A generalisation of the Pythagorean hodograph quintic spiral

An existing planar Pythagorean hodograph (PH) quintic spiral, with zero curvature at one end, is generalised to form a two parameter family of PH quintic spirals. The additional degree of freedom allows specification of an ending angle of tangent and curvature. Its shape and curvature compares well to that of the clothoid which has applications in areas such as highway design and robot path planning. It is thus a viable nonuniform rational B-spline alternative for such applications. It is also useful for other computer aided design or computer-aided geometric design applications in which drawing curves with controlled curvature, e.g. fair curves, is important.