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A method for 6 degree of freedom (6-DOF) path-planning for Autonomous Underwater Vehicles (AUV) is presented. It is based on an augmentation of Rapidly-exploring Random Trees (RRT) and the Probabilistic Roadmap Method (PRM) with a plane-fitting method as part of 3D underwater mapping. This is of particular interest for Safety, Security, and Rescue Robotics (SSRR) missions with AUV, which tend to occur not in plain open waters but in complex environments. Examples include harbor security, infrastructure inspection after disasters, and military reconnaissance. The special representation of the 3D map used here allows for significantly faster generation of paths than with state of the art point clouds. The method is evaluated with experiments using real world data from a Tritech Eclipse sonar. We present results of 6-DOF path-planning through a 3D map that is generated in a larger underwater structure, namely the Lesumer Sperrwerk, a flood gate in the river Lesum in Bremen, Germany.