Corner cutting curves and a new characterization of Be´zier and B-spline curves
Computer Aided Geometric Design
The NURBS book (2nd ed.)
Journal of Computational and Applied Mathematics
Curve and surface construction using variable degree polynomial splines
Computer Aided Geometric Design
Applications of b-spline approximation to geometric problems of computer-aided design.
Applications of b-spline approximation to geometric problems of computer-aided design.
Computer-aided design applications of the rational b-spline approximation form.
Computer-aided design applications of the rational b-spline approximation form.
On a class of weak Tchebycheff systems
Numerische Mathematik
A general class of Bernstein-like bases
Computers & Mathematics with Applications
Unified and extended form of three types of splines
Journal of Computational and Applied Mathematics
Rational B-Splines for Curve and Surface Representation
IEEE Computer Graphics and Applications
Polynomial cubic splines with tension properties
Computer Aided Geometric Design
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The classical B-spline functions of order k=2 are recursively defined as a special combination of two consecutive B-spline functions of order k-1. At each step, this recursive definition is based, in general, on different reparametrizations of the strictly increasing identity (linear core) function @f(u)=u. This paper generalizes the concept of the classical normalized B-spline functions by considering monotone increasing continuously differentiable nonlinear core functions instead of the classical linear one. These nonlinear core functions are not only interesting from a theoretical perspective, but they also provide a large variety of shapes. We show that many advantageous properties (like the non-negativity, local support, the partition of unity, the effect of multiple knot values, the special case of Bernstein polynomials and endpoint interpolation conditions) of the classical normalized B-spline functions remain also valid for this generalized case, moreover we also provide characterization theorems for not so obvious (geometrical) properties like the first and higher order continuity of the generalized normalized B-spline functions, C^1 continuous envelope contact property of the family of curves obtained by altering a selected knot value between its neighboring knots. Characterization theorems are illustrated by test examples. We also outline new research directions by ending our paper with a list of open problems and conjectures underpinned by numerous successful numerical tests.