The process of conducting a mission for an autonomous aircraft includes determining the set of waypoints (flight planning) and the path for the aircraft to fly (path planning). The autonomous aircraft is an under-actuated system, having less control inputs than degrees of freedom and has two nonholonomic (non integrable) kinematic constraints. Consequently, the set of feasible trajectories will be restricted and the problem of trajectory generation becomes more complicated than a simple interpolation. Care must be taken in the selection of the basic primitives to respect the kinematic and dynamic limitations. The topic of this paper is trajectory generation using parametric curves. The problem can be formulated as follows: to lead the autonomous aircraft from an initial configuration qi to a final configuration qf in the absence of obstacles, find a trajectory q(t) for 0 ≤t ≤ T. The trajectory can be broken down into a geometric path q(s), s being the curvilinear abscissa and s=s(t) a temporal function. In 2D the curves fall into two categories: * Curves whose coordinates have a closed form expressions, for example B-splines, quintic polynomials or polar splines. * Curves whose curvature is a function of their arc length for example clothoids, cubic spirals, quintic or intrinsic splines. Some 3D solutions will be presented in this paper and their effectiveness discussed towards the problem in hand.