Improperly parametrized rational curves
Computer Aided Geometric Design
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
Curves and surfaces for computer aided geometric design (3rd ed.): a practical guide
The rational cubic Be´zier representation of conics
Computer Aided Geometric Design
A Menagerie of Rational B-Spline Circles
IEEE Computer Graphics and Applications
Accurate Parametrization of Conics by NURBS
IEEE Computer Graphics and Applications
High accuracy approximation of helices by quintic curves
Computer Aided Geometric Design
Necessary and sufficient conditions for rational quartic representation of conic sections
Journal of Computational and Applied Mathematics
An approximation of circular arcs by quartic Bézier curves
Computer-Aided Design
Technical Section: Generating fair, C2 continuous splines by blending conics
Computers and Graphics
C 1 NURBS representations of G 1 composite rational Bézier curves
Computing - Geometric Modelling, Dagstuhl 2008
Approximation of conic sections by curvature continuous quartic Bézier curves
Computers & Mathematics with Applications
Modeling with rational biquadratic splines
Computer-Aided Design
Approximating conic sections by constrained Bézier curves of arbitrary degree
Journal of Computational and Applied Mathematics
| Hi-index | 0.00 |
This paper presents a special representation for conic sections in the form of a rational quartic Bézier curve which has the same weight for all control points but the middle one. This representation allows a conic section to be joined with other conics in the same form or other integral B-spline curves in a way that the joined curve still possesses C1 continuity in the homogeneous space, which is not possible if rational quadratic representation is adopted. This also allows the creation of skinned surfaces from section curves containing conic sections to possess better parametrization and curvature property.