Computer Aided Geometric Design - Special issue: Topics in CAGD
A recursive proof of a B-spline identity for degree elevation
Computer Aided Geometric Design
A fast algorithm to raise the degree of spline curves
Computer Aided Geometric Design
The NURBS book
A geometric look at corner cutting
Computer Aided Geometric Design
A simple, efficient degree raising algorithm for B-spline curves
Computer Aided Geometric Design
Algorithms for degree-raising of splines
ACM Transactions on Graphics (TOG)
Computer Aided Geometric Design
Knot intervals and multi-degree splines
Computer Aided Geometric Design
Computer Aided Geometric Design
Fast degree elevation and knot insertion for B-spline curves
Computer Aided Geometric Design
Computer Aided Geometric Design
Changeable degree spline basis functions
Journal of Computational and Applied Mathematics
Explicit representations of changeable degree spline basis functions
Journal of Computational and Applied Mathematics
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In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree B-spline basis functions, is constructed and discussed by the integral definition of spline. The transformation formulas between usual and bi-degree B-spline basis functions leads to the corner cutting for degree elevation of B-spline curves.