document: p-Bezier curves , spirals , and sectrix curves We elucidate the connection between Bezier curves in polar coordinates , also called p-Bezier or focal Bezier curves , and certain families of spirals and sectrix curves . p-Bezier curves are the analogue in polar coordinates of nonparametric Bezier curves in Cartesian coordinates . Such curves form a subset of rational Bezier 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-Bezier 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
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