Curves with rational Frenet-Serret motion Original Research Article

This paper examines a special type of rational curves called rational Frenet-Serret (RF) curves distinguished by the property that the motion of their Frenet-Serret frame is rational. It is shown that a rational curve is an RF curve if and only if it has rational speed and rational curvature. The paper derives a general representation formula for RF curves suitable for geometric design and provides a geometric survey of special RF curves. The special case of a cubic helix is examined thoroughly. Additionally the paper discusses several applications including examples for the design of rational sweeping surfaces, rational pipe surfaces and rational transition surfaces joining sweeps with G1 continuity.