p-Bezier curves, spirals, and sectrix curves

摘要

We elucidate the connection between Bexier 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.