Methods for parameterized trajectory planning for dynamic soaring are discussed. Two parameterizations based on flight path are described: the first uses cubic splines, with parameters defining the locations of a set of control points; the second uses skewed/flattened sinusoids, where parameters define skewness, flatness, amplitude, and frequency. Both parameterizations are continuous to at least C2, allowing smooth trajectories to be planned and flown. A trajectory following controller tracks the planned trajectories. Both parameterizations are compared with a collocation method and show faster convergence as well as improved performance in cases where wind fields are not known precisely. A deep neural network is developed to permit fast computation of trajectories under changing wind conditions. Convergence of trajectories using this deep neural network method is shown in simulation.