Infinite Control Points-A Method for Representing Surfaces of Revolution Using Boundary Data
IEEE Computer Graphics and Applications
An introduction to splines for use in computer graphics & geometric modeling
An introduction to splines for use in computer graphics & geometric modeling
Curves and surfaces for computer aided geometric design
Curves and surfaces for computer aided geometric design
Real rational curves are not “unit speed”
Computer Aided Geometric Design
Mo¨bius reparametrizations of rational B-splines
Computer Aided Geometric Design
NURBS for Curve and Surface Design
NURBS for Curve and Surface Design
A Menagerie of Rational B-Spline Circles
IEEE Computer Graphics and Applications
From Conics to NURBS: A Tutorial and Survey
IEEE Computer Graphics and Applications
Computer-aided design applications of the rational b-spline approximation form.
Computer-aided design applications of the rational b-spline approximation form.
Determination of geometrical invariants of rationally parametrized conic sections
Mathematical Methods for Curves and Surfaces
A rational quartic Bézier representation for conics
Computer Aided Geometric Design
Approximating Surfaces of Revolution by Nonrational B-Splines
IEEE Computer Graphics and Applications
High accuracy approximation of helices by quintic curves
Computer Aided Geometric Design
Sampling points on regular parametric curves with control of their distribution
Computer Aided Geometric Design
Necessary and sufficient conditions for rational quartic representation of conic sections
Journal of Computational and Applied Mathematics
Optimal parameterization of rational quadratic curves
Computer Aided Geometric Design
Graphical Models
Journal of Computational Physics
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It is well known that NURBS curves provide an exact representation of conics. Nevertheless, if this representation is exact on the geometric point of view (that is, the shape), the resulting parametrization is usually bad. For instance, the highest known continuity for a circle represented by a NURBS curve is only C1. This article presents a new reparametrization technique, called zigzag reparametrization, that improves the parametrization of a NURBS curve or surface according to a given criterion. To illustrate the technique, we study here the parametrization of the circle, but the method may be used in many other reparametrization applications.