Modifying the shape of rational B-splines. part 1: curves
Computer-Aided Design
NURB curves and surfaces: from projective geometry to practical use
NURB curves and surfaces: from projective geometry to practical use
The NURBS book
Two different forms of C-B-splines
Computer Aided Geometric Design
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Curves and Surfaces for Computer-Aided Geometric Design: A Practical Code
Computer Aided Geometric Design
Complex rational Bézier curves
Computer Aided Geometric Design
Unifying C-curves and H-curves by extending the calculation to complex numbers
Computer Aided Geometric Design
Optimal properties of the uniform algebraic trigonometric B-splines
Computer Aided Geometric Design
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In CAGD curves are described mostly by means of the combination of control points and basis functions. If we associate weights with basis functions and normalize them by their weighted sum, we obtain another set of basis functions that we call quotient bases. We show some common characteristics of curves defined by such quotient basis functions. Following this approach we specify the rational counterpart of the recently introduced cyclic basis, and provide a ready to use tool for control point based exact description of a class of closed rational trigonometric curves and surfaces. We also present the exact control point based description of some famous curves (Lemniscate of Bernoulli, Zhukovsky airfoil profile) and surfaces (Dupin cyclide and the smooth transition between the Boy surface and the Roman surface of Steiner) to illustrate the usefulness of the proposed tool.