Computer Aided Geometric Design
Fundamentals of interactive computer graphics
Fundamentals of interactive computer graphics
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
Interpolation with interval and point tension controls using cubic weighted v-splines
ACM Transactions on Mathematical Software (TOMS)
Local control of interval tension using weighted splines
Computer Aided Geometric Design
Local Control of Bias and Tension in Beta-splines
ACM Transactions on Graphics (TOG)
Computational Geometry for Design and Manufacture
Computational Geometry for Design and Manufacture
Geometric Continuity of Parametric Curves
Geometric Continuity of Parametric Curves
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
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We present a Bézier representation of &tgr;-splines, curvature and torsion-continuous quintics, which were introduced in CAGD by Hagen in 1985 [32]. Explicit formulas are given for the conversion from Bézier representation to &tgr;-spline representation, and vice versa. Thus, by embedding the Bézier representation in a &Bgr;-spline representation of curvature and torsion-continuous quintic spline curves, given in [20], a &Bgr;-spline-Bézier representation of &tgr;-splines results.Second, positivity conditions for the design parameters of the Bézier representation and certain ranges of tension values are derived, which ensure properties like the convex hull and the variation-diminishing property of the &Bgr;-spline-Bézier representation.