Cubic C-Bézier Spiral for Two Point Fair Interpolation with Zero Curvature at One End

Using cubic C-Bézier curve, a method is studied to design a fair curve which interpolates two points with zero curvature at one end. The monotone curvature interpolation curve is composed of straight line, a single spiral and circular arc which all can be represented precisely by C-Bézier curves. Available shape parameter on cubic C-Bézier spiral can further adjust the shape of the interpolation curve. Meanwhile, the method is simple and easy to implement because it only needs to solve one equation to get its positive root. The method is generally suitable for any application where it is required to smoothly fit a curve between two given points with zero curvature at one end.