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AUVs increasingly are being used to collect data in the benthic environment. Many of these data collection tasks require that the AUV is able to follow the terrain at standoff distances on the order of meters (e.g. benthic imaging). However, terrain following with an AUV is a challenging problem when the terrain is rough, and the task becomes even more difficult when using motion-constrained vehicles such as torpedo-style AUVs. One option to improve the terrain-following capability of these vehicles is to incorporate a trajectory following control law. This requires, however, the generation of a trajectory. This paper presents a spline-based trajectory planning technique that exploits prior knowledge of terrain shape and explicitly takes motion constraints into consideration. Details of a the trajectory planning method are provided. The method forms terrain following trajectories by using a spline-based representation of the underlying terrain. A vehicle turning radius constraint along the trajectory is mapped to spline surface curvature constraints by leveraging the continuous nature of the spline-based terrain representation. A curvature-constrained spline surface is then fit to bathymetry by solving an optimization problem. If a feasible solution does not exist, the AUV is not able to survey the site under the specified turning radius constraint. Consequently, this method can also be used as a design tool to determine an AUV's actuation requirements to survey a given terrain. Examples of planned trajectories for an MBARI Dorado AUV over Monterey Bay bathymetry are provided.