Offset-rational sinusoidal spirals in Bezier form
Mineur et al. [Mineur, Y, Lichah, T., Castelain, J.M., Giaurrie, H., 1998. A shape controlled fitting method for Bezier curves. Computer Aided Geometric Design 15 (9), 879-891] presented a remarkable family of Bezier curves, characterized by a control polygon with constant angle at each vertex and constant ratio between lengths of consecutive edges. We note that such curves belong to a classical family of polynomial sinusoidal spirals that encompasses Tschirnhausen's cubic, and can also be expressed as p-Bezier curves (Bezier curves in polar coordinates). These spirals have rational offsets, obtained simply by adding two p-Bezier curves, namely the spiral and a circle. Such a construction includes the offset to a parabola. (C) 2007 Elsevier B.V. All rights reserved.
sinusoidal spiral p-bezier curve rational offset tschimhausen's cubic