Projective transformations of the parameter of a Bernstein-Bézier curve
ACM Transactions on Graphics (TOG)
Skinning techniques for interactive B-spline surface interpolation
Computer-Aided Design
Rational continuity: parametric, geometric, and Frenet frame continuity of rational curves
ACM Transactions on Graphics (TOG) - Special issue on computer-aided design
The NURBS book
Curves and surfaces for CAGD: a practical guide
Curves and surfaces for CAGD: a practical guide
NURBS: From Projective Geometry to Practical Use
NURBS: From Projective Geometry to Practical Use
Procedurally Representing Lofted Surfaces
IEEE Computer Graphics and Applications
A rational quartic Bézier representation for conics
Computer Aided Geometric Design
Rational B-Splines for Curve and Surface Representation
IEEE Computer Graphics and Applications
Modeling with rational biquadratic splines
Computer-Aided Design
G1 continuous approximate curves on NURBS surfaces
Computer-Aided Design
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This paper is concerned with the re-representation of a G 1 composite rational Bézier curve. Although the rational Bézier curve segments that form the composite curve are G 1 continuous at their joint points, their homogeneous representations may not be even C 0 continuous in the homogeneous space. In this paper, an algorithm is presented to convert the G 1 composite rational Bézier curve into a NURBS curve whose nonrational homogeneous representation is C 1 continuous in the homogeneous space. This re-representation process involves reparameterization using Möbius transformations, smoothing multiplication and parameter scaling transformations. While the previous methods may fail in some situations, the method proposed in this paper always works.