Single-valued curves in polar coordinates
Computer-Aided Design
The conformal map z→z2 of the hodograph plane
Computer Aided Geometric Design
Single-valued surfaces in spherical coordinates
Computer Aided Geometric Design
Offset-rational parametric plane curves
Computer Aided Geometric Design
Hermite interpolation with Tschirnhausen cubic spirals
Computer Aided Geometric Design
Proof of the nonintersection conjecture of Hoffmann and Peters
Computer Aided Geometric Design
Degree elevation for p-Be´zier curves
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue dedicated to Paul de Faget de Casteljau
A closed algebraic interpolation curve
Computer Aided Geometric Design
Mathematical Methods for Curves and Surfaces
Offset-rational sinusoidal spirals in Bézier form
Computer Aided Geometric Design
A novel generalization of Bézier curve and surface
Journal of Computational and Applied Mathematics
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We elucidate the connection between Bézier curves in polar coordinates, also called p-Bézier or focal Bézier curves, and certain families of spirals and sectrix curves, p-Bézier curves are the analogue in polar coordinates of nonparametric Bézier curves in Cartesian coordinates. Such curves form a subset of rational Bézier curves characterized by control points on radial directions regularly spaced with respect to the polar angle, and weights equal to the inverse of the polar radius. We show that this subset encompasses several classical sectrix curves, which solve geometrically the problem of dividing an angle into equal spans, and also spirals defining the trajectories of particles in central fields, First, we identify as p-Bézier curves a family of sinusoidal spirals that includes Tschirnhausen's cubic. Second, the trisectrix of Maclaurin and their generalizations, called arachnidas. Finally, a special class of epi spirals that encompasses the trisectrix of Delanges.