  In this letter, we propose a general real-space method for the generation of
nonparaxial accelerating beams with arbitrary predefined convex trajectories.
Our results lead to closed-form expressions for the required phase at the input
plane. We present such closed-form results for a variety of caustic curves:
besides circular, elliptic, and parabolic, we find for the first time general
power-law and exponential trajectories. Furthermore, by changing the initial
amplitude we can design different intensity profiles along the caustic.
