G2 curves composed of planar cubic and Pythagorean hodograph quintic spirals Original Research Article

Spiral segments are useful in the design of fair curves. They are important in CAD/CAM applications, the design of highway and railway routes, trajectories of mobile robots and other similar applications. A Pythagorean hodograph curve has the properties that its arc-length is a polynomial of its parameter, and the formula for its offset is a rational algebraic expression. Recent work demonstrated the composition of G2 curves by joining circular arcs and/or straight line segments with cubic Bézier spiral segments and Pythagorean hodograph quintic spiral segments. These spiral segments are members of wider classes of spiral segments which are now examined. Selecting members from these wider classes of spiral segments allows for more flexible curve design; it is not necessary to incorporate circular arcs and straight line segments when using them.