Curvature continuous curves and surfaces
Computer Aided Geometric Design
A geometric investigation of the rational bezier scheme of computer aided design
Computers in Industry
The sphere as a rational Be´ier surface
Computer Aided Geometric Design
An intuitive approach to geometric continuity for parametric curves and surfaces
Proceedings of Graphics Interface '85 on Computer-generated images: the state of the art
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
Computer Aided Geometric Design - Special issue: Topics in CAGD
On the use of infinite control points in CAGD
Computer Aided Geometric Design - Special issue: Topics in CAGD
Curve and surface constructions using rational B-splines
Computer-Aided Design
Computer graphics and geometric modeling using Beta-splines
Computer graphics and geometric modeling using Beta-splines
Mathematical methods in computer aided geometric design
Algebraic aspects of geometric continuity
Mathematical methods in computer aided geometric design
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
The art of computer programming, volume 1 (3rd ed.): fundamental algorithms
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
IEEE Computer Graphics and Applications
Geometric Continuity of Parametric Curves
Geometric Continuity of Parametric Curves
Beta Continuity and Its Application to Rational Beta-splines
Beta Continuity and Its Application to Rational Beta-splines
Computer-aided design applications of the rational b-spline approximation form.
Computer-aided design applications of the rational b-spline approximation form.
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
The beta-spline: a local representation based on shape parameters and fundamental geometric measures
Geometric continuity: a parametrization independent measure of continuity for computer aided geometric design (curves, surfaces, splines)
Polar forms for geometrically continuous spline curves of arbitrary degree
ACM Transactions on Graphics (TOG)
Geometric Continuity of Parametric Curves: Three Equivalent Characterizations
IEEE Computer Graphics and Applications
From Conics to NURBS: A Tutorial and Survey
IEEE Computer Graphics and Applications
A circle-preserving C2 Hermite interpolatory subdivision scheme with tension control
Computer Aided Geometric Design
C 1 NURBS representations of G 1 composite rational Bézier curves
Computing - Geometric Modelling, Dagstuhl 2008
Graphical Models
Curvature of approximating curve subdivision schemes
Proceedings of the 7th international conference on Curves and Surfaces
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The parametric, geometric, or Frenet frame continuity of a rational curve has often been ensured by requiring the homogeneous polynomial curve associated with the rational curve to possess either parametric, geometric, or Frenet frame continuity, respectively. In this paper, we show that this approach is overly restrictive and derive the constraints on the associated homogeneous curve that are both necessary and sufficient to ensure that the rational curve is either parametrically, geometrically, or Frenet frame continuous.